1.5.7: Relationships, Sexuality, and Contraception- Optional Continued Learning
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The videos below provide an opportunity to expand on your learning from the chapter. As you watch the video, make a list of what you notice and what you wonder. This is a great strategy to listen purposefully, engage with the content, and look for deeper opportunities for self growth, self-reflection, and learning.
What do you notice ?
- How does this topic support, expand, or challenge the content in the chapter?
- How does this topic connect to health topics from other chapters?
- How does this topic connect with your prior learning, your experiences, your work, your family, or your life in general?
- How does this topic help you to more fully understand health and wellness?
What do you wonder ?
- How has this topic sparked your curiosity?
- What would you like to know more about?
- What questions did you have as you reviewed the topic?
- What other popular and scholarly sources support or refute this topic?
Videos for continued learning and application
Note: These videos are intended to more fully reflect on health. You might agree or disagree with the videos and that is ok! Utilize these videos to critically think through the topics and identify other sources, both scholarly and popular, to convey your learning.
Got a wicked problem? First, tell me how you make toast
How peer educators can transform sex education
How to disagree productively and find common ground
How to fix a broken heart
How to speak so that people want to listen
The difference between healthy and unhealthy love
The end of Roe v. Wade — and what comes next for reproductive freedom
The physics of human sperm vs. the physics of the sperm whale
What doctors should know about gender identity
What is love?


10.1.1: Interventions and Problem Solving
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Social issues impair social functioning and negatively impact the lives of individuals, groups, and organizations (Bruhn and Rebach 2007). People effected by a particular social issue may face a variety of obstacles and challenges associated with the problem including labeling, stigma, discrimination, and isolation. Sociological practitioners work to address the problem by changing the social setting, arrangement, norms, and behaviors surrounding the issue and the people involved. A sociological practitioner may serve as the facilitator of this social change, a broker by acting on the behalf of others for change, or a clinician by providing direct services or help to change the situation of individuals and families.
There are six approaches most commonly used by sociological and other professional practitioners, communities, and clients to address social problems and create change. To resolve or improve situations, different problems require different approaches based on the client needs and social resources available to them. Each sociological approach incorporates a different level of analysis to assess the problem with a specific focal area of intervention. When social change requires different levels of analysis, sociological approaches must identify and explore multiple solutions across continuums. Not all approaches result in an expeditious solution. Sociological approaches and interventions take planning and time to implement and can take years to gain permanent change or improve people’s lives.
Process of Intervention
Regardless of approach, sociologists follow an incremental process of intervention to remedy a social problem. Each sociological approach includes a process of intervention that includes an assessment, planning, implementation, and evaluation phase. There are no timelines of completion defined within each phase. Rather the sociological practitioner, clients, and other impacted individuals or groups set deadlines and completion parameters based on context and need.
The first phase examines the social problem and needs of those it impairs. This is an investigative stage to gather information and understand the situation to define the problem (Bruhn and Rebach 2007). A sociological practitioner must first identify the presenting problem and client(s). The presenting problem refers to the client’s perspective of the problem as they see it in their own words (Bruhn and Rebach 2007). The assessment is a discovery phase of the history and evolution of the problem within the geographic region to find out who is seeking help and why. The assessment also helps determine the role or involvement of the sociological practitioner in the intervention.
An assessment is a case study guided by the nature of the problem and clients (Bruhn and Rebach 2007). Data collection may include interviews, focus groups, surveys, and secondary analysis (e.g., analytic data, educational records, criminal records, medical files, etc.). Findings and results are presented and discussed with clients and other involved parties to formulate solutions and objectives of intervention.
The next stage in the process is to plan the steps for achieving intervention objectives. The plan is a formal (written) agreement among interventionists (including the sociological practitioner) and client(s) outlining the objectives and roles and responsibilities of each person involved. The plan will include observable, measurable objectives that include: 1) subject and verb stating the condition to achieve, 2) amount or percentage of reduction or improvement of the condition, and 3) timeframe or deadline for completion (Bruhn and Rebach 2007). Both process and outcome objectives must be delineated in the plan. Process objectives will focus on program operations or services, and outcome objectives concentrate on the results of the intervention against baseline data (i.e., data collected prior to intervention). Interventionists and clients work together to develop a plan so everyone has an equal voice and understanding of their duties, obligations, and work to complete in the implementation phase.
Consider a social problem you would like to address in your community. Conduct secondary analysis of the issue to identify the presenting problem, clientele, and existing community services. Explore nonprofit and public agencies in your community working on the problem you chose to help you gather information.
After completing your analysis, draft four observable, measurable objectives of intervention for the problem and population you wish to address. Two objectives must focus on process and two on outcomes. All outcomes must include a verb and subject stating the condition to achieve, amount or percentage of reduction or improvement of the condition, and timeframe or deadline for completion.
The third phase in the process centers on implementation. In this stage, the plan commences according to the steps outlined in the formal agreement. Implementation puts the plan into action by following the proposed sequence and schedule. This phase engages strategies in order to accomplish objectives. For example, solving chronic poverty in your community might require employing several strategies such as improving K-12 education, increasing higher education enrollments and job skills training, providing access to health care, and developing employment opportunities. During the implementation phase, interventionists and collaborators will initiate and work on each strategy for change.
The final phase in the process of intervention is evaluation. Sociologists use evaluation to find out if a program, service, or intervention works (Steele and Price 2008). There are two types of evaluation. A process or formative evaluation gathers information to help improve or change a program, service, or intervention. Did everything occur and work according to plan? Sociological practitioners work with clients to determine program strengths, weaknesses, and areas of improvement to strengthen or adapt the program (Steele and Price 2008). An outcome or summative evaluation measures the impact of the program, service, or intervention on clients or participants. Were benchmarks achieved or changes made? Practitioners measure changes in clients over the duration of their participation from start to completion. The impact evaluation determines if change occurred, any unintended outcomes, and the long-term effects.
Evaluation is an ongoing task tracking program progress from beginning to end (Bruhn and Rebach 2007). Interventionists and practitioners must monitor the program continuously to ensure the service or intervention is advancing toward change, and adjustments or alternatives are deployed to increase effectiveness in a timely manner. The goal of evaluation is to know why a program, service, or intervention succeeded or failed to reform or adapt present and future support and solutions. Evaluation is a mechanism of continual improvement by regularly providing information and identifying unintended consequences.
Evaluation requires both quantitative and qualitative data (see page 5) using a variety of data collection methods and tools to gather information (e.g., tests, questionnaires, archival data, etc.). Data collection tools vary from program to program, sometimes tools exist to conduct an evaluation, and other times practitioners must develop them (Viola and McMahon 2010). Practitioners lead in the development of data collection protocols, tools, and instruments for review by participants (e.g., clients and community members) before they are ready to use.
As a contributing member of an evaluation team, sociological practitioners (see page 3) must be aware of role-conflict . It is imperative to avoid role-conflict in a participatory evaluation model. In other words, practitioners must be aware of their role within the evaluative context or situation as to whether one is serving as a researcher, practitioner, or interventionist (i.e., clinical sociologist). It is difficult to implement the scientific method (process and procedures) in the field within the standards of academic research when serving as a practitioner (Bruhn and Rebach 2007). Sociological practitioners or interventionists do not always have control over the evaluation research, study environment, or time to complete an evaluative study as prescribed by the scientific method.
The Workforce Internship Networking (WIN) Center at West Hill College Lemoore in California connects and supports students and alumni by providing employment, occupational readiness, and job placement information and resources to advance personal career goals. The WIN Center provides a space for employers and students to connect. At the WIN Center, students and alumni receive skills training, employment and internship application assistance, and support in creating a professional profile.
- Describe why it might be important to evaluate the WIN Center.
- Considering the importance of evaluating college campus programs, how often would you recommend evaluating the WIN Center’s programs and services? What should the evaluation examine?
- What role could program monitoring play in the overall evaluation of the WIN Center?
- If you were responsible for overseeing program monitoring and the evaluation of the WIN Center, what data would you collect to assess its impact?
In addition, evaluations may cause tension between practitioners (interventionists) and evaluation associates. Interventionists are responsible for providing data and keeping records while implementing program activities. Conflicting demands for an interventionists’ time and energy during the program implementation process may lead to a delay in gathering and sharing data with evaluators. Evaluation is not always equally valued, and some interventionists may consider evaluation unimportant or a threat to their work or process resulting in uncooperative behavior or interest.


5.1: Creating Different Document Types in Microsoft Word
By the end of this section, you will be able to:
- Create a template
- Create a business memo
- Create a letterhead and an envelope
- Create a business card
- Create a brochure and a flyer
- Create an invoice
- Create a business plan
- Create a résumé and a cover letter
Having different document types ready to go can be useful, in both everyday life and your professional life. When it comes to something like applying to jobs or schools—a task that requires writing a similar document, multiple times—you don’t want to waste time by starting from scratch for each application. You can do this by using a template, which we learned about in Creating and Working in Documents. This section will show you how to create your own template for a few different document types, including memos, letters, envelopes, business cards, brochures, flyers, and invoices.
Templates
In Creating and Working in Documents, we defined what templates are and where to find them in Microsoft Word . There are also a number of templates available on the internet. Word has web search capability so that you can look for additional templates on templates.office.com, as you can see in Figure 5.2. On the Office template website, there are thousands of templates that can help entrepreneurs and small businesses start making their business more systematic. You can find Word templates for email advertisements, calendars, brochures, memos, business cards, invoices, business plans, warehouse receipts, and more. Once you download the template , you can populate it with data and further modify its appearance.
Using prebuilt templates can be incredibly useful, but sometimes you might use a custom document type often enough that you want to save it as your own template. To do this, go to the File tab and use the Save As command to save the document with the .dotx extension. That will save the document as a template. This means that every time you open this .dotx file, a new file will be created, with all your formatting already in place. Once you make your edits to the new document, use the Save As command again to save the template file (.dotx) as a standard Word document file (.docx), making sure to choose the .docx extension to keep the changes. This will ensure that your edits are saved to a new document not to the template file. The .docx files are standard Word documents used for editing and sharing, while .dotx files are Word templates used for creating new documents with a consistent format and style. These same steps need to be followed when building a template for any kind of file, whether it is a memo, envelope, brochure, flyer, or invoice.
While Word comes with many fantastic templates installed, there are many more available online that are free and can be used with Word. A Google search will garner thousands of available templates. You will likely come across Canva in your search. Canva does provide access to some free templates; however, these files must be edited in that service and are saved and downloaded in file types that are not necessarily fully compatible in Word. When searching for templates, be sure to verify they are indeed compatible with Word and come from a verified and trusted source.
Business Memos
Word has templates for memos and newsletters. These are similar forms of communication in that they both inform a large group of new changes or trends in a company and may call for action. Yet there are some differences. Memos are used internally, while newsletters are for external audiences. Memos also usually have a standardized format. Newsletters have more freedom of form and may incorporate a lot of graphics. Like brochures and flyers, both have been digitized in the form of emails.
Despite the widespread use of email, printed business memos are still commonly used to communicate important information within a company. Memos typically follow a specific format, which formal company email transmittals may also do today. One common structure is to include an opening thesis statement, the main issue, and a closing statement. The opening is an introduction, and it may recall some relevant past activities, or current activity. The main issue should include the changes that are being announced to the company. The closing is a reminder of the current project general objectives. It may also include a complimentary closing, such as, “Thank you for your kind attention,” or something similar. Last comes the signature, which is the sender’s name, job title, and email address.
Like an email, a memo should always include fields for To (the employees), From (typically management), and CC, which stands for “carbon copy.” In the 1980s, before personal computers, letters were typewritten, and a piece of carbon paper was inserted between two sheets to make a copy of the letter. The copy created by the carbon paper was the “carbon copy,” or “CC.” CC’ing others is a process still used in emails today, although of course there is no physical hard copy involved.
Memos should also include fields for the Date and a Subject. You can see a memo template that was downloaded from Microsoft’s template page in Figure 5.3.
Newsletters can follow a similar format but consider that your audience will be different. You may want to use different language, incorporate graphics, or include more details. Newsletters may not only communicate information and updates to an external audience but are often used as advertising. Microsoft’s newsletter templates are a good place to get started if you are not sure how to format your newsletter.
Newsletters are the most popular email advertisement form. Read this step-by-step guide to writing a newsletter at Readz.com. You can find advice on newsletter creation, the audience, the types of newsletter formats, idea prompts, and more.
Letterhead and Envelopes
A letterhead is a type of heading that contains company contact information and a logo. It can be used in many scenarios, both personal and professional. Figure 5.4 shows an example of a professional letterhead for a business. The logo and company contact information will go at the top right of the document. The information in the template is generic so that you can customize the template with your specific company information.
Business letterheads are also used in conjunction with company envelopes. You may have preprinted company envelopes with the company logo on them. If not, you can create one using templates. When corresponding by mail, it is much more professional to have a printed envelope with the recipient’s information, rather than have handwritten details. While we will cover creating envelopes for larger mailings in the next section, here we are focused on printing one or two envelopes.
Word has templates and other customizable capabilities to create printed, custom envelopes. You just need to fill in your address with your name in the left corner, and fill the recipient’s data in the middle. To print the envelope, you will need to load the envelope in the correct orientation in the printer. Then, you will go to the File tab and select Print. Printers can vary by brand, so consult the owner’s manual for your printer or search online for the proper way to print an envelope.
Using the Envelopes command is another solution, and it allows for more customization. You first need to make sure that your address is saved into Word’s settings. This is done through the Options command, located on the File tab. Selecting the Options command will open a window, and inside that window you will see a tab called Advanced. This is where you can set your address, as Figure 5.5 shows.
From the Tools menu, click on Envelopes. You can make formatting changes here. Also, in the Tools menu, there is an option for Labels, which has a similar functionality for preparing mailing labels.
Next, go to the Mailings tab and select Envelopes. In Figure 5.6, you can see the dialog box that will appear. The blank address is the recipient’s address, and on the bottom is your autogenerated mailing address. If you want to change the envelope size, choose Options, and you will see a combo box with the standard sizes (Figure 5.7). When you finish typing the recipient’s address, click on Add to document.
As Figure 5.8 shows, the envelope is inserted as the first page of the document, and along it, there is a section break. If you want to repeat the styling and envelope size again, it would be a good idea to create the envelope in a new blank document, and then save it as a .dotx.
Business Cards
A business card is a small, typically wallet-sized card that contains your contact and company information. It is usually given to clients or potential clients when you meet them, so that they have your contact information easily available. Business cards may be provided to you by your company, or, if you are self-employed, you may make them yourself. They usually contain basic contact information, like your name, your position (title) with the company, your phone number, and your email address, in addition to some eye-catching design elements, like a logo or image. Business cards are usually printed on thick, sturdy paper called cardstock . Many companies will order business cards for their employees using approved company designs and layout; at WorldCorp, the marketing department is responsible for providing business cards to employees.
You can easily design a business card in Word and send it out for printing at a business card printing shop, where you will likely have a few different cardstock options (lighter or heavier weight, glossy or matte finish). You could also purchase the cardstock and print the business cards on your own. This paper is generally perforated and some major paper companies that produce this type of paper have templates for their products in Word. Some of these printing companies may want your design in .pdf format. As we discussed in Creating and Working in Documents, having a document in .pdf format means that the design elements will not change at all, no matter who opens the file. If you send the printing company a design in .docx format, some elements might move when they open the file depending on which program they are using to open and print the file.
In Figure 5.9, you can see most of a business card template that we downloaded from Microsoft. The page has ten business cards per page. Simply fill out the information in the fields provided. Once you fill in one area of the first card, it will auto-populate the same area in all the remaining cards.
Brochures and Flyers
Both large and small businesses use advertisements to display what the company offers and detail the specifications of the offer. Brochures and flyers are a printed form of advertisement. Although many advertisements are found on the internet these days, printed ads are still popular. Flyers tend to be graphic-oriented, contain minimal text, and often advertise an event or temporary promotion. Brochures can be an introduction for a company or specific product and may be used for a longer duration than a flyer.
As with many documents discussed so far, the best way to create a brochure or flyer is to download a template from Microsoft, and then fill in the information. Because brochures and flyers can be image-heavy and can have complicated layouts, using a template is the fastest and easiest way to create them. With a template, you can establish a base layout, and then easily change the images and the color scheme.
In Figure 5.10 and Figure 5.11, notice the default design of a brochure from Microsoft’s template page called Business Brochure. The brochure is two pages, as it is designed for double-sided printing. The brochure is also set in a three-column layout that is meant to be a trifold design. The layout is there, and all you need to do is change images, the color scheme (if desired), and the text.
At WorldCorp, the marketing department plans a holiday toy drive each year.  You can use this template to create the brochure for the event. We will walk through the steps to create this brochure in the following sections.
To change the two images, right-click on one of them and select Change Picture , as shown in Figure 5.12, then browse to the folder where the image is and select Insert.
On a Mac, the command is Control+right-click .
If the new image is too wide, use the command Crop from the Picture Tools Format tab. To change the color scheme for the whole brochure, go to the Design tab and click on the Color drop-down menu, as in Figure 5.13. Changing the colors this way will change the color palette for the whole brochure. Finally, to change the actual text, put your cursor on any of the panels of the brochure and change it manually. In this example, you changed the pictures and the text on the first page of the brochure to include details of the toy drive at WorldCorp.
To create a flyer, choose a flyer template from Microsoft’s templates, and follow the same steps as for creating a brochure. As you can see in Figure 5.14, flyer templates are just one, single page, meant to be printed single-sided on one sheet of paper.
Invoices
An invoice is an important document. It is essentially a bill given to a customer for a product or service provided by a company. You may encounter invoices either as a recipient or the sender. If you are the one purchasing a good or service, you will receive an invoice. The invoice tells you how much you need to pay. If you are the one selling the goods or services, you will need to create the invoice yourself, then send it to the company or person making the purchase. In both cases, an invoice should always explain what was provided, sold, and what is owed.
There are many kinds of invoices for many kinds of businesses, but all invoices should have a date, invoice number, description of the goods sold or services performed, the quantity, the price per item, the total, and the payment due date. The Microsoft 365 collection of templates has many designs and types of invoices by industry. Using a template to design your invoice can be helpful because invoices often include complex table formatting that can be difficult to design. The invoices can vary based on whether you are providing a service, such as maintenance (for which you might charge an hourly rate), or providing an actual product, like WorldCorp’s laptops and TVs (for which you might charge a per-price fee or flat rate).
You can create an invoice by following the same steps outlined above for brochures and flyers: by creating a new document and selecting an invoice template. Just as you would with the other document types, click in the text boxes to make the necessary adjustments to the information in the invoice. Figure 5.15 shows some of the different invoice templates available.
Business Plans
A business plan is a document that describes a company’s plan for growth and profitability. Business plans may have different uses and applications depending on the type of business and stage of growth that the business is experiencing. For instance, some start-up business plans are used to seek funding for a venture. They may describe a detailed short-term plan for the company’s first few months of activity, then a broader long-term plan for future growth. There are also business plans for established companies, such as capacity-building business plans. These types of plans are used to explain why a company needs funding to buy a new capital asset, such as a manufacturing plant, or to refurbish an existing one. The business plan templates you will find in the Microsoft Office database will give you a head start on designing and formatting your business plan, but keep in mind that these templates will not give any advice on what to include or what kind of language to use in your business plan. For that, you can get some examples of an already-made business plan online. Figure 5.16 shows an example of the first couple of pages of a business plan template in Word.
Résumés and Cover Letters
As you start your career and begin your job search, you will want to present yourself as a serious candidate, ready to take on challenges. One way to put yourself on the right track toward professionalism is by having a résumé . A résumé displays your work experience, academic degrees, and overall skills. Some résumé experts say that you should limit your résumé to one or two pages, but depending on the position, you may want to describe your studies and experience in more detail.
Like business cards, résumés can be simple or more imaginative. While a visual, graphics-heavy résumé may be eye-catching, a plain text document may be more practical. When you apply for a position, you will often be directed to an area of the company’s website where you are prompted to upload your résumé to their system. Then, using computer software, they scan the document for critical information such as keywords, years of experience, and skills, and then filter the résumés that meet the desired job requirements. These computer programs do not read drawings and designs well, so a creative or graphics-heavy résumé may not be interpreted well by this technology.
If you need to print your résumé, it is appropriate to add your personal letterhead to the top of the document. While letterheads are often used to present company information, as we learned earlier in the chapter, you can also create a personal letterhead. This type of letterhead is essentially a professional branding of your personal data, displaying your name, position (if applicable), mailing address, email address, and telephone number. It might have a simple graphic design, like a solid color bar, or a more intricate design or logo. Using a consistent letterhead across all your communications will add a look of professionalism and could help increase your job prospects. That consistency confirms to the potential employer your ability to see “the bigger picture” and your ability to visualize the tied-together documents.
Another way to use your personal letterhead is on a cover letter . Cover letters always have a distinct purpose: to present you as a person, and your skills and relevant experience, in a brief manner. Writing a letter on your own personal letterhead shows professionalism, as well as gives the recipient an opportunity to write back or respond. Like a business memo, there is a specific way to structure a cover letter. It should always include the date, your letterhead, the recipient’s address, salutation, complimentary closing, and signature. The body of the cover letter should address these aspects in different paragraphs, usually in this order:
- The introduction: discussion of the job position that is being offered, and your interest in applying.
- The second paragraph: your work history summary. You need to be brief and cover the main points of your career. Also include the relevant skills you possess for the job. If you are applying for a management position, include your management responsibilities in past jobs, for example.
- The third paragraph: description of how you fit the job offered. You might also want to add your overall career objectives here, and explain how this job furthers these.
- The conclusion: a closing paragraph that includes your willingness to be right for the job, and your motivation for applying to this company.
Normally, cover letters are one page, and at most, two pages. You may adjust the mentioned format by adding new paragraphs to add more detail on your work experience and skills.
The templates covered in this section can help you develop your personal letterhead and cover letter. There are several options for résumé and cover letter templates in Word. Figure 5.17 shows a sample cover letter, and Figure 5.18 shows just a few of the options available through Microsoft. As with the other templates, simply replace the generic text in the template with your specific information.
As you grow in your own profession, you might want to consider developing your own brand. This will include how you present yourself on social media, as well as all media and supporting documents you might use to advertise yourself and your “product”—you. Corporations often use brand guidelines to ensure consistency across all brand items, such as business cards, letterhead, envelopes, and logos. Here are logo guidelines from Mitsubishi Motors for example. These guidelines give specific details on how to use, and not use, the company logo in different circumstances.
When developing your own personal brand, consider using the following steps:
- First, investigate personal brands. Canva offers a guide to personal branding that can help. Seek out individuals who do this well. What elements are they using and why is their strategy effective?
- Next, design your business card. You might also want to consider developing your own logo; however, there are many free, online resources available that can help you with this. Once you have a business card, design your other stationery.
- Finally, develop a memo and invoice design from scratch. These will be important as your personal business grows, and you have regular business communication and contracts to support your business.


11.5: Measures of Central Tendency
Let's begin by trying to find the most "typical" value of a data set.
Note that we just used the word "typical" although in many cases you might think of using the word "average." We need to be careful with the word "average" as it means different things to different people in different contexts. One of the most common uses of the word "average" is what mathematicians and statisticians call the arithmetic mean , or just plain old mean for short. "Arithmetic mean" sounds rather fancy, but you have likely calculated a mean many times without realizing it; the mean is what most people think of when they use the word "average".
The mean of a set of data is the sum of the data values divided by the number of values.
Marci’s exam scores for her last math class were: 79, 86, 82, 94. The mean of these values would be:
Solution
\[\frac{79+86+82+94}{4}=85.25. \nonumber \]
Typically we round means to one more decimal place than the original data had. In this case, we would round 85.25 to 85.3.
The number of touchdown (TD) passes thrown by each of the 31 teams in the National Football League in the 2000 season are shown below.
37 33 33 32 29 28 28 23 22 22 22 21 21 21 20
20 19 19 18 18 18 18 16 15 14 14 14 12 12 9 6
Solution
Adding these values, we get 634 total TDs. Dividing by 31, the number of data values, we get \(\frac{634}{31} = 20.4516\). It would be appropriate to round this to 20.5.
It would be most correct for us to report that “The mean number of touchdown passes thrown in the NFL in the 2000 season was 20.5 passes,” but it is not uncommon to see the more casual word “average” used in place of “mean.
The price of a jar of peanut butter at 5 stores was: $3.29, $3.59, $3.79, $3.75, and $3.99. Find the mean price.
- Answer
-
Add texts here. Do not delete this text first.
The one hundred families in a particular neighborhood are asked their annual household income, to the nearest $5 thousand dollars. The results are summarized in a frequency table below.
\(\begin{array}{|l|l|}
\hline \textbf { Income (thousands of dollars) } & \textbf { Frequency } \\
\hline 15 & 6 \\
\hline 20 & 8 \\
\hline 25 & 11 \\
\hline 30 & 17 \\
\hline 35 & 19 \\
\hline 40 & 20 \\
\hline 45 & 12 \\
\hline 50 & 7 \\
\hline
\end{array}\)
Solution
Calculating the mean by hand could get tricky if we try to type in all 100 values:
\[\frac{15 + \cdots + 15 + 20 + \cdots+20 + 25 + \cdots + 25 + \cdots}{100} \nonumber \]
We could calculate this more easily by noticing that adding 15 to itself six times is the same as \(15 \cdot 6=90\). Using this simplification, we get
\[\frac{15 \cdot 6+20 \cdot 8+25 \cdot 11+30 \cdot 17+35 \cdot 19+40 \cdot 20+45 \cdot 12+50 \cdot 7}{100}=\frac{3390}{100}=33.9 \nonumber \]
The mean household income of our sample is 33.9 thousand dollars ($33,900).
Extending off the last example, suppose a new family moves into the neighborhood example that has a household income of $5 million ($5000 thousand). Adding this to our sample, our mean is now:
Solution
\[\frac{15 \cdot 6+20 \cdot 8+25 \cdot 11+30 \cdot 17+35 \cdot 19+40 \cdot 20+45 \cdot 12+50 \cdot 7+5000 \cdot 1}{101}=\frac{8390}{101}=83.069 \nonumber \]
While 83.1 thousand dollars ($83,069) is the correct mean household income, it no longer represents a “typical” value.
Imagine the data values on a see-saw or balance scale. The mean is the value that keeps the data in balance, like in the picture below.
If we graph our household data, the $5 million data value is so far out to the right that the mean has to adjust up to keep things in balance
For this reason, when working with data that have outliers – values far outside the primary grouping – it is common to use a different measure of center, the median .
To find the median, begin by listing the data in order from smallest to largest, or largest to smallest.
If the number of data values, \(N\), is odd, then the median is the middle data value. This value can be found by rounding \(\frac{N}{2}\) up to the next whole number.
If the number of data values is even, there is no one middle value, so we find the mean of the two middle values (values \(\frac{N}{2}\) and \(\frac{N}{2} + 1\))
Returning to the football touchdown data, we would start by listing the data in order. Luckily, it was already in decreasing order, so we can work with it without needing to reorder it first.
37 33 33 32 29 28 28 23 22 22 22 21 21 21 20
20 19 19 18 18 18 18 16 15 14 14 14 12 12 9 6
Solution
Since there are 31 data values, an odd number, the median will be the middle number, the 16 th data value (\frac{31}{2} = 15.5\), round up to 16, leaving 15 values below and 15 above). The 16 th data value is 20, so the median number of touchdown passes in the 2000 season was 20 passes. Notice that for this data, the median is fairly close to the mean we calculated earlier, 20.5.
Find the median of these quiz scores: 5 10 8 6 4 8 2 5 7 7
We start by listing the data in order: 2 4 5 5 6 7 7 8 8 10
Solution
Since there are 10 data values, an even number, there is no one middle number. So we find the mean of the two middle numbers, 6 and 7, and get \(\frac{6+7}{2} = 6.5\).
The median quiz score was 6.5.
The price of a jar of peanut butter at 5 stores were: $3.29, $3.59, $3.79, $3.75, and $3.99. Find the median price.
- Answer
-
First we put the data in order: $3.29, $3.59, $3.75, $3.79, $3.99. Since there are an odd number of data, the median will be the middle value, $3.75.
Let us return now to our original household income data
\(\begin{array}{|l|l|}
\hline \textbf { Income (thousands of dollars) } & \textbf { Frequency } \\
\hline 15 & 6 \\
\hline 20 & 8 \\
\hline 25 & 11 \\
\hline 30 & 17 \\
\hline 35 & 19 \\
\hline 40 & 20 \\
\hline 45 & 12 \\
\hline 50 & 7 \\
\hline
\end{array}\)
Solution
Here we have 100 data values. If we didn’t already know that, we could find it by adding the frequencies. Since 100 is an even number, we need to find the mean of the middle two data values - the 50 th and 51 st data values. To find these, we start counting up from the bottom:
\[\begin{array}{ll} \text{There are 6 data values of \$15, so} & \text{Values 1 to } 6 \text{ are \$15 thousand } \\ \text{The next 8 data values are \$20, so } & \text{Values 7 to } (6+8)=14 \text{ are \$20 thousand} \\ \text{The next 11 data values are \$25, so} & \text{ Values 15 to } (14+11)=25 \text{ are \$25 thousand} \\ \text{The next 17 data values are \$30, so} & \text{Values 26 to } (25+17)=42 \text{ are \$30 thousand} \\ \text{The next 19 data values are \$35, so} & \text{Values 43 to } (42+19)=61 \text{ are \$35 thousand} \end{array} \nonumber \]
From this we can tell that values 50 and 51 will be $35 thousand, and the mean of these two values is $35 thousand. The median income in this neighborhood is $35 thousand.
If we add in the new neighbor with a $5 million household income, then there will be 101 data values, and the 51 st value will be the median. As we discovered in the last example, the 51 st value is $35 thousand. Notice that the new neighbor did not affect the median in this case. The median is not swayed as much by outliers as the mean is.
In addition to the mean and the median, there is one other common measurement of the "typical" value of a data set: the mode .
The mode is the element of the data set that occurs most frequently.
The mode is fairly useless with data like weights or heights where there are a large number of possible values. The mode is most commonly used for categorical data, for which median and mean cannot be computed.
In our vehicle color survey, we collected the data
\(\begin{array}{|l|l|}
\hline \textbf { Color } & \textbf { Frequency } \\
\hline \text { Blue } & 3 \\
\hline \text { Green } & 5 \\
\hline \text { Red } & 4 \\
\hline \text { White } & 3 \\
\hline \text { Black } & 2 \\
\hline \text { Grey } & 3 \\
\hline
\end{array}\)
For this data, Green is the mode, since it is the data value that occurred the most frequently.
It is possible for a data set to have more than one mode if several categories have the same frequency, or no modes if each every category occurs only once.
Reviewers were asked to rate a product on a scale of 1 to 5. Find
- The mean rating
- The median rating
- The mode rating
\(\begin{array}{|l|l|}
\hline \textbf { Rating } & \textbf { Frequency } \\
\hline 1 & 4 \\
\hline 2 & 8 \\
\hline 3 & 7 \\
\hline 4 & 3 \\
\hline 5 & 1 \\
\hline
\end{array}\)
- Answer
-
- The mean is \(\frac{1 \cdot 4+2 \cdot 8+3 \cdot 7+4 \cdot 3+5 \cdot 1}{23} \approx 2.5\)
- There are 23 data values, so the median will be the 12 th data value. Ratings of 1 are the first 4 values, while a rating of 2 are the next 8 values, so the 12 th value will be a rating of 2. The median is 2.
- The mode is the most frequent rating. The mode rating is 2.


14.5: Exercises
Examples \(14.1–14.5\) in the first section each describe an action of a group \(G\) on a set \(X\text{,}\) which will give rise to the equivalence relation defined by \(G\)-equivalence. For each example, compute the equivalence classes of the equivalence relation, the \(G\) - equivalence classes .
Compute all \(X_g\) and all \(G_x\) for each of the following permutation groups.
- \(X= \{1, 2, 3\}\text{,}\) \(G=S_3=\{(1), (1 \, 2), (1 \, 3), (2 \, 3), (1 \, 2 \, 3), (1 \, 3 \, 2) \}\)
- \(X = \{1, 2, 3, 4, 5, 6\}\text{,}\) \(G = \{(1), (1 \, 2), (3 \, 4 \, 5), (3 \, 5 \, 4), (1 \, 2)(3 \, 4 \, 5), (1 \, 2)(3 \, 5 \, 4) \}\)
Compute the \(G\)-equivalence classes of \(X\) for each of the \(G\)-sets in Exercise \(14.5.2\). For each \(x \in X\) verify that \(|G|=|{\mathcal O}_x| \cdot |G_x|\text{.}\)
Let \(G\) be the additive group of real numbers. Let the action of \(\theta \in G\) on the real plane \({\mathbb R}^2\) be given by rotating the plane counterclockwise about the origin through \(\theta\) radians. Let \(P\) be a point on the plane other than the origin.
- Show that \({\mathbb R}^2\) is a \(G\)-set.
- Describe geometrically the orbit containing \(P\text{.}\)
- Find the group \(G_P\text{.}\)
Let \(G = A_4\) and suppose that \(G\) acts on itself by conjugation; that is, \((g,h)~\mapsto~ghg^{-1}\text{.}\)
- Determine the conjugacy classes (orbits) of each element of \(G\text{.}\)
- Determine all of the isotropy subgroups for each element of \(G\text{.}\)
Find the conjugacy classes and the class equation for each of the following groups.
- \(\displaystyle S_4\)
- \(\displaystyle D_5\)
- \(\displaystyle {\mathbb Z}_9\)
- \(\displaystyle Q_8\)
Write the class equation for \(S_5\) and for \(A_5\text{.}\)
If a square remains fixed in the plane, how many different ways can the corners of the square be colored if three colors are used?
How many ways can the vertices of an equilateral triangle be colored using three different colors?
Find the number of ways a six-sided die can be constructed if each side is marked differently with \(1, \ldots, 6\) dots.
Up to a rotation, how many ways can the faces of a cube be colored with three different colors?
Consider \(12\) straight wires of equal lengths with their ends soldered together to form the edges of a cube. Either silver or copper wire can be used for each edge. How many different ways can the cube be constructed?
Suppose that we color each of the eight corners of a cube. Using three different colors, how many ways can the corners be colored up to a rotation of the cube?
Each of the faces of a regular tetrahedron can be painted either red or white. Up to a rotation, how many different ways can the tetrahedron be painted?
Suppose that the vertices of a regular hexagon are to be colored either red or white. How many ways can this be done up to a symmetry of the hexagon?
A molecule of benzene is made up of six carbon atoms and six hydrogen atoms, linked together in a hexagonal shape as in Figure \(14.28\).
- How many different compounds can be formed by replacing one or more of the hydrogen atoms with a chlorine atom?
- Find the number of different chemical compounds that can be formed by replacing three of the six hydrogen atoms in a benzene ring with a \(CH_3\) radical.
\(Figure \text { } 14.28.\) A benzene ring
How many equivalence classes of switching functions are there if the input variables \(x_1\text{,}\) \(x_2\text{,}\) and \(x_3\) can be permuted by any permutation in \(S_3\text{?}\) What if the input variables \(x_1\text{,}\) \(x_2\text{,}\) \(x_3\text{,}\) and \(x_4\) can be permuted by any permutation in \(S_4\text{?}\)
How many equivalence classes of switching functions are there if the input variables \(x_1\text{,}\) \(x_2\text{,}\) \(x_3\text{,}\) and \(x_4\) can be permuted by any permutation in the subgroup of \(S_4\) generated by the permutation \((x_1, x_2, x_3, x_4)\text{?}\)
A striped necktie has \(12\) bands of color. Each band can be colored by one of four possible colors. How many possible different-colored neckties are there?
A group acts faithfully on a \(G\)-set \(X\) if the identity is the only element of \(G\) that leaves every element of \(X\) fixed. Show that \(G\) acts faithfully on \(X\) if and only if no two distinct elements of \(G\) have the same action on each element of \(X\text{.}\)
Let \(p\) be prime. Show that the number of different abelian groups of order \(p^n\) (up to isomorphism) is the same as the number of conjugacy classes in \(S_n\text{.}\)
Let \(a \in G\text{.}\) Show that for any \(g \in G\text{,}\) \(gC(a) g^{-1} = C(gag^{-1})\text{.}\)
Let \(|G| = p^n\) be a nonabelian group for \(p\) prime. Prove that \(|Z(G)| \lt p^{n - 1}\text{.}\)
Let \(G\) be a group with order \(p^n\) where \(p\) is prime and \(X\) a finite \(G\)-set. If \(X_G = \{ x \in X : gx = x \text{ for all }g \in G \}\) is the set of elements in \(X\) fixed by the group action, then prove that \(|X| \equiv |X_G| \pmod{ p}\text{.}\)
If \(G\) is a group of order \(p^n\text{,}\) where \(p\) is prime and \(n \geq 2\text{,}\) show that \(G\) must have a proper subgroup of order \(p\text{.}\) If \(n \geq 3\text{,}\) is it true that \(G\) will have a proper subgroup of order \(p^2\text{?}\)


1.4: Multiplying and Dividing Decimals
Learning Objectives
- Use multiplication and division when evaluating expressions with decimals
Multiplying and dividing decimals can become complex, but we’re going to start with some basic multiplication by ten to warm-up.
Multiply by Powers of \(10\)
In many fields, especially in the sciences, it is common to multiply decimals by powers of \(10\). Let’s see what happens when we multiply \(1.9436\) by some powers of \(10\).
Look at the results without the final zeros. Do you notice a pattern?
\(\begin{array}{ccc}1.9436\left(10\right)\hfill & =& 19.436\hfill \\ 1.9436\left(100\right)\hfill & =& 194.36\hfill \\ 1.9436\left(1000\right)\hfill & =& 1943.6\hfill \end{array}\)
The number of places that the decimal point moved is the same as the number of zeros in the power of ten. The table below summarizes the results.
| Multiply by | Number of zeros | Number of places decimal point moves |
|---|---|---|
| \(10\) | \(1\) | \(1\) place to the right |
| \(100\) | \(2\) | \(2\) places to the right |
| \(1,000\) | \(3\) | \(3\) places to the right |
| \(10,000\) | \(4\) | \(4\) places to the right |
We can use this pattern as a shortcut to multiply by powers of ten instead of multiplying using the vertical format. We can count the zeros in the power of \(10\) and then move the decimal point that same of places to the right.
So, for example, to multiply \(45.86\) by \(100\), move the decimal point \(2\) places to the right.
Sometimes when we need to move the decimal point, there are not enough decimal places. In that case, we use zeros as placeholders. For example, let’s multiply \(2.4\) by \(100\). We need to move the decimal point \(2\) places to the right. Since there is only one digit to the right of the decimal point, we must write a \(0\) in the hundredths place.
Multiply a decimal by a power of \(10\)
- Move the decimal point to the right the same number of places as the number of zeros in the power of \(10\).
- Write zeros at the end of the number as placeholders if needed.
In the following video we show more examples of how to multiply a decimal by 10, 100, and 1000.
example
Multiply \(5.63\) by factors of
1. \(10\)
2. \(100\)
3. \(1000\)
[reveal-answer q=”296737″]Show Answer[/reveal-answer]
[hidden-answer a=”296737″]
Solution
By looking at the number of zeros in the multiple of ten, we see the number of places we need to move the decimal to the right.
| 1. | |
| \(56.3\left(10\right)\) | |
| There is \(1\) zero in \(10\), so move the decimal point \(1\) place to the right. | |
| \(56.3\) |
| 2. | |
| \(5.63\left(100\right)\) | |
| There are \(2\) zeros in \(100\), so move the decimal point \(2\) places to the right. | |
| \(563\) |
| 3. | |
| \(5.63\left(1000\right)\) | |
| There are \(3\) zeros in \(1000\), so move the decimal point \(3\) places to the right. | |
| A zero must be added at the end. | \(5,630\) |
[/hidden-answer]
TRY IT
[ohm_question]146599[/ohm_question]
Multiplying Decimals
Multiplying decimals is very much like multiplying whole numbers—we just have to determine where to place the decimal point. The procedure for multiplying decimals will make sense if we first review multiplying fractions.
Do you remember how to multiply fractions? To multiply fractions, you multiply the numerators and then multiply the denominators.
So let’s see what we would get as the product of decimals by converting them to fractions first. We will do two examples side-by-side below. Look for a pattern.
| A | B | |
|---|---|---|
| \(\left(0.3\right)\left(0.7\right)\) | \(\left(0.2\right)\left(0.46\right)\) | |
| Convert to fractions. | \(\left({\Large\frac{3}{10}}\right)\left({\Large\frac{7}{10}}\right)\) | \(\left({\Large\frac{2}{10}}\right)\left({\Large\frac{46}{100}}\right)\) |
| Multiply. | \({\Large\frac{21}{100}}\) | \({\Large\frac{92}{1000}}\) |
| Convert back to decimals. | \(0.21\) | \(0.092\) |
There is a pattern that we can use. In A, we multiplied two numbers that each had one decimal place, and the product had two decimal places. In B, we multiplied a number with one decimal place by a number with two decimal places, and the product had three decimal places.
How many decimal places would you expect for the product of \(\left(0.01\right)\left(0.004\right)?\) If you said “five”, you recognized the pattern. When we multiply two numbers with decimals, we count all the decimal places in the factors—in this case two plus three—to get the number of decimal places in the product—in this case five.
Once we know how to determine the number of digits after the decimal point, we can multiply decimal numbers without converting them to fractions first. The number of decimal places in the product is the sum of the number of decimal places in the factors. The rules for multiplying positive and negative numbers apply to decimals too.
Multiply decimal numbers
- Determine the sign of the product.
- Write the numbers in vertical format, lining up the numbers on the right.
- Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
- Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. If needed, use zeros as placeholders.
- Write the product with the appropriate sign.
example
Multiply: \(\left(3.9\right)\left(4.075\right)\)
Solution
| \(\left(3.9\right)\left(4.075\right)\) | |
| Determine the sign of the product. The signs are the same. | The product will be positive. |
| Write the numbers in vertical format, lining up the numbers on the right. | |
| Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points. | |
| Place the decimal point. Add the number of decimal places in the factors \(\left(1+3\right)\). Place the decimal point 4 places from the right. | |
| The product is positive. | \(\left(3.9\right)\left(4.075\right)=15.8925\) |
try it
[ohm_question]146596[/ohm_question]
In the following video we show another example of how to multiply two decimals.
Dividing Decimals
Just as with multiplication, division of decimals is very much like dividing whole numbers — we have to figure out where the decimal point must be placed.
To understand decimal division, let’s consider the multiplication problem
\(\left(0.2\right)\left(4\right)=0.8\)
Remember, a multiplication problem can be rephrased as a division problem. So we can write
\(0.8\div 4=0.2\)
We can think of this as “If we divide 8 tenths into four groups, how many are in each group?” The number line below shows that there are four groups of two-tenths in eight-tenths. So \(0.8\div 4=0.2\).
Using long division notation, we would write
Notice that the decimal point in the quotient is directly above the decimal point in the dividend.
To divide a decimal by a whole number, we place the decimal point in the quotient above the decimal point in the dividend and then divide as usual. Sometimes we need to use extra zeros at the end of the dividend to keep dividing until there is no remainder.
Divide a decimal by a whole number
- Write as long division, placing the decimal point in the quotient above the decimal point in the dividend.
- Divide as usual.
example
Divide: \(0.12\div 3\)
Solution
| \(0.12\div 3\) | |
| Write as long division, placing the decimal point in the quotient above the decimal point in the dividend. | |
| Divide as usual. Since \(3\) does not go into \(0\) or \(1\) we use zeros as placeholders. | |
| \(0.12\div 3=0.04\) |
try it
[ohm_question]146600[/ohm_question]
Watch the following video to see another example of how to divide a decimal by a whole number.
Most commonly, this calculation will be done with money while shopping. Prices of products tend to be presented as a combination of dollars and cents (i.e. \(\$5.75\), \(2.99\), or \(\$25.60\)). You can then divide by the number of items or the number of units to determine the cost per item or unit.
example
Suppose a case of \(24\) water bottles cost \($3.99\). To find the price per water bottle, we would divide \($3.99\) by \(24\), and round the answer to the nearest cent (hundredth).
Divide: \($3.99\div 24\)
[reveal-answer q=”929706″]Show Answer[/reveal-answer]
[hidden-answer a=”929706″]
Solution
| \($3.99\div 24\) | |
| Place the decimal point in the quotient above the decimal point in the dividend. | |
| Divide as usual. When do we stop? Since this division involves money, we round it to the nearest cent (hundredth). To do this, we must carry the division to the thousandths place. | |
| Round to the nearest cent. | \($0.166\approx $0.17\) |
| \($3.99\div 24\approx $0.17\) |
This means the price per bottle is \(17\) cents.
[/hidden-answer]
try it
[ohm_question]145993[/ohm_question]
[ohm_question]156951[/ohm_question]
Next, we will divide a whole number by a decimal.
example
Divide: \(4\div 0.05\)
[reveal-answer q=”616625″]Show Answer[/reveal-answer]
[hidden-answer a=”616625″]
Solution
| \(4\div 0.05\) | |
| The signs are the same. | The quotient is positive. |
|
Make the divisor a whole number by ‘moving’ the decimal point all the way to the right.
Move the decimal point in the dividend the same number of places, adding zeros as needed. |
|
|
Divide.
Place the decimal point in the quotient above the decimal point in the dividend. |
|
| Write the quotient with the appropriate sign. | \(4\div 0.05=80\) |
We can relate this example to money. How many nickels are there in four dollars? Because \(4\div 0.05=80\), there are \(80\) nickels in \($4\).
[/hidden-answer]
try it
[ohm_question]146607[/ohm_question]
The following example shows how to divide a whole number by a decimal using base ten blocks.


3.4: Alkyl Groups
-
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Objectives
After completing this section, you should be able to
- recognize and name any alkyl group that can be considered to have been formed by the removal of a terminal hydrogen atom from a straight-chain alkane containing ten or fewer carbon atoms.
- explain what is meant by a primary, secondary, tertiary or quaternary carbon atom.
- represent the various types of organic compounds using the symbol “R” to represent any alkyl group.
Key Terms
Make certain that you can define, and use in context, the key terms below.
- alkyl group
- methyl group
- isopropyl group
- sec -butyl group
- isobutyl group
- tert -butyl group
- primary carbon
- secondary carbon
- tertiary carbon
- quaternary carbon
Study Notes
The differences among primary, secondary, tertiary and quaternary carbon atoms are explained in the following discussion. A convenient way of memorizing this classification scheme is to remember that a primary carbon atom is attached directly to only one other carbon atom, a secondary carbon atom is attached directly to two carbon atoms, and so on.
The IUPAC system requires first that we have names for simple unbranched chains and second, that we have names for simple alkyl groups that may be attached to the chains. An alkyl group is formed by removing one hydrogen from the alkane chain. The removal of this hydrogen results in a stem change from -ane to -yl to indicate an alkyl group. The removal of a hydrogen from methane, CH 4 , creates a methyl group -CH 3 . Likewise, the removal of a hydrogen from ethane, CH 3 CH 3 , creates an ethyl group -CH 2 CH 3 . The nomenclature pattern can continue to provide a series of straight-chain alkyl groups from straight chain alkanes with a hydrogen removed from the end. Note, the letter R is used to designate a generic (unspecified) alkyl group.
| Alkane | Name | Alkyl Group | Name (Abbreviation) |
|---|---|---|---|
| CH 4 | Methane | -CH 3 | Methyl (Me) |
| CH 3 CH 3 | Ethane | -CH 2 CH 3 | Ethyl (Et) |
| CH 3 CH 2 CH 3 | Propane | -CH 2 CH 2 CH 3 | Propyl (Pr) |
| CH 3 CH 2 CH 2 CH 3 | Butane | -CH 2 CH 2 CH 2 CH 3 | Butyl (Bu) |
| CH 3 CH 2 CH 2 CH 2 CH 3 | Pentane | -CH 2 CH 2 CH 2 CH 2 CH 3 | Pentyl |
| CH 3 CH 2 CH 2 CH 2 CH 2 CH 3 | Hexane | -CH 2 CH 2 CH 2 CH 2 CH 2 CH 3 | Hexyl |
Prior to the systematic nomenclature developed for organic chemistry, prefixes were used to specify the connection point of straight-chain and branched-chain alkyl groups. Although the modern nomenclature system, discussed in the next section, is preferred these older terms are still often used, especially in solvents and reagents. Thus, an understanding of these prefixes is important to understanding organic chemistry. Notice that the total number of carbons in the alkyl subsistent is still indicated with the prefix + yl . For methyl and ethyl alkyl groups there is only one possible connection point so connection prefixes are not necessary. Starting with a three carbon alkyl group (propyl) the possibility of multiple connection points necessitates connection prefixes. These prefixes are often abbreviated with a letter which is italicized.
Normal ( n )
The prefix "n" is used to indicate a connection at the end of a straight-chain alkane. This prefix is not commonly used to just indicate alkyl subsistent as discussed above. However it is sometime used to indicate the connection of a functional group onto a straight alkane.
Iso ( i )
Starting with propyl alkyl groups there is the possibility of a connection other than the very end. The prefix "iso" implies that the connection ends with a (CH 3 ) 2 CH- group.
Secondary ( Sec )
With butyl straight-chain alkyl groups there is the possibility of a connection on the second carbon from the end of the chain. These alkyl groups are given the prefix " Sec. " This is not used for pentyl or hexyl groups because there is more than one structure that are not identical that could be named as sec-pentyl or sec-hexyl.
Tertiary ( tert or t )
Starting with four carbon alkyl groups, there is an isomer which can have a connection to a tertiary carbon. These alkyl groups get the prefix " t ."
Example:
The naming system described above is often used to describe halogens which contain only a few carbons. The halogen is shown as bonded to the connection point of the alkyl group.
Classification of carbon atoms
Carbons have a special terminology to describe how many other carbons they are attached to. This allows for an easy description of branching in alkanes. Also, we will find that the number of carbons attached to a given atom will have subtle effects on its chemistry.
- Primary carbons (1 o ) attached to one other C atom.
- Secondary carbons (2 o ) are attached to two other C’s.
- Tertiary carbons (3 o ) are attached to three other C’s.
- Quaternary carbons (4 o ) are attached to four C's.
The figure below use the group "R" to represent an alkyl group of unspecified length. R typically used to represent alkyl groups but an also represent a part of a molecule which is either unspecified or not germane to the discussion.
This terminology will be used repeatedly in organic chemistry to describe the number of carbons attached to a specific atom, however, the atom will not always a carbon.
Example \(\PageIndex{1}\)
Please indicate the the number of 1 o , 2 o , 3 o , and 4 o carbons in the following molecule:
- The molecule has five Primary carbons (1 o ).
- The molecule has one Secondary carbon (2 o ).
- The molecule has one Tertiary carbon (3 o ).
- The molecule has one Quaternary carbon (4 o )
Hydrogen atoms are also classified in this manner. A hydrogen atom attached to a primary carbon atom is called a primary hydrogen ect.
- Primary hydrogens (1 o ) are attached to carbons bonded to one other C atom
- Secondary hydrogens (2 o ) are attached to carbons bonded to two other C’s
- Tertiary hydrogens (3 o ) are attached to carbons bonded to three other C’s
- It is not possible to have a quaternary hydrogen (4 o ).
Example \(\PageIndex{2}\)
Please indicate the the number of 1 o , 2 o , and 3 o , hydrogens are in the following molecule:
- The molecule has fifteen Primary (1 o ) hydrogens.
- The molecule has two Secondary (2 o ) hydrogens.
- The molecule has one Tertiary (3 o ) hydrogen.
Exercises
Exercise \(\PageIndex{1}\)
Determine whether the H’s indicated in the following structure are 1 o , 2 o , or 3 o .
- Answer
-
Exercise \(\PageIndex{2}\)
Determine whether the H’s indicated in the following structure is 1 o , 2 o , or 3 o .
- Answer
-
Exercise \(\PageIndex{3}\)
Determine whether the carbons indicated in the structure below are 1 o , 2 o , 3 o , or 4 o .
- Answer
-
Exercise \(\PageIndex{4}\)
Determine whether the carbons indicated in the structure below are 1 o , 2 o , 3 o , or 4 o .
- Answer
-
Exercise \(\PageIndex{5}\)
Please indicate the total number of each type 1 o , 2 o , 3 o , and 4 o carbons in the following molecule.
- Answer
-
There are 5 primary (1 o ) C’s , 2 secondary (2 o ) C’s , 1 tertiary (3 o ) C and 1 quaternary (4 o ) C in the structure (seen color coded below).
Exercise \(\PageIndex{6}\)
Please indicate the total number of each type 1 o , 2 o , 3 o , and 4 o carbons in the following molecule.
- Answer
-
There are 8 primary (1 o ) C’s , 7 secondary (2 o ) C’s , 2 tertiary (3 o ) C’s and 2 quaternary (4 o ) C’s in the structure (seen color coded below).


13.2: §88. Adjectives from the Present Base (-AX, -UUS, -ULUS, -IDUS)
We can swiftly review a number of adjective-forming suffixes that were regularly added to the LATIN PRESENT INFINITIVE BASE.
1. -AX . This suffix could be combined with a present verb base (e.g., ten-ere , “hold”) to form a 3rd declension adjective of the type tenax , tenac-is , “inclined to hold,” with English derivatives like tenacious and tenacity (L ten-ac-itas ). [1] Here is a sample:
| LATIN INFINITIVE | LATIN MEANING | LATIN ADJECTIVE | ENGLISH DERIVATIVES |
| aud ē re | “dare” | audax | audacious, audacity |
| vivere | “live” | vivax | vivacious, vivacity |
| capere | “take” | capax | capacious, capacity |
| rapere | “seize” | rapax | rapacious, rapacity |
| loqui | “speak” | loquax | loquacious, loquacity |
| pugnare | “fight” | pugnax | pugnacious, pugnacity |
2. -UUS . We met several of these adjectives in Chapter 4 (§26), though you weren’t told at the time that they derived from verbs. If noc ē re is “to harm,” then nocuus (E nocuous ) is “inclined to harm,” “harmful,” and innocuus (E innocuous ) is its opposite. The root of tangere appears as tig- in contiguus ; so English contiguous means “touching together.” From con-tinere (“hold together”) came continuus , whence continuous and continuity . Deciduus is derived from de-cidere , a compound of cadere ; therefore deciduous leaves are “inclined to fall down.” What is the etymology of conspicuous ?
3. -ULUS . Very similar in meaning, this suffix had limited use in Latin. Bibulus (< bibere ) is the etymon of English bibulous (“tending to drink”), and tremulus (< tremere ), of tremulous (“inclined to tremble”). Other English examples are pendulous ( pendere , “hang”), querulous ( queri , “complain”), and garrulous ( garrire , “chatter”).
4. -IDUS . These adjectives often correspond with deverbative nouns in -or , of the type introduced in §74. Thus tim ē re (“to fear”) gave rise to the noun timor (reflected in E timorous ) and the adjective timidus (“inclined to fear”) > English timid . Similarly,
| pall ē re (“to be pale”) | > pallor (noun) | pallidus (adj.), E pallid |
| rig ē re (“to be stiff”) | > rigor | rigidus , E rigid |
| tum ē re (“to swell”) | > tumor | tumidus , E tumid [cf. tumescent , -ence ] |
Other English adjectives of this type include: fervid, liquid, livid, stupid, squalid, valid, vapid, lucid, rapid, and vivid . [2]
-
The
-acious
ending on
tenacious
is derived from French
tenacieux
, which was influenced by the Latin
-osus
type of adjective. There was never a Latin form “
tenaciosus.
” ↵
-
All but the last three have corresponding
-or
nouns, both in Latin and in English. Except for
rapid
(
rapere
) and
vivid
(
vivere
) all these adjectives are derived from 2nd conjugation verbs. ↵


19.1: Introduction
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- Allison Perlman
- University of California Press
When Alex Nogales, president and CEO of the National Hispanic Media Coalition (NHMC), narrates the history of his organization, he tells a story of continuity and change. The core mission of the group—to integrate Latinas/os into more jobs behind and in front of the camera, ameliorate derogatory images of Latinas/os in the media, and advocate for telecommunications policies that serve the needs of Latina/o publics—has remained consistent since the NHMC was founded in 1986. What has changed, according to Nogales, is the organization’s strategies, which have evolved with the group’s experiences in media activism and advocacy. In his telling, the NHMC went from being a comparatively naïve organization, committed to addressing the exigent concerns of local communities, to a sophisticated group capable of exerting meaningful pressure on a national scale, especially via participation in the policymaking sphere. 1
The NHMC’s emphasis on media labor has been in keeping with the priorities of other identity-based media advocacy groups who have worked to bring people of color into media industry workforces at all levels. For the NHMC, to ensure that Latinas/os have access to these jobs is, like other equal employment advocacy, to enable them to participate in a sector that had historically discriminated against them; in addition, it is to transform the kinds of stories told and perspectives voiced in media texts, from news reports to entertainment programming. While securing Latina/o jobs has been a consistent goal of the NHMC, it has had to navigate a legal environment increasingly hostile to race-conscious policies to promote diversity and a regulatory system increasingly committed to media deregulation. In response, the NHMC, like other advocacy groups, has had to rethink how to promote diversity in the absence of what had been essential regulatory tools and in a climate unreceptive to such interventions.
Media advocacy, the kind of actions undertaken by groups like the NHMC, thus not only has been centrally concerned with media labor, but has constituted its own form of work. The work of media advocacy often is a labor-intensive enterprise, one that relies on myriad forms of capital—financial, cultural, institutional—to function. While media advocacy has often depended on uncompensated labor, from the work of volunteers whose contributions create the scaffolding upon which media advocacy efforts are built to the citizens who respond to calls to action by filing letters with or calling the Federal Communications Commission (FCC) or members of Congress, it also has been guided by media advocacy professionals. These are professionals in two senses of the term: they have expertise and they are compensated for their labor.
To examine media advocacy as work is to alter the kinds of questions we ask and the kind of narratives we construct. While there are meaningful differences in how scholars have understood the political stakes, moments of opportunity, and mobilizing structures and strategies of media advocacy efforts, what they share is an understanding of media advocacy as a social movement or as a form of civic participation that has sought to transform the media to meet the communication needs of citizens in a democracy. Media advocacy campaigns are often narrated as David-and-Goliath stories, in which public interest groups try to reform the media only to be defeated by better-resourced media corporations that more successfully manipulate public opinion and gain sway over public officials.
The emphasis of media advocacy scholarship, furthermore, often is the media advocacy campaign, a temporally bounded effort undertaken at a particularly propitious moment when political changes or new technologies introduce fissures that make reform seem possible. 2 Media advocacy has also often been analyzed along a success/failure binary, an assessment of how and why media advocacy has or has not attained its desired goals. As the first section of this article discusses, to see media advocacy as work is to shift our focus off outcomes and onto process and to rethink the success/failure binary that has structured much of media advocacy scholarship. Media advocacy for groups like the NHMC is a long-term, multifaceted commitment that shifts with technological, political, and regulatory changes, as well as with the increasing savvy of the media advocates themselves. Their work is continuing, not contingent on singular campaigns or issues. Viewed through this lens, media advocacy can be seen less as a rhythmic exercise in hope and failure and more as a continuous hum of activity that sometimes yields actionable policy changes, in which communities outside the official regulatory sphere make themselves legible as stakeholders in the policymaking process. To consider media advocacy as work is to see it as ongoing, cumulative, and flexible.
In addition, as the second section demonstrates, many contemporary media advocacy groups in the United States are engaged in media work , labor that contributes to, rather than interferes with, media production and the interests of media companies. Media advocacy, however, has been invisible to scholars of media labor, who mostly have been interested in how the production process under which media are made, as well as the occupational cultures and power relations structuring the mode of production, affects the narratives, values, and images that media audiences consume. Deploying ethnographic and historical methods, and focusing on a range of media, this subfield traditionally has focused on above-the-line workers (directors, writers, producers, and executives); labor within these texts is imagined as both the creative labor of artists and the managerial labor of executives, the friction between them understood as alternately stifling and generative for the production of media texts. 3
More recent scholarship, however, has expanded the methods and subjects of media labor scholarship. John Caldwell, for example, has blended ethnographic research with sophisticated discourse analysis to investigate not only the diverse range of labor practices—both above and below the line—that constitute film and television production, but the discursive labor involved in shaping and sustaining the occupational cultures within the entertainment industry. 4 In a similar vein, Vicki Mayer, in her Below the Line , has broadened the definition of production to include the “invisible labor” that is constitutive of television production but frequently absented in both industry and academic discourse. 5 Conceptions of media labor thus have been extended to the myriad forms of work that contribute to media production and to the discursive formations that sustain its division of labor.
While media advocacy has often existed outside media production, it has also intersected with, and contributed to, both the workflow of media production and the underlying assumptions about audience and narrative that structure it. For decades, media advocacy groups’ work with media producers has been a constitutive part of their reform efforts. Increasingly, however, this collaboration has extended to advocacy groups using their position as representatives of the public to promote the policy agenda of media corporations. As the second section discusses, for some organizations, media advocacy work thus has given way to media work, their adversarial role transformed into a collaborative—or, to some critics, collusive—one with media and telecommunications corporations.


7.10: Exercises
Does a cation gain protons to form a positive charge or does it lose electrons?
Iron(III) sulfate [Fe 2 (SO 4 ) 3 ] is composed of Fe 3 + and ions. Explain why a sample of iron(III) sulfate is uncharged.
Which of the following atoms would be expected to form negative ions in binary ionic compounds and which would be expected to form positive ions: P, I, Mg, Cl, In, Cs, O, Pb, Co?
Which of the following atoms would be expected to form negative ions in binary ionic compounds and which would be expected to form positive ions: Br, Ca, Na, N, F, Al, Sn, S, Cd?
Predict the charge on the monatomic ions formed from the following atoms in binary ionic compounds:
- (f) Cs
Predict the charge on the monatomic ions formed from the following atoms in binary ionic compounds:
- (f) In
Write the electron configuration for each of the following ions:
- (k) Fe 2 +
Write the electron configuration for the monatomic ions formed from the following elements (which form the greatest concentration of monatomic ions in seawater):
- Cl
- Na
- Mg
- Ca
- K
- Br
- Sr
- F
Write out the full electron configuration for each of the following atoms and for the monatomic ion found in binary ionic compounds containing the element:
- (f) S
From the labels of several commercial products, prepare a list of six ionic compounds in the products. For each compound, write the formula. (You may need to look up some formulas in a suitable reference.)
Why is it incorrect to speak of a molecule of solid NaCl?
What information can you use to predict whether a bond between two atoms is covalent or ionic?
Predict which of the following compounds are ionic and which are covalent, based on the location of their constituent atoms in the periodic table:
-
(i) CaO
(j) IBr
(k) CO 2
Explain the difference between a nonpolar covalent bond, a polar covalent bond, and an ionic bond.
From its position in the periodic table, determine which atom in each pair is more electronegative:
-
(f) Ba or P
(g) N or K
From its position in the periodic table, determine which atom in each pair is more electronegative:
-
(f) Se or P
(g) C or Si
From their positions in the periodic table, arrange the atoms in each of the following series in order of increasing electronegativity:
- C, F, H, N, O
- Br, Cl, F, H, I
- F, H, O, P, S
- Al, H, Na, O, P
- Ba, H, N, O, As
From their positions in the periodic table, arrange the atoms in each of the following series in order of increasing electronegativity:
- As, H, N, P, Sb
- Cl, H, P, S, Si
- Br, Cl, Ge, H, Sr
- Ca, H, K, N, Si
- Cl, Cs, Ge, H, Sr
Which atoms can bond to sulfur so as to produce a positive partial charge on the sulfur atom?
Which is the most polar bond?
- C–C
- C–H
- N–H
- O–H
- Se–H
Identify the more polar bond in each of the following pairs of bonds:
-
(f) SO or PO
(g) CN or NN
Which of the following molecules or ions contain polar bonds?
-
(f) H
2
S
(g)
Write the Lewis symbols for each of the following ions:
- (f) Li +
Many monatomic ions are found in seawater, including the ions formed from the following list of elements. Write the Lewis symbols for the monatomic ions formed from the following elements:
- Cl
- Na
- Mg
- Ca
- K
- Br
- Sr
- F
Write the Lewis symbols of the ions in each of the following ionic compounds and the Lewis symbols of the atom from which they are formed:
- (f) KF
In the Lewis structures listed here, M and X represent various elements in the third period of the periodic table. Write the formula of each compound using the chemical symbols of each element:
(a)
(b)
(c)
(d)
Write the Lewis structure for the diatomic molecule P 2 , an unstable form of phosphorus found in high-temperature phosphorus vapor.
Write Lewis structures for the following:
- (k) CN –
Write Lewis structures for the following:
-
(i) HCCH
(j) ClCN
(k)
Write Lewis structures for the following:
- ClF 3
- PCl 5
- BF 3
Write Lewis structures for the following:
- SeF 6
- XeF 4
- Cl 2 BBCl 2 (contains a B–B bond)
Write Lewis structures for:
- HONO
Correct the following statement: “The bonds in solid PbCl 2 are ionic; the bond in a HCl molecule is covalent. Thus, all of the valence electrons in PbCl 2 are located on the Cl – ions, and all of the valence electrons in a HCl molecule are shared between the H and Cl atoms.”
Write Lewis structures for the following molecules or ions:
- SbH 3
- XeF 2
- Se 8 (a cyclic molecule with a ring of eight Se atoms)
Methanol, H 3 COH, is used as the fuel in some race cars. Ethanol, C 2 H 5 OH, is used extensively as motor fuel in Brazil. Both methanol and ethanol produce CO 2 and H 2 O when they burn. Write the chemical equations for these combustion reactions using Lewis structures instead of chemical formulas.
Many planets in our solar system contain organic chemicals including methane (CH 4 ) and traces of ethylene (C 2 H 4 ), ethane (C 2 H 6 ), propyne (H 3 CCCH), and diacetylene (HCCCCH). Write the Lewis structures for each of these molecules.
Carbon tetrachloride was formerly used in fire extinguishers for electrical fires. It is no longer used for this purpose because of the formation of the toxic gas phosgene, Cl 2 CO. Write the Lewis structures for carbon tetrachloride and phosgene.
Identify the atoms that correspond to each of the following electron configurations. Then, write the Lewis symbol for the common ion formed from each atom:
- 1 s 2 2 s 2 2 p 5
- 1 s 2 2 s 2 2 p 6 3 s 2
- 1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 4 s 2 3 d 10
- 1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 4 s 2 3 d 10 4 p 4
- 1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 4 s 2 3 d 10 4 p 1
The arrangement of atoms in several biologically important molecules is given here. Complete the Lewis structures of these molecules by adding multiple bonds and lone pairs. Do not add any more atoms.
(a) the amino acid serine:
(b) urea:
(c) pyruvic acid:
(d) uracil:
(e) carbonic acid:
A compound with a molar mass of about 28 g/mol contains 85.7% carbon and 14.3% hydrogen by mass. Write the Lewis structure for a molecule of the compound.
A compound with a molar mass of about 42 g/mol contains 85.7% carbon and 14.3% hydrogen by mass. Write the Lewis structure for a molecule of the compound.
Two arrangements of atoms are possible for a compound with a molar mass of about 45 g/mol that contains 52.2% C, 13.1% H, and 34.7% O by mass. Write the Lewis structures for the two molecules.
How are single, double, and triple bonds similar? How do they differ?
Write resonance forms that describe the distribution of electrons in each of these molecules or ions.
- selenium dioxide, OSeO
- nitrate ion,
- nitric acid, HNO 3 (N is bonded to an OH group and two O atoms)
- benzene, C 6 H 6 :
(e) the formate ion:
Write resonance forms that describe the distribution of electrons in each of these molecules or ions.
- sulfur dioxide, SO 2
- carbonate ion,
- hydrogen carbonate ion, (C is bonded to an OH group and two O atoms)
- pyridine:
(e) the allyl ion:
Write the resonance forms of ozone, O 3 , the component of the upper atmosphere that protects the Earth from ultraviolet radiation.
Sodium nitrite, which has been used to preserve bacon and other meats, is an ionic compound. Write the resonance forms of the nitrite ion,
In terms of the bonds present, explain why acetic acid, CH 3 CO 2 H, contains two distinct types of carbon-oxygen bonds, whereas the acetate ion, formed by loss of a hydrogen ion from acetic acid, only contains one type of carbon-oxygen bond. The skeleton structures of these species are shown:
Write the Lewis structures for the following, and include resonance structures where appropriate. Indicate which has the strongest carbon-oxygen bond.
- CO 2
- CO
Toothpastes containing sodium hydrogen carbonate (sodium bicarbonate) and hydrogen peroxide are widely used. Write Lewis structures for the hydrogen carbonate ion and hydrogen peroxide molecule, with resonance forms where appropriate.
Determine the formal charge of each element in the following:
- HCl
- CF 4
- PCl 3
- PF 5
Determine the formal charge of each element in the following:
- H 3 O +
- NH 3
- H 2 O 2
Calculate the formal charge of chlorine in the molecules Cl 2 , BeCl 2 , and ClF 5 .
Calculate the formal charge of each element in the following compounds and ions:
- F 2 CO
- NO –
- H 2 CCH 2
- ClF 3
- SeF 6
Draw all possible resonance structures for each of these compounds. Determine the formal charge on each atom in each of the resonance structures:
- O 3
- SO 2
Based on formal charge considerations, which of the following would likely be the correct arrangement of atoms in nitrosyl chloride: ClNO or ClON?
Based on formal charge considerations, which of the following would likely be the correct arrangement of atoms in hypochlorous acid: HOCl or OClH?
Based on formal charge considerations, which of the following would likely be the correct arrangement of atoms in sulfur dioxide: OSO or SOO?
Draw the structure of hydroxylamine, H 3 NO, and assign formal charges; look up the structure. Is the actual structure consistent with the formal charges?
Iodine forms a series of fluorides (listed here). Write Lewis structures for each of the four compounds and determine the formal charge of the iodine atom in each molecule:
- IF
- IF 3
- IF 5
- IF 7
Write the Lewis structure and chemical formula of the compound with a molar mass of about 70 g/mol that contains 19.7% nitrogen and 80.3% fluorine by mass, and determine the formal charge of the atoms in this compound.
Which of the following structures would we expect for nitrous acid? Determine the formal charges:
Sulfuric acid is the industrial chemical produced in greatest quantity worldwide. About 90 billion pounds are produced each year in the United States alone. Write the Lewis structure for sulfuric acid, H 2 SO 4 , which has two oxygen atoms and two OH groups bonded to the sulfur.
Which bond in each of the following pairs of bonds is the strongest?
-
(e) C–H or O–H
(f) C–N or C–O
Using the bond energies in Table 7.2, determine the approximate enthalpy change for each of the following reactions:
Using the bond energies in Table 7.2, determine the approximate enthalpy change for each of the following reactions:
When a molecule can form two different structures, the structure with the stronger bonds is usually the more stable form. Use bond energies to predict the correct structure of the hydroxylamine molecule:
How does the bond energy of HCl( g ) differ from the standard enthalpy of formation of HCl( g )?
Using the standard enthalpy of formation data in Appendix G, show how the standard enthalpy of formation of HCl( g ) can be used to determine the bond energy.
Using the standard enthalpy of formation data in Appendix G, calculate the bond energy of the carbon-sulfur double bond in CS 2 .
Using the standard enthalpy of formation data in Appendix G, determine which bond is stronger: the S–F bond in SF 4 ( g ) or in SF 6 ( g )?
Using the standard enthalpy of formation data in Appendix G, determine which bond is stronger: the P–Cl bond in PCl 3 ( g ) or in PCl 5 ( g )?
Complete the following Lewis structure by adding bonds (not atoms), and then indicate the longest bond:
Use the bond energy to calculate an approximate value of Δ H for the following reaction. Which is the more stable form of FNO 2 ?
Use principles of atomic structure to answer each of the following: 1
- The radius of the Ca atom is 197 pm; the radius of the Ca 2+ ion is 99 pm. Account for the difference.
- The lattice energy of CaO( s ) is –3460 kJ/mol; the lattice energy of K 2 O is –2240 kJ/mol. Account for the difference.
- Given these ionization values, explain the difference between Ca and K with regard to their first and second ionization energies.
| Element | First Ionization Energy (kJ/mol) | Second Ionization Energy (kJ/mol) |
|---|---|---|
| K | 419 | 3050 |
| Ca | 590 | 1140 |
(d) The first ionization energy of Mg is 738 kJ/mol and that of Al is 578 kJ/mol. Account for this difference.
The lattice energy of LiF is 1023 kJ/mol, and the Li–F distance is 200.8 pm. NaF crystallizes in the same structure as LiF but with a Na–F distance of 231 pm. Which of the following values most closely approximates the lattice energy of NaF: 510, 890, 1023, 1175, or 4090 kJ/mol? Explain your choice.
For which of the following substances is the least energy required to convert one mole of the solid into separate ions?
- MgO
- SrO
- KF
- CsF
- MgF 2
The reaction of a metal, M, with a halogen, X 2 , proceeds by an exothermic reaction as indicated by this equation: For each of the following, indicate which option will make the reaction more exothermic. Explain your answers.
- a large radius vs. a small radius for M +2
- a high ionization energy vs. a low ionization energy for M
- an increasing bond energy for the halogen
- a decreasing electron affinity for the halogen
- an increasing size of the anion formed by the halogen
The lattice energy of LiF is 1023 kJ/mol, and the Li–F distance is 201 pm. MgO crystallizes in the same structure as LiF but with a Mg–O distance of 205 pm. Which of the following values most closely approximates the lattice energy of MgO: 256 kJ/mol, 512 kJ/mol, 1023 kJ/mol, 2046 kJ/mol, or 4008 kJ/mol? Explain your choice.
Which compound in each of the following pairs has the larger lattice energy? Note: Mg 2+ and Li + have similar radii; O 2– and F – have similar radii. Explain your choices.
- MgO or MgSe
- LiF or MgO
- Li 2 O or LiCl
- Li 2 Se or MgO
Which compound in each of the following pairs has the larger lattice energy? Note: Ba 2+ and
K + have similar radii; S 2– and Cl – have similar radii. Explain your choices.
- K 2 O or Na 2 O
- K 2 S or BaS
- KCl or BaS
- BaS or BaCl 2
Which of the following compounds requires the most energy to convert one mole of the solid into separate ions?
- MgO
- SrO
- KF
- CsF
- MgF 2
Which of the following compounds requires the most energy to convert one mole of the solid into separate ions?
- K 2 S
- K 2 O
- CaS
- Cs 2 S
- CaO
The lattice energy of KF is 794 kJ/mol, and the interionic distance is 269 pm. The Na–F
distance in NaF, which has the same structure as KF, is 231 pm. Which of the following values is the closest approximation of the lattice energy of NaF: 682 kJ/mol, 794 kJ/mol, 924 kJ/mol, 1588 kJ/mol, or 3175 kJ/mol? Explain your answer.
Explain why the HOH molecule is bent, whereas the HBeH molecule is linear.
What feature of a Lewis structure can be used to tell if a molecule’s (or ion’s) electron-pair geometry and molecular structure will be identical?
Explain the difference between electron-pair geometry and molecular structure.
Why is the H–N–H angle in NH 3 smaller than the H–C–H bond angle in CH 4 ? Why is the H–N–H angle in identical to the H–C–H bond angle in CH 4 ?
Explain how a molecule that contains polar bonds can be nonpolar.
As a general rule, MX n molecules (where M represents a central atom and X represents terminal atoms; n = 2 – 5) are polar if there is one or more lone pairs of electrons on M. NH 3 (M = N, X = H, n = 3) is an example. There are two molecular structures with lone pairs that are exceptions to this rule. What are they?
Predict the electron pair geometry and the molecular structure of each of the following molecules or ions:
- SF 6
- PCl 5
- BeH 2
Identify the electron pair geometry and the molecular structure of each of the following molecules or ions:
- CF 4
- BF 3
- BeCl 2
What are the electron-pair geometry and the molecular structure of each of the following molecules or ions?
- (f)
Predict the electron pair geometry and the molecular structure of each of the following ions:
- (f) XeF 4
Identify the electron pair geometry and the molecular structure of each of the following molecules:
-
(f) XeO
2
F
2
(Xe is the central atom)
(g) (Cl is the central atom)
Predict the electron pair geometry and the molecular structure of each of the following:
- (f)
Which of the following molecules and ions contain polar bonds? Which of these molecules and ions have dipole moments?
- (f)
Which of these molecules and ions contain polar bonds? Which of these molecules and ions have dipole moments?
- (f) XeF 4
Which of the following molecules have dipole moments?
- CS 2
- SeS 2
- CCl 2 F 2
- PCl 3 (P is the central atom)
- ClNO (N is the central atom)
Identify the molecules with a dipole moment:
- SF 4
- CF 4
- Cl 2 CCBr 2
- CH 3 Cl
- H 2 CO
The molecule XF 3 has a dipole moment. Is X boron or phosphorus?
The molecule XCl 2 has a dipole moment. Is X beryllium or sulfur?
Is the Cl 2 BBCl 2 molecule polar or nonpolar?
There are three possible structures for PCl 2 F 3 with phosphorus as the central atom. Draw them and discuss how measurements of dipole moments could help distinguish among them.
Describe the molecular structure around the indicated atom or atoms:
- (i) each of the carbon atoms in allene, H 2 CCCH 2
Draw the Lewis structures and predict the shape of each compound or ion:
- CO 2
- SO 3
A molecule with the formula AB 2 , in which A and B represent different atoms, could have one of three different shapes. Sketch and name the three different shapes that this molecule might have. Give an example of a molecule or ion for each shape.
A molecule with the formula AB 3 , in which A and B represent different atoms, could have one of three different shapes. Sketch and name the three different shapes that this molecule might have. Give an example of a molecule or ion that has each shape.
Draw the Lewis electron dot structures for these molecules, including resonance structures where appropriate:
- CS 2
- CS
- predict the molecular shapes for and CS 2 and explain how you arrived at your predictions
What is the molecular structure of the stable form of FNO 2 ? (N is the central atom.)
A compound with a molar mass of about 42 g/mol contains 85.7% carbon and 14.3% hydrogen. What is its molecular structure?
Use the simulation to perform the following exercises for a two-atom molecule:
- Adjust the electronegativity value so the bond dipole is pointing toward B. Then determine what the electronegativity values must be to switch the dipole so that it points toward A.
- With a partial positive charge on A, turn on the electric field and describe what happens.
- With a small partial negative charge on A, turn on the electric field and describe what happens.
- Reset all, and then with a large partial negative charge on A, turn on the electric field and describe what happens.
Use the simulation to perform the following exercises for a real molecule. You may need to rotate the molecules in three dimensions to see certain dipoles.
- Sketch the bond dipoles and molecular dipole (if any) for O 3. Explain your observations.
- Look at the bond dipoles for NH 3 . Use these dipoles to predict whether N or H is more electronegative.
- Predict whether there should be a molecular dipole for NH 3 and, if so, in which direction it will point. Check the molecular dipole box to test your hypothesis.
Use the Molecule Shape simulator to build a molecule. Starting with the central atom, click on the double bond to add one double bond. Then add one single bond and one lone pair. Rotate the molecule to observe the complete geometry. Name the electron group geometry and molecular structure and predict the bond angle. Then click the check boxes at the bottom and right of the simulator to check your answers.
Use the Molecule Shape simulator to explore real molecules. On the Real Molecules tab, select H 2 O. Switch between the “real” and “model” modes. Explain the difference observed.
Use the Molecule Shape simulator to explore real molecules. On the Real Molecules tab, select “model” mode and S 2 O. What is the model bond angle? Explain whether the “real” bond angle should be larger or smaller than the ideal model angle.
Footnotes
- 1 This question is taken from the Chemistry Advanced Placement Examination and is used with the permission of the Educational Testing Service.