7.16A: Detecting Uncultured Microorganisms
Using metagenomics, the microbial constituents of the world can be identified by culturing each individual species.
LEARNING OBJECTIVES
Recognize the methods used to detect uncultured microorganisms
Key Takeaways
Identification of bacteria in the laboratory is particularly relevant in medicine, where the correct treatment is determined by the bacterial species causing an infection. Consequently, the need to identify human pathogens was a major impetus for the development of techniques to identify bacteria.
Early studies have shown that the microbial life around us in the air, sea, and soil is very diverse and only a small fraction of the species are known. One limitation of identifying human pathogens or conventional sequencing begins with a culture of identical cells as a source of DNA. However, early metagenomic studies revealed that there are probably large groups of microorganisms in many environments that cannot be cultured and thus cannot be sequenced. These early studies focused on 16S ribosomal RNA sequences which are relatively short, often conserved within a species, and generally different between species. Many 16S rRNA sequences have been found which do not belong to any known cultured species, indicating that there are numerous non-isolated organisms out there. These surveys of ribosomal RNA (rRNA) genes taken directly from the environment revealed that cultivation based methods find less than 1% of the bacterial and archaeal species in a sample.
The discovery of such diversity led to the field of metagenomics, which is the study of metagenomes, genetic material recovered directly from environmental samples. Rather than culturing a microbe, this approach takes a sample and identifies the different species in it by sequencing all the species simultaneously. However, recovery of DNA sequences longer than a few thousand base pairs from environmental samples was very difficult until recent advances in molecular biological techniques. More specifically, the construction of libraries in bacterial artificial chromosomes (BACs) provided better vectors for molecular cloning.
Advances in bioinformatics, refinements of DNA amplification, and the proliferation of computational power have greatly aided the analysis of DNA sequences recovered from environmental samples. These advances have allowed the adaptation of shotgun sequencing to metagenomic samples. The approach, used to sequence many cultured microorganisms and the human genome, randomly shears DNA, sequences many short sequences, and reconstructs them into a consensus sequence.
Shotgun sequencing and screens of clone libraries reveal genes present in environmental samples. This can be helpful in understanding the ecology of a community, particularly if multiple samples are compared to each other. This was further followed by high-throughput sequencing which did the same process as the shotgun sequencing but at a much bigger scale in terms of the amount of DNA that could sequenced from one sample. This provides information both on which organisms are present and what metabolic processes are possible in the community. Using metagenomics, and the resultant sequencing of uncultured microbes, metagenomics has the potential to advance knowledge in a wide variety of fields. It can also be applied to solve practical challenges in medicine, engineering, agriculture, and sustainability.
Key Points
- Many organisms that can cause diseases are not culturable, so a unicellular culture cannot be obtained.
- Initial studies of microbial fauna showed that they are more diverse than expected and contained many microbes that were not culturable.
- Advances in molecular biological techniques allow the sequencing of all or at least many of the genomes of microbes found in a sample.
Key Terms
- shotgun sequencing : A DNA sequencing technique in which a large number of small fragments of a long DNA strand are generated at random, sequenced, and reassembled to form a sequence of the original strand.
- culturable : Able to be cultured (grown in a suitable environment).
- high-throughput sequencing : Technologies that parallelize the sequencing process, producing thousands or millions of sequences at once.


8.3: Introduction to Factor Groups
We now return to the notion of equipping \(G/H\text{,}\) when \(H\unlhd G\text{,}\) with a group structure. We have already saw that left coset multiplication on \(G/H\) is well-defined when \(H\unlhd G\) (Theorem \(8.1.1\)); it turns out that given this, it is very easy to prove that \(G/H\) under this operation is a group.
Before we prove this, we introduce a change in our notation: We initiate the convention of frequently using \(N\text{,}\) rather than \(H\text{,}\) to denote a subgroup of a group \(G\) when we know that that subgroup is normal in \(G\text{.}\)
Theorem \(\PageIndex{1}\)
Let \(G\) be a group with identity element \(e\text{,}\) and let \(N\: G\text{.}\) Then \(G/N\) is a group under left coset multiplication (that is, under the operation \((aN)(bN)=abN\) for all \(a,b\in G\)), and \(|G/N|=(G:N)\) (in particular, if \(|G|\lt \infty\text{,}\) then \(|G/N|=|G|/|N|\)).
- Proof
-
We already know that since \(N⊴G\), left coset multiplication on \(G/N\) is well-defined; further, by definition, that \((aN)(bN)=abN∈G/N\) for every \(aN,bN∈G/N\).
Associativity of this operation on \(G/N\) follows from the associativity of \(G\)'s operation: indeed, if \(aN, bN, cN∈G/N\), then
\(\begin{array}& ((aN)(bN))(cN)&=(abN)(cN)\\&=(ab)cN\\&=a(bc)N\\&=(aN)(bcN)\\&=(aN)((bN)(cN)). \end{array}\)
Next, \(N=eN∈G/N\) acts as an identity element since for all \(a∈G\),
\((aN)(N)=aeN=aN \text{ and } N(aN)=eaN=aN\).
Finally, let \(aN∈G/N\). Then \(a^{−1}N∈G/N\) with \((aN)(a^{−1}N)=aa^{−1}N=N\) and \((a^{−1}N)(aN)=a^{−1}aN=N\).
So \(G/N\) is a group under left coset multiplication. Since \((G:N)\) is, by definition, the cardinality of \(G/N\), we're done.
Definition: Factor Group
When \(G\) is a group and \(N\unlhd G\text{,}\) the above group (\(G/N\) under left coset multiplication) is called a factor group or quotient group .
Example \(\PageIndex{1}\)
Let \(G=\mathbb{Z}\) and \(N=3\mathbb{Z}\text{.}\) Then \(N\) is normal in \(G\text{,}\) since \(G\) is abelian, so the set \(G/N=\{N,1+N,2+N\}\) is a group under left coset multiplication. Noting that \(N=0+N\text{,}\) it is straightforward to see that \(G/N\) (that is, \(\mathbb{Z}/3\mathbb{Z}\)) has the following group table:
| \(+\) | \(0+N\) | \(1+N\) | \(2+N\) |
|---|---|---|---|
| \(0+N\) | \(0+N\) | \(1+N\) | \(2+N\) |
| \(1+N\) | \(1+N\) | \(2+N\) | \(0+N\) |
| \(2+N\) | \(2+N\) | \(0+N\) | \(1+N\) |
Clearly, if we ignore all the \(+N's\) after the \(0\)'s, \(1\)'s, and \(2'\) in the above table, and consider \(+\) to be addition mod 3, rather than left coset addition in \(\mathbb{Z}/3\mathbb{Z}\text{,}\) we obtain the group table for \(\mathbb{Z}_3\text{:}\)
| \(+\) | \(0\) | \(1\) | \(2\) |
|---|---|---|---|
| \(0\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(2\) | \(0\) |
| \(2\) | \(2\) | \(0\) | \(1\) |
Thus, we see that \(\mathbb{Z}/3\mathbb{Z}\) is isomorphic to \(\mathbb{Z}_3\text{.}\)
This is not a coincidence! In fact, we have the following:
Theorem \(\PageIndex{2}\)
Let \(n,d \in \mathbb{Z}^+\) with \(d\) dividing \(n\text{.}\) Then we have:
- \(n\mathbb{Z}\unlhd d\mathbb{Z}\) and \(\langle d\rangle \unlhd \mathbb{Z}_n\text{;}\)
- \(d\mathbb{Z}/n\mathbb{Z}\simeq \mathbb{Z}_{n/d}\) (special case: \(\mathbb{Z}/n\mathbb{Z} \simeq \mathbb{Z}_n\)); and
- \(Z_n/\langle d\rangle \simeq \mathbb{Z}_d\text{.}\)
- Proof
-
- Since dd is a positive divisor of \(n\), \(n\mathbb{Z}\) and \(\langle d \rangle\) are clearly subgroups of, respectively, \(d\mathbb{Z}\) and \(\mathbb{Z}n\). Moreover, since \(d\mathbb{Z}\) and \(\mathbb{Z}n\) are abelian, all of their subgroups are normal.
- This follows from the facts that \(d\mathbb{Z}/n\mathbb{Z}= \langle d+n\mathbb{Z} \rangle\), hence is cyclic, and that \(|d\mathbb{Z}/n\mathbb{Z}|=(d\mathbb{Z}:n\mathbb{Z})=n/d\) (see Example \(7.3.3\)). (Unpacking the statement that \(d\mathbb{Z}/n\mathbb{Z}= \langle d+n\mathbb{Z} \rangle\): Notice that \(d\mathbb{Z}=\langle d \rangle\), so every element of \(d\mathbb{Z}\) is of the form \(kd\) for some integer \(k\). Thus, every element of \(d\mathbb{Z}/n\mathbb{Z}\) is of the form \(kd+n\mathbb{Z}\) for some integer \(k\). But for each \(k∈\mathbb{Z}\), using the definition of left coset multiplication we have that \(kd+n\mathbb{Z}=k(d+n\mathbb{Z})\). So \(d\mathbb{Z}/n\mathbb{Z}= \langle d+n\mathbb{Z} \rangle\).)
- Similarly, since \(\mathbb{Z}_n=\langle 1 \rangle, \mathbb{Z}n/ \langle d \rangle=\langle 1+ \langle d \rangle \rangle\), so is cyclic. Since \((\mathbb{Z}_n: \langle d \rangle)=d\) (again, see Example \(7.3.3\)), \(\mathbb{Z}n/ \langle d \rangle\) is isomorphic to \(\mathbb{Z}d\), as desired.
Q.E.D.
Example \(\PageIndex{2}\)
Let \(N=\langle (123)\rangle \leq S_3\text{.}\) Since \((S_3:N)=2\text{,}\) \(N\) must be normal in \(S_3\text{,}\) so \(S_3/N\) is a group under left coset multiplication. Since \(|S_3/N|=2\text{,}\) \(S_3/N\) must be isomomorphic to \(\mathbb{Z}_2\text{.}\)
In the above examples, we were able to identify \(G/N\) up to isomorphism relatively easily because we could determine that \(G/N\) was cyclic. In general, however, it can be quite difficult to identify the group structure of a factor group. We explore some powerful tools we can use in this identification in the next section, but first we note a couple properties of \(G\) that are “inherited” by any of its factor groups.
Theorem \(\PageIndex{3}\)
Let \(G\) be a group and \(N\unlhd G\text{.}\) Then:
- If \(G\) is finite, then \(G/N\) is finite.
- If \(G\) is abelian, then \(G/N\) is abelian; and
- If \(G\) is cyclic, then \(G/N\) is cyclic.
- Proof
-
- Clearly this holds, since in this case \(|G/N|=|G|/|N|\).
- The proof of this statement is left as an exercise for the reader.
- Let \(G\) be cyclic. Then there exists \(a∈G\) with \(G=\langle a \rangle\). We claim \(G/N=\langle aN \rangle\). Indeed:
\(\langle aN \rangle={(aN)i:i∈\mathbb{Z}}={aiN:i∈\mathbb{Z}}\).
But every element of \(G\) is an integer power of \(a\), so this set equals \(\{xN:x∈G\}\), that is, it equals \(G/N\).
Note
However, \(G\) can be nonabelian [noncyclic, nonfinite] and yet have a normal subgroup \(N\) such that \(G/N\) is abelian [cyclic, finite]. (See the examples below.) Intuitively, the idea is that modding out a group by a normal subgroup can introduce abelianness or cyclicity, or finiteness, but not remove one of those characteristics.
Example \(\PageIndex{3}\)
\(S_3\) is nonabelian (and therefore of course noncyclic), but we saw above that \(N=\langle (123)\rangle\) is a normal subgroup of \(S_3\) with \(S_3/N \simeq \mathbb{Z}_2\text{,}\) a cyclic (and therefore of course abelian) group.
Example \(\PageIndex{4}\)
\(\mathbb{Z}\) is an infinite group, but it has finite factor group \(\mathbb{Z}/2\mathbb{Z}\text{.}\)
What do the (normal) subgroups of a factor group \(G/N\) look like? Well, they come from the (normal) subgroups of \(G\text{!}\) We have the following theorem, whose proof is tedious but straightforward.
Theorem \(\PageIndex{4}\): Correspondence Theorem
Let \(G\) be a group, and let \(K\unlhd G\text{.}\) Then the subgroups of \(G/K\) are exactly those of the form \(H/K\text{,}\) where \(H\leq G\) with \(K\subseteq H\text{.}\) Moreover, the normal subgroups of \(G/K\) are exactly those of the form \(N/K\text{,}\) where \(N\unlhd G\) with \(K\subseteq N\text{.}\)
Example \(\PageIndex{5}\)
Let \(N=18\mathbb{Z}\) in \(\mathbb{Z}\text{.}\)
We end this chapter by noting that given any group \(G\) and factor group \(G/N\) of \(G\text{,}\) there is a homomorphism from \(G\) to \(G/N\) that is onto. Before we define this homomorphism, we provide some more terminology.
Definition: Epimorphism and Monomorphism
Let \(\phi: G\to G'\) be a homomorphism of groups. Then \(\phi\) is can be called an epimorphism if \(\phi\) is onto, and a monomorphism if \(\phi\) is one-to-one. (Of course, we already know that an epimorphism that is also a monomorphism is called an “isomorphism.”)
We now present the following theorem, whose straightforward proof is left to the reader.
Theorem \(\PageIndex{5}\)
Let \(G\) be a group and let \(N\unlhd G\text{.}\) Then the map \(\Psi: G\to G/N\) defined by \(\Psi(g)=gN\) is an epimorphism.
Definition: Canonical Epimorphism
We call this map \(\Psi\) the canonical epimorphism from \(G\) to \(G/N\).
Notice that given \(N\unlhd G\text{,}\) the kernel of the canonical epimorphism from \(G\) to \(G/N\) is \(N\text{.}\) Thus, putting this fact together with the fact that every kernel of a homomorphism is a normal subgroup of the homomorphism's domain, we have the following:
Theorem \(\PageIndex{6}\)
Let \(G\) be a group and \(N\) a subset of \(G\text{.}\) Then \(N\) is a normal subgroup of \(G\) if and only if \(N\) is the kernel of a homomorphism from \(G\) to some group \(G'\text{.}\)


3.8: We're Engaged! Aren't We?
When you create business profiles on social media, you may aim to increase the number of followers through content marketing. Increasing your follower base is certainly important for your brand, but you should also focus on increasing engagement for long-term benefits.
Social media engagement refers to likes, comments, and shares on posts by other social media users. Snot all of your followers are active and many of them may forget about you after liking your page on Facebook or following you on Instagram. In this sense, engagement is far more impactful since it indicates that your followers not only see your posts, but also interact with you one way or another.
The phrase out of sight, out of mind is certainly true and is applicable in the scenario of business marketing. With the internet making it easier to reach a global audience and promote and sell products without hassles, more and more businesses are entering the market and leading to increased competition.  But it won’t take long for them to switch to your competitor brands if you ghost them and your content stops reaching their social media timeline.
If they often interact with your brand, the social media algorithm would show them your content on priority and ensure that they remember you. Therefore, not only should you create engaging content, but also monitor the engagement rate.
There are many different tools available that can help you keep track of customer engagement on social media including Twitter Counter, Buzzlogix, Zoho Social, and Agorapulse that can help you monitor the engagement rate as well as brand reputation across social platforms.
What If They Don’t Talk Back?
Customer engagement is a key concern for brands. The more customers interact with social media posts, the more impact your business makes in the market. This is a good sign because engagement is the driving force of ROI and makes the business profitable down the road.
However, even though business marketers try their best to attract the target audience and encourage them to like or comment on their posts, they are not always able to achieve this goal. This situation is troublesome and can make you wonder why your entire efforts are going in vain.
To get the answer, you should first analyze your current social media strategy. It’s possible that your content is of low-quality or doesn’t interest your audience. It’s also a possibility that your choice of social website isn’t right. With this detailed analysis, you may find out potential issues with your strategy and revise it to address those issues.
However, it should also be noted that defective strategy isn’t always the cause of low engagement. You may need to develop more interesting content to capture the attention. It may be a good idea to hold live Q&A sessions.
Customers are no longer interested in listening to faceless brands. They rather find the human side of brands more attractive and engage with them on social media. By introducing them to your team and interacting with them via live sessions, you can win their trust and increase engagement.
Customer-generated content can also help you in this regard. You shouldn’t only create and share your own content, but also retweet, or like, or share relevant posts by followers. For instance, if you find an interesting post of your followers discussing the niche or topic related to your business, you should consider sharing it with your follower base.
Influencer marketing can also be a good option. You can get in touch with social media influencers who have built a community of followers and ask them to promote your brand. When they endorse your business, their followers will visit your social profile and may engage with the content if they find it interesting.
Should I Still Use Email?
Some people claim that email is a feature of the past and has lost its importance over time. However, digital marketers are well-aware this statement is far from the truth. Despite the popularity of other online marketing methods, email promotions are still extremely effective.
Most consumers check their emails on a daily basis which is why there is no better way for marketers to share information about their market offerings and latest product launches. You can send newsletters to customers and leads and invite them to read the latest blog posts, visit your social media, and learn about what’s new.
Email is relevant in the era of social media because it is a helpful tool for increasing website traffic and generating or capturing qualified leads. You can also curate content and send customized information to customer groups as per their interests. This targeted information can help in building strong relationships and entice customers to interact with you.
Once they are directed to your website to get more information, there is a good chance they will go through the list of products you sell and purchase them soon.
What If They’re Upset
Businesses that value their customers work extra hard to provide them an unprecedented and memorable experience. However, they may not be able to achieve this goal every time. Despite your best efforts, some customers may still be unhappy and dissatisfied.
Unhappy customers often post negative reviews about brands on social media pages or Facebook groups. If you notice such a review, you should get ready to resolve the situation instead of losing your cool.
You should calmly listen to customers and apologize for the mistake. If it was a genuine problem, then you should empathize and assure them that the management would look into the matter and resolve the problem at the earliest. You can also send them a gift or discount voucher to make up for their bad experience.
Some customers may accept your apology and let it go, but some customers get too angry and they don’t listen to social media managers. They may continue posting negative reviews about your business and hurt your brand reputation.
In this scenario, the best strategy is to use tracking tools like Mention that keep you updated about discussions and reviews about your business. With this real-time information, you can tackle the situation and spread positive messages about your brand to prevent them from further hurting your business.
Don’t Feed the Trolls
Some angry customers post negative reviews because they genuinely faced a bad experience with your company. But remember that some social media users deliberately post provocative content against other users and businesses out of habit.
They poke fun at others and humiliate them with derogatory content. Interacting with such trolls and responding to their comments can further ignite the situation. So, you need to tactfully handle the situation.
First of all, write terms and policies for your community where followers are expected to be respectful of others and refrain from using offensive language. You can politely ask trolls to be mindful in the light of community policies. You can respond to fake posts regarding your business with facts or ignore them. You can also come up with witty responses to diffuse the situation.
However, social media trolls don’t go away easily and they may keep trying to instigate you. Don’t get into the trap and stay calm and respectful to protect your brand image.
Do the Hokey Pokey: Turn Complaints into Gold
Brands that often receive negative comments and reviews tend to lose customers and damage the reputation. But customer complaints and negative comments aren’t as bad as they are perceived.
These posts give you a chance to identify and recognize your mistakes. Your business processes or products may be harmful in some manner or fail to meet the needs of customers. Instead of treating these comments as trash and ignoring them, you should treat them as feedback and make the most of this constructive feedback to enhance service quality.
If a customer points out that the behavior of the staff wasn’t good, you should pay attention to them. Offering excuses won’t do good as it gives the impression that you don’t consider customer complaints important. You can rather arrange training sessions for team members to help them boost their skillset and improve service quality.
You should encourage customers and social media followers to offer suggestions for further improving your business processes. Also, once you implement a customer suggestion, you should post it on social media and appreciate customer feedback.
Do You Even Care?
Customer service is a challenging job. You need to listen to customer complaints and suggestions, and bear their anger while taking the blame for intentional or unintentional mistakes.
No matter what type of business you manage, effective customer service is the key to success. You should always prioritize customers and work hard to add value to them. Similarly, listening to and addressing customer issues is equally important for a business.
Customers are now aware of their rights and they don’t want to do anything with businesses that ignore them. To become an effective business leader or social media marketer, you ought to care about your customers. You don’t want to receive negative reviews due to the negligence of your team. You should develop a culture within the organization where staff members consider it their first and foremost responsibility to take care of customers and leave no stone unturned in achieving customer satisfaction.
This approach strengthens relationships with customers and creates a lasting bond.


20.5: Substituent Effects on Acidity
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Objectives
After completing this section, you should be able to
- list a given series of carboxylic acids in order of increasing or decreasing acidity.
- explain the difference in acidity between two or more given carboxylic acids.
- arrange a series of substituted benzoic acids in order of increasing or decreasing acidity.
- determine whether a given substituted benzoic acid will be more or less acidic than benzoic acid.
- decide which of two or more substituted benzoic acids is the most acidic, and explain your decision on the basis of the electron‑withdrawing or electron‑releasing ability of the substituent.
- use the K a (or p K a ) of a substituted benzoic acid to predict the effect that the substituent has on the susceptibility of the benzene ring to electrophilic attack.
Study Notes
You have already seen how the presence of an electron‑withdrawing or electron‑releasing group affects the stability of a positively charged carbocation. Now you see how these groups affect the stability of carboxylate anions, and in turn, determine the dissociation constant of a carboxylic acid.
The Inductive Effect
As seen in Section 20.2 , there can be substantial range in the acidities of carboxylic acids. From the table in Section 20.2 , we see that trifluoroacetic acid (K a = 0.59) is almost than 60,000 times more acidic than butanoic acid (K a = 1.51 X 10 -5 ). These vast differences in acidity can be almost exclusively explained by the inductive effect of substituents attached to the carboxylic acids.
The inductive effect is an experimentally observed effect of the transmission of charge through a chain of atoms in a molecule, resulting in a permanent dipole in a bond. In a carboxylic acid group the presence of halogens (such as fluorine) on adjacent carbons increases the acidity of the carboxylic acid group by stabilizing the carboxylate conjugate base.
Withdrawing Inductive Effects
A fluorine atom is more electronegative than a hydrogen atom, and thus it is able to ‘induce’, or ‘pull’ the electron density of covalent bonds towards itself. In the fluoroacetate anion, the electrons in the C-F covalent bond are pulled toward the fluorine giving the carbon a partial positive charge. The positively charged carbon, in turn, draws electron density away from the carboxylate anion, dispersing the charge, and creating a stabilizing effect. Stabilizing the carboxylate anion increases the acidity of the corresponding carboxylic acid. In this context, the fluorine substituent is acting as an electron-withdrawing group .
Fluoroacetate anion stabilized by electron withdrawing inductive effect of fluorine
A similar effect is seen when other electron-withdrawing groups are attached to -CH 2 CO 2 H. As the power of the electron-withdrawing group becomes stronger there is a corresponding drop in the pK a of the carboxylic acid.
The presence of multiple electron-withdrawing groups compounds the inductive effect and continues to increase the acidity of the carboxylic acid. Dichloroacetic is a stronger acid than chloroacetic acid, and trichloroacetic acid is even stronger.
The inductive effects of chlorine be clearly seen when looking at the electrostatic potential maps of acetic acid (Left) and trichloroacetic acid (Right). The O-H bond in trichloroacetic acid is highly polarized, as shown by the dark blue color making it a much stronger acid than acetic acid.
Because inductive effects are not transmitted effectively through covalent bonds, the acid-strengthening effect falls off rapidly as the number of sigma bonds between the carboxylic acid and the electron-withdrawing group increases. A distance of three sigma bonds almost completely eliminates chlorine's inductive effect in 4-chlorobutanoic acid, giving it a similar pK a value to unsubstituted butanoic acid.
Donating Inductive Effects
Alkyl groups (hydrocarbons) are inductively electron-donating. In this case, the inductive effects pushes electron density onto the carboxylate anion, producing a destabilizing effect, decreasing the acidity of the carboxylic acid.
Lengthening the alkyl chain of a carboxylic acid can increase this inductive effect but it no longer decreases the acidity further after the chain is about three carbons long.
The Acidity of Substituted Benzoic Acids
Extensive research has been performed on the acidity of substituted benzoic acids. Benzoic acid itself is a somewhat stronger acid than acetic acid. The carboxyl group of benzoic acid is attached to an sp 2 -hybridized carbon which is more electronegative and electron-withdrawing than the sp 3 -hybridized carbon attached to the carboxyl group of acetic acid. In Section 2.9 it was discussed that carbon becomes more electron-withdrawing as the s character of its hybrid orbitals increases. The same effect is seen in acrylic acid which is also more acidic than acetic acid.
In Section 16.4 it was discussed that substituents had a marked effect on the electron density of an aromatic ring and on the rate of electrophilic aromatic substitutions. Electron-donating substituents increase the electron density of the aromatic ring, activating it, and increasing the rate of electrophilic substitutions. Electron-withdrawing groups decreased electron density, deactivating the aromatic ring, and reduced the rate of electrophilic substitution.
In a similar fashion, substituents have an effect on the acidity of benzoic acids. Benzoic acids with deactivating substituents, such a nitro group (-NO 2 ), in the meta or para position tend to be more acidic. The deactivating substituents remove electron density, stabilizes the negative charge of the carboxylate anion, and increasing the acidity of the carboxylic acid.
The opposite effect occurs with electron donating substituents. Electron-donating substituents in the meta or para position destabilize the carboxylate anion making the benzoic acid less acidic.
A closer look at the effects of electron-withdrawing and electron-donating substituents in the meta or para position can be seen in the pK a values of various benzoic acids as shown in the table below. Notice the trend in the following table where electron donating substituents (X) at the meta or para positions lead to weaker acids while those having more electron withdrawing substituents generate stronger acids.
| X | pK a - Para | pK a - Meta | Substituent Type | |
|---|---|---|---|---|
| —NH 2 | 4.8 | 4.7 | Donating | |
| —OH | 4.6 | 4.1 | Donating | |
| —OCH 3 | 4.50 | 4.1 | Donating | |
| —CH 3 | 4.4 | 4.3 | Donating | |
| —H | 4.20 | 4.20 | ||
| —Cl | 4.00 | 3.8 | Withdrawing | |
| —Br | 4.0 | 3.8 | Withdrawing | |
| —NO 2 | 3.4 | 3.5 | Withdrawing |
| X | pK a - Ortho | Substituent Type | |
|---|---|---|---|
| —NH 2 | 4.7 | Donating | |
| —H | 4.20 | ||
| —OCH 3 | 4.1 | Donating | |
| —CH 3 | 3.9 | Donating | |
| —OH | 3.0 | Donating | |
| —Cl | 2.9 | Withdrawing | |
| —Br | 2.9 | Withdrawing | |
| —NO 2 | 2.2 | Withdrawing |
Example
The following molecule, p -cyanobenzoic acid, has a pK a of 3.55. Does the cyano substituent activate or deactivate the aromatic ring towards electrophilic aromatic substitution?
The pK a of benzoic acid is 4.2 which means it is a weaker acid than p -cyanobenzoic acid. This this means that the cyano substituent is deactivating the ring.
Example
1. Draw the bond-line structures and arrange the following compounds in order of increasing acidity: 4-nitrobenzoic acid; 4-aminobenzoic acid; 4-chlorobenzoic acid; and benzoic acid. Try to use the expected inductive effects of the substituents to determine the acidity rather than looking at the pK a table.
- Answer
-
1.
Exercises
1) For the following pairs, which is expected to be the stronger acid? Explain your answer.
d) acrylic aid vs. propiolic acid (image)
2) Oxalic acid is a dicarboxylic acid with two acidic protons. The first proton is much more acidic (pK a = 1.20) than a typical carboxylic acid. However, Heptanedioic acid's first acidic proton has a pK a much closer to that of a typical carboxylic acid. Explain these differences.
(image)
3) The carboxylic acid of 4-formylbenzoic acid has a pK a of 3.75. Is this molecule likely to be more reactive or less reactive than benzene toward electrophilic aromatic substitution?
Solutions
1)
a) Consider the inductive effects of the substituents attached to the carboxylic acid. The tert - butyl group is electron-donating which should decrease the acidity of the carboxylic acid . The trimethylammonium substituent is positively charged and can be a powerful electron-withdrawing sub stituent . This should increase the acidity of the carboxylic acid. The compound ( CH 3 ) 3 N CH 2 CO 2 H is expected to be a stronger acid than ( CH 3 ) 3 CCH 2 CO 2 H . The acidity constants for these two compounds match the predictions.
(image)
b) Having an electron-withdrawing hydroxyl group at the C-2 stabilizes the carboxylate ion of lactic acid through inductive effects.
(image)
This should make lactic acid more acidic than propanoic acid.
c) Due to the presence of a highly electronegative oxygen, the carbonyl group is expected to be more strongly electron-withdrawing than a carbon–carbon double bond. Thus, pyruvic acid should be a stronger acid than acrylic acid.
(image pyruvic and acrylic acid)
d) The main difference between the two compounds is the hybridization of the carbon attached to the carboxylic acid. The alkyne substituent has an sp hybridized carbon which should make it more electron-withdrawing than the alkene's sp 2 hybridized carbon.
2) With oxalic acid one carboxyl group acts as an inductive electron-withdrawing group which increases the acidity of the other carboxylic acid. This inductive effect is only relevant with the two carboxyl groups are separated by only a few bonds. In heptanedioic acid, the carboxyl groups are separated by five carbon which effectively negates the inductive effect .
3) Benzoic acid (pK a = 4.2) has a higher pK a and is more acidic than 4-formylbenzoic acid (pK a = 3.75). This means that the formyl group is removing electrons from the aromatic ring making it deactivated toward electrophilic aromatic substitution.


3.1: Ethics
-
- Last updated
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Skills to Develop
- Discuss how research involving human subjects is regulated
- Summarize the processes of informed consent and debriefing
Today, scientists agree that good research is ethical in nature and is guided by a basic respect for human dignity and safety. However, as you will read in the feature box, this has not always been the case. Modern researchers must demonstrate that the research they perform is ethically sound. This section presents how ethical considerations affect the design and implementation of research conducted today.
Research Involving Human Participants
Any experiment involving the participation of human subjects is governed by extensive, strict guidelines designed to ensure that the experiment does not result in harm. Any research institution that receives federal support for research involving human participants must have access to an institutional review board (IRB) . The IRB is a committee of individuals often made up of members of the institution’s administration, scientists, and community members. The purpose of the IRB is to review proposals for research that involves human participants. The IRB reviews these proposals with the principles mentioned above in mind, and generally, approval from the IRB is required in order for the experiment to proceed.
Figure \(\PageIndex{1}\): An institution’s IRB meets regularly to review experimental proposals that involve human participants. (credit: modification of work by Lowndes Area Knowledge Exchange (LAKE)/Flickr)
An institution’s IRB requires several components in any experiment it approves. For one, each participant must sign an informed consent form before they can participate in the experiment. An informed consent form provides a written description of what participants can expect during the experiment, including potential risks and implications of the research. It also lets participants know that their involvement is completely voluntary and can be discontinued without penalty at any time. Furthermore, the informed consent guarantees that any data collected in the experiment will remain completely confidential. In cases where research participants are under the age of \(18\), the parents or legal guardians are required to sign the informed consent form.
While the informed consent form should be as honest as possible in describing exactly what participants will be doing, sometimes deception is necessary to prevent participants’ knowledge of the exact research question from affecting the results of the study. Deception involves purposely misleading experiment participants in order to maintain the integrity of the experiment, but not to the point where the deception could be considered harmful. For example, if we are interested in how our opinion of someone is affected by their attire, we might use deception in describing the experiment to prevent that knowledge from affecting participants’ responses. In cases where deception is involved, participants must receive a full debriefing upon conclusion of the study—complete, honest information about the purpose of the experiment, how the data collected will be used, the reasons why deception was necessary, and information about how to obtain additional information about the study.
DIG DEEPER: Ethics and the Tuskegee Syphilis Study
Unfortunately, the ethical guidelines that exist for research today were not always applied in the past. In 1932, poor, rural, black, male sharecroppers from Tuskegee, Alabama, were recruited to participate in an experiment conducted by the U.S. Public Health Service, with the aim of studying syphilis in black men. In exchange for free medical care, meals, and burial insurance, \(600\) men agreed to participate in the study. A little more than half of the men tested positive for syphilis, and they served as the experimental group (given that the researchers could not randomly assign participants to groups, this represents a quasi-experiment). The remaining syphilis-free individuals served as the control group. However, those individuals that tested positive for syphilis were never informed that they had the disease.
While there was no treatment for syphilis when the study began, by 1947 penicillin was recognized as an effective treatment for the disease. Despite this, no penicillin was administered to the participants in this study, and the participants were not allowed to seek treatment at any other facilities if they continued in the study. Over the course of \(40\) years, many of the participants unknowingly spread syphilis to their wives (and subsequently their children born from their wives) and eventually died because they never received treatment for the disease. This study was discontinued in 1972 when the experiment was discovered by the national press (Tuskegee University, n.d.). The resulting outrage over the experiment led directly to the National Research Act of 1974 and the strict ethical guidelines for research on humans described in this chapter. Why is this study unethical? How were the men who participated and their families harmed as a function of this research?
Figure \(\PageIndex{2}\): A participant in the Tuskegee Syphilis Study receives an injection.
For more information on this and other studies that contributed to our current thoughts on ethics in research, watch this video:
Summary
Ethics in research is an evolving field, and some practices that were accepted or tolerated in the past would be considered unethical today. Researchers are expected to adhere to basic ethical guidelines when conducting experiments that involve human participants. Any experiment involving human participants must be approved by an IRB. Participation in experiments is voluntary and requires informed consent of the participants. If any deception is involved in the experiment, each participant must be fully debriefed upon the conclusion of the study.
Glossary
- debriefing
- when an experiment involved deception, participants are told complete and truthful information about the experiment at its conclusion
- deception
- purposely misleading experiment participants in order to maintain the integrity of the experiment
- informed consent
- process of informing a research participant about what to expect during an experiment, any risks involved, and the implications of the research, and then obtaining the person’s consent to participate
- Institutional Review Board ( IRB )
- committee of administrators, scientists, and community members that reviews proposals for research involving human participants
Contributors
-
Rose M. Spielman with many significant contributors. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the creative commons license and may not be reproduced without the prior and express written consent of Rice University. For questions regarding this license, please contact<EMAIL_ADDRESS>.Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


3.5: Module 16 Competency Test No.3 Open Book
16
Module 16 Competency Test No.3 Open Book
Wally Baumback
Learning Outcomes
When you have completed this module, you will be able to:
- Within a two hour time limit, complete a written exam and a lab exercises.
Competency Tests
The Inventor book was written with competency based modules. What that means is that you have not completed each module until you have mastered it. The Competency Test module contains multiple choice questions and a comprehensive lab exercise to test your mastery of the set of modules that you completed. There are no answers or keys supplied in a Competency Test module since it is meant to be checked by your instructor. If there are any parts of this module that you have trouble completing, you should go back and reread the module or modules containing the information that you are having trouble with. If necessary, redo as many lab exercises required until you fully understand the material.
If you are Completing this book:
- Without the aid of an instructor, complete the written test and the lab exercise.
- In a classroom with an instructor, the instructor will give instructions on what to do after you have completed this module.
Multiple Choice Questions
Select the BEST answer.
-
Which on of the following statements is true?
- Construction objects are drawn with the command CONSTRUCTION.
- Construction objects will not be used when the sketch is converted into a 3D feature.
- Construction objects cannot be used to constrain the sketch.
- Construction objects cannot be used as dimensional constraints.
- Construction objects will be used when the sketch is converted into a 3D feature.
-
When is it
best
to place fillets and chamfers on a solid model?
- The last thing you do to complete the solid.
- The first thing after the base sketch it is revolved.
- Before the base model is created.
- When the sketches are being created.
- The first thing after the base sketch is extruded.
-
Which snap mode is used to snap to the location where two object cross?
- On
- Midpoint
- Intersection
- Point
- Center
-
Which one of the following function keys, when pressed, enables the display of the constraint icons?
- F2
- F4
- F6
- F8
- F10
-
What two commands are used to create a solid model?
- REVOLVE AND OFFSET
- EXTRUDE and REVOLVE
- EXTRUDE and FILLET
- PROJECT and SOLID
- EXTRUDE and MODEL
-
Which key or keys, when pressed while you are selecting objects, will allow you to select more then one object in the selection set?
- Only TAB
- Either ALT or SHIFT
- Either CTRL or ALT
- Either TAB or CTRL
- Either CTRL or SHIFT.
-
What does the REVOLVE command do when it finds a centerline in the base sketch it is revolving?
- It automatically uses the centerline as the axis of revolution.
- It prompts you to select the axis of revolution.
- It extrudes the base sketch using it as the centre.
- It ignores the centerline.
- It allows you to select another axis as the axis of revolution.
-
Which snap mode is used when you want to snap to the centre of a line?
- On
- Midpoint
- Intersection
- Point
- Center
-
Which geometrical constraint is used to make 4 circles all the same diameter when only one of them is dimensioned?
- Tangent
- Concentric
- Coincident
- Center
- Equal
-
What one of the following is used to change the properties of a selected object from a drawing object to a construction object?
- Construction menu
- Construction icon
- Construction line
- Construction circle
- Construction object
Lab Exercise 16-1
Time allowed: 60 minutes.
| Part Name | Project | Units | Template | Color | Material |
| Inventor Lab Lab 16-1 | Inventor Course | Inches | English-Modules Part (in).ipt | Chrome – Polished Blue | N/A |
Step 1
Note the location of X0Y0Z0. Draw the necessary sketches and revolve or extrude them to produce the 3D model. (Figure Step 1)
Step 2
Draw the base sketch on the Front view. (Figure Step 2)
Step 3
Apply all of the necessary geometrical and dimensional constraints to fully constrain all sketches. Ensure that all objects, on all sketches, display purple on a black background.
Step 4
Create the fillets and chamfers after the solid model is totally constructed.
Step 5
Apply the colour shown. (Figure Step 5A, 5B, and 5C)
Lab Exercise 16-2
Time allowed: 60 minutes.
| Part Name | Project | Units | Template | Color | Material |
| Inventor Lab Lab 16-2 | Inventor Course | Millimeters | Metric-Modules Part (mm).ipt | Silicon Nitrite – Polished | N/A |
Step 1
Note the location of X0Y0Z0. Draw the base sketch on the Right Side view and revolve it to create the base model. (Figure Step 1A, 1B, 1C, and 1D)
Step 2
Draw the necessary sketches and extrude them to complete the model.
Step 3
Apply all of the necessary geometrical and dimensional constraints to fully constrain all sketches. Ensure that all objects, on all sketches, display purple on a black background.
Step 4
Create the fillets after the solid model is totally constructed.
Step 5
Apply the colour shown. (Figure Step 5A and 5B)


16.4: Other Occurrences of Six-Four Chords
16.4 Other Occurrences of Six-Four Chords
Second-inversion chords with the fifth of the chord in the bass, also known as 46chords, are special chords found only in four situations in classical music.
- Cadential six-four (discussed in the previous section)
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Passing six-four: the bass line will look like a passing-tone figure, with three stepwise ascending or descending notes, and the middle chord will be a 46 chord
-
Pedal six-four: the bassline will consist of three repeated notes, and the middle chord will be a 46 chord.
- Melodic bass six-four: in this situation, the bass voice has the melody; when the fifth of the chord occurs in this bass voice melody, the result will be a 46 chord.


9.5: Coordination Numbers and Structures
Why do coordination complexes form the structures they do?
As with all chemical structure, coordination complexes form the structures they do so as to best stabilize the metal center and ligands through the formation of metal-ligand bonds while avoiding destabilizing interactions like steric repulsions. The issue then is how many metal-ligand bonds should be formed and how those bonds should be arranged spatially to give the largest net stabilization possible. This question will eventually be considered in detail in connection with the nature of bonding in coordination compounds . For now, it will be helpful to think about it in terms of seven factors:
The stabilizing effect of metal-ligand bond formation.
The driving force for complex formation is the stabilization of electrons in covalent chemical bonds. In the vast majority of cases, this largely involves stabilization of the ligand lone pair as it experiences the effective nuclear charge of the metal, although a few instances involve stabilization of metal electrons by ligand nuclei (inverse ligand fields). Regardless, metal-ligand bond formation is stabilizing and classified by the way it preferences the addition of ligands to the complex.
Steric effects, specifically steric repulsions between ligands.
One reason coordination numbers do not increase indefinitely is that only so many ligands can fit around a metal. Exactly how many depends on
- the size of the metal center. This is one of the more important factors. Many metals tend to exhibit preferred coordination numbers, which depend on their oxidation state and size as shown in Figure \(\sf{\PageIndex{1}}\). Larger inner transition metals like the Lanthanides and Actinides can accommodate 9-12 sterically undemanding ligands, while the smaller transition metals tend to accommodate up to six, although larger coordination numbers are more common for low valent metals and as size increases on moving from right to left across the transition metal block of the periodic table. Thus, the early transition metal molybdenum forms seven- and eight-coordinate [Mo III (CN) 7 ] 4- and [Mo IV (CN) 8 ] 4- with the sterically undemanding cyano ligand.
- the size of the ligands. As long as ligands are not excessively rigid and bulky, their size is less important than the size of the metal in determining the number of ligands that coordinate. Ligands' ability to donate electrons to the metal center also tends to influence coordination number more than ligand size. However, all other things being equal for a given metal and ligand donor ability, small ligands allow higher coordination numbers while fewer bulky ligands will fit around the metal center.
- how the ligand bonds to the metal. Again, all other things being equal, ligands that are more sterically demanding in the vicinity of the metal center tend to limit the ability of other ligands to bind more than those which bind through a small extended group. For example, a bulky isocyanide like t-BuCN will sterically crowd the metal less than a bulky phosphine like t-BuH 2 P would. For this reason the effective size of a ligand is sometimes rated in terms of either a cone angle of space they are estimated to occupy around the metal (called the Tolman cone angle, it is commonly used to evaluate phosphines' steric bulk) or in terms of the percentage of the metal's coordination sphere the ligand occupies (called the percent buried volume, it is used to estimate the steric impact of N -heterocyclic carbenes).
Repulsion between M-L bonding electrons on different ligands.
For many complexes, steric effects are neither the only effects nor the most important. Among the additional factors that should be considered are the repulsions that occur between the electrons that different ligands donate to the metal-ligand bonding. These electron-electron repulsions affect the
-
Coordination number.
When a ligand donates its electrons to a metal center to form a new metal-ligand bond, the electron density around the metal increases, raising the overall energy of the other M-L bonding electrons. This increased repulsion often limits the number of coordinated ligands. As more ligands are added, the electron-electron repulsions keep increasing until the lowering of energy of the ligand electrons in the new bond is insufficient to compensate for the raising of energy of the existing M-L bonding electrons. Based on this effect alone,
- larger metals tend to achieve higher coordination numbers than smaller ones because the electron-electron repulsions are spread across a larger coordination sphere.
- With a given metal, ligands that are more electron donating have a greater tendency to form complexes with lower coordination numbers with a given metal than similar neutral ones do. This is why anionic ligands (which tend to be better electron donors) tend to give lower coordination numbers than comparable neutral ligands (which tend to be weaker donors). Thus Co 2 + forms CoCl 4 2 - with chloro ligands but [Co(H 2 O) 6 ] 2+ with aqua ligands.
- Coordination geometry. In the Kepert model for the shapes of coordination complexes, this intraligand repulsion determines the most stable coordination geometry by causing the ligands to move as far apart from one another on the metal's coordination sphere as possible.
Formally, according to the Kepert model
- any of the metal's valence electrons not involved in metal-ligand bonds occupy (n-1) d orbitals and function as core electrons. As core electrons they do not influence the molecular shape.
- electrons involved in bonding to a given ligand constitute an electron group that repels all other electron groups around the metal.
- all other things being equal, the complex will form the geometry that maximizes the intra-electron group repulsions.
Notice the similarities of these postulates to those of VSEPR theory. In predicting coordination geometries in terms of electron-electron repulsions, the Kepert model is just an extension of VSEPR theory to coordination compounds. The difference between VSEPR theory and the Kepert model is that in the Kepert model, only electrons involved in metal-ligand bonds count.
Coordination geometries predicted by the Kepert model for coordination numbers two through nine are given in Figure \(\sf{\PageIndex{2}}\). As may be seen from the geometries listed in Figure \(\sf{\PageIndex{2}}\), these are just equivalent to VSEPR geometries for cases in which the number of electron groups is equal to the coordination number.
The difference between optimal and suboptimal coordination geometries is greater with few ligands, and becomes smaller as ligands become increasingly dispersed across the metal's coordination sphere. In complexes containing five, seven, eight, or higher coordinate metals, there are a number of geometries that are similar in energy to the preferred geometry. These geometries, which should be regarded as accessible, are also listed in Figure \(\sf{\PageIndex{2}}\).
d-electron effects
A few coordination geometries are noticeably absent from the Kepert-preferred and Kepert-accessible geometries in Figure \(\sf{\PageIndex{1}}\). These include the trigonal prismatic geometries formed by compounds like W(CH 3 ) 6 and the very common square planar geometry illustrated by complexes like [PtCl 4 ] 2- and [IrClH(PPh 3 ) 2 ]. One of the reasons the Kepert model fails to predict the existence of such structures is its neglect of directional interactions involving d electrons on the metal center. Metal d electrons exert a profound influence on almost all properties of transition metal complexes, including their structures. The way in which this occurs will be explored at length in the next chapter . For now, it is enough to note that both the ligand-donated electrons surrounding a metal center and the electrons occupying particular d orbitals on that metal are oriented in specific directions relative to one another. Because of this, the strength of the interactions between the ligand and metal d electrons depends on the number of d electrons present, how strongly metal-ligand binding affects their energy, and how the ligands are arranged about the metal center. The impact of these effects, here termed ligand field effects, differs from case to case and can include
- distortions of the complex's geometry. For instance, an ideal octahedral coordination geoemtry might be tetragonally distorted by flattening or elongating it.
- imparting a strong preference for non-Kepert coordination geometries. This is why, for example, 2nd and 3rd row complexes in which the metal has a d 8 electron configuration are almost always square planar.
- stabilizing non-Kepert geometries enough to permit complexes to adopt them in the presence of a rigid or semirigid ligand that prefers to coordinate the metal in that geometry. 3
Because of these effects, square planar and trigonal prismatic geometries are also observed, and the list of coordination geometries given in Figure \(\sf{\PageIndex{2}}\) may be extended to that shown in Figure \(\sf{\PageIndex{3}}\).
Ligand constraints imposed by rigid or semirigid ligands
Rigid or semirigid ligands influence the coordination geometry of metal complexes in two main ways:
- Bulky rigid ligands that crowd the metal center prevent other ligands from binding. Thus such ligands are useful for preparing low-coordinate complexes.
- Rigid and semirigid ligands can impose their preferred coordination geometry on a metal center. This is because these ligands energetically prefer to adopt a particular conformation when they bind a metal center. In doing so they shift the coordination geometry energy landscape toward that preferred geometry. If the shift is large enough relative to the native preference due to ligand repulsion and ligand field effects, the complex will either adopt the ligand-preferred geometry or be distorted in the direction of the ligand-preferred geometry. Examples are given in Figure \(\sf{\PageIndex{4}}\).
The influence of ligands on coordination geometry is important in living systems, in which proteins and nucleic acids can act as rigid or semirigid ligands. The ability of these ligands to distort the coordination geometries of metal atoms in ways that enable them to perform specific functions is so common that the resulting distorted geometries are termed entactic states. A particularly spectacular case of an entactic state involves the blue copper proteins azurin and plastocyanin, the structure of which is given in Figure \(\sf{\PageIndex{5}}\).
As may be seen from the structure in Figure \(\sf{\PageIndex{5}}\), the copper in plastocyanin exibits a distorted tetrahedral coordination geometry. The protein is said to act like a medieval torture device called a rack in stretching the metal into its distorted geometry. This distortion makes it easier for the copper center to undergo facile redox reactions, enabling it to better function as an electron carrier.
Crystal packing effects, in which the energy-lowering packing of molecules and ions in a crystal drives the distortion of a complex's structure away from what it would adopt in the gas phase or solution
This effect is similar to that of ligand constraints except that in this case it arises not from the structure internal to a ligand but out of the forces involves in maximizing the stabilization energy of a crystal. With lower coordination number complexes, packing effects can shift the conformations of flexible ligands but only give rise to very small distortions of the overall coordination geometry. Packing effects can drive a shift in the overall coordination geometry of higher coordination number complexes, for which packing effects are significant relative to the small difference in energy between geometries. Thus while [Mo(CN) 8 ] 4- has a square antiprismatic coordination geometry, in solution it exhibits a dodecahedral coordination geometry in the crystals of many of its salts.
Relativistic effects on orbital energies
The proximity of fast moving electrons to massive nuclei in the heavier transition elements results in relativistic expansion and contraction of orbitals. The net results are that
- heavier elements tend to be smaller than expected. This effect preferences lower coordination numbers.
- the relative energies of orbitals shift. Orbitals which become contracted are lowered in energy while those which are expanded increase in energy, as shown for the case of gold in Figure \(\sf{\PageIndex{6A}}\).
The combination of smaller sizes and altered orbital energies affects coordination preferences. Relativistic effects contribute to the greater tendency of Au I relative to other group 11 metals to form linear two-coordinate complexes. As shown in Figure \(\sf{\PageIndex{6B}}\), the relative closeness in energy of the 6 s and 5 d orbitals of gold makes mixing of these orbitals more favorable, facilitating the ability of gold to form two-coordinate complexes with strong sigma bonds oriented 180/(^{\circ}\) from one another.
What structures do coordination complexes form?
Metal complexes with coordination numbers ranging from one to 16 are known, although values greater than seven are rare for the transition metals. In this section, examples of common coordination geometries will be presented in order of coordination number.
Coordination Number 1.
Condensed phase monocoordinate complexes are unknown for the transition metals, although the post-transition metals Tl and In form monocoordinate complexes with the bulky ligands triazapentadienyl and 2,6-tris(2,4,6-triisopropylphenyl)benzene as shown in Figure \(\sf{\PageIndex{7}}\).
Coordination Number 2.
A coordination number of 2 is rare outside of d 10 complexes of the group 11 metals and mercury , specifically, Cu + , Ag + , Au + , and Hg 2 + . In accordance with the predictions of the Kepert model these give linear complexes.
Among these,
- Cu + more commonly gives tetrahedral complexes but can be coaxed to give linear ones. The most prominent example is [CuCl 2 ] - , which forms when CuCl is treated with concentrated HCl under anerobic conditions.
- Ag + also commonly forms tetrahedral or trigonal planar complexes but can give linear ones. The most prominent example is [Ag(NH 3 ) 2 ] + , which can be formed by treating silver slats with concentrated aqueous or liquid ammonia.
- Au + almost always forms linear complexes, but many of these formally two-coordinate complexes associate as depicted in Figure \(\sf{\PageIndex{8}}\). The ability of Au + to form linear complexes with cyanide is even used to selectively extract metallic gold from low grade ores. The stability of [Au(CN) 2 ] - means that the dissolution of metallic gold in aqueous cyanide is thermodynamically favorable under aerobic conditions.
\[\sf{4~Au~~+~~8~CN^-~~+~~O_2~~+~~2~H_2O~~\longrightarrow~~4~[Au(CN)_2]^-~~+~~4~OH^-} \nonumber \]
- Hg 2 + , like Au + , benefits from relativistic effects and more commonly forms two-coordinate complexes with a linear geometry. Among these is [Hg(CN) 2 ]. However, its preference for linearity is not as rigid as for Au + , and so complexes with a variety of coordination geometries are known.
And by means of honorary mention, the mercury(I) ion, Hg 2 2 + , forms linear complexes of the type L-Hg-Hg-L, although since Hg 2 2 + is often considered as a single unit, these aren't always considered to be two-coordinate complexes.
Two-coordinate complexes may also be formed through the use of bulky ligands that only allow for the binding of two to the metal center. The classic examples are given in Figure \(\sf{\PageIndex{9}}\).
Coordination Number 3
Three-coordinate complexes are similar to two-coordinate ones in that they are rare and, aside from the constraining influence of ligands, usually limited to d 10 metal ions such as Cu + , Ag + , Au + , Hg 2 + , and Pt(0). As expected from the Kepert model, in the absence of constraining ligands, three-coordinate complexes are trigonal planar.
Coordination Number 4
The two common four-coordinate geometries are tetrahedral and square planar.
Tetrahedral complexes are commonly formed by metals possessing either a d 0 or d 10 electron configuration. Monometallic examples of d 0 configurations include TiCl 4 , VO 4 3 - , WS 4 2 - , MnO 4 - , CrO 4 2 - , and OsO 4 , while d 10 examples are [Ni(CO) 4 ], [HgBr 4 ] 2- , [ZnCl 4 ] 2- , and [CdI 4 ] 2- . For other electron configurations, tetrahedral complexes are known but much less common. Examples usually involve good donor ligands and include [FeCl 4 ] - (d 5 ), [CoCl 4 2 - ] (d 6 ), and [NiCl 4 ] 2- (d 7 ).
Second and third row transition metal centers with d 8 electron configurations like Rh + , Ir + , Pd 2 + , Pt 2 + , and Au 3 + almost exclusively exhibit square planar geometries . Beyond this, square planar geometries are often formed by Ni 2 + (d 8 ), Ni 3 + (d 7 ), and Cu 2 + (d 9 ). Examples of square planar complexes include [Cu(acac) 2 ]; [PtCl 4 ] 2- ;Wilkinson's catalyst, [RhCl(PPh 3 ) 3 ]; and Vaska's complex, trans -[Ir(CO)Cl(PPh 3 ) 2 ].
Coordination Number 5
The two common coordination geometries for five-coordinate complexes are trigonal bipyramidal and square pyramidal.
Homoleptic [Ni(CN) 5 ] 3- possesses a square pyramidal structure, although the geometry is more common for macrocyclic complexes like the iron protoporphyrin of deoxymyoglobin shown in figure \(\sf{\PageIndex{4}}\) and for complexes containing oxo and nitrido ligands, examples of which are shown in Figure \(\sf{\PageIndex{12}}\).
In the absence of rigid constraining ligands, the relatively low energy difference between the trigonal bipyramidal and square pyramidal coordination geometries provides a mechanism for interconversion of the axial and equatorial ligands in a trigonal planar complex. For example, pentacarbonyliron(0) exhibits fluxionality involving a square pyramidal intermediate via a Berry pseudorotation mechanism, as shown in Figure \(\sf{\PageIndex{13}}\).
Coordination Number 6
The two common coordination geometries for coordination number 8 are octahedral and trigonal prismatic.
Trigonal prismatic coordination is related to octahedral coordination as shown in Figure \(\sf{\PageIndex{15}}\). As may be seen in Figure \(\sf{\PageIndex{15}}\), an octahedral coordination sphere is just a trigonal antiprism in which all edge lengths are identical. Rotation of one triangular face relative to its opposite until the two are eclipsed gives a trigonal prismatic geometry. In fact, since continuation of this rotation gives another octahedral complex, the trigonal prismatic geometry is an intermediate in isomerization reactions involving octahedral complexes.
In contrast to octahedral coordination geometries, trigonal prismatic coordination (and distorted versions thereof) are rare and occur mostly for d 0 , d 1 , and d 2 configurations. Examples of trigonal prismatic metal centers include the d 2 Mo 4 + centers in MoS 2 , d 1 [Re(S 2 C 2 Ph 2 ) 3 ] - , and d 0 [Ta(CH 3 ) 6 ] - , of which the latter two structures are given in Figure \(\sf{\PageIndex{16}}\). Semirigid ligands like that shown in Figure \(\sf{\PageIndex{4C}}\) may be used to encourage the adoption of a trigonal prismatic geometry, although once the number of d electrons present exceeds two, the preference for octahedral coordination is too great for a trigonal prismatic geometry to occur.
Coordination Number 7
Seven-coordinate complexes are rare outside of the relatively large early transition metals, lanthanides, and actinides. The three common seven-coordinate geometries are pentagonal bipyramidal, monocapped octahedral, and monocapped trigonal prismatic. The latter two are often called capped octahedral and capped trigonal prismatic, with the mono- prefix being understood.
Although intraligand repulsions are smaller in the pentagonal bipyramidal coordination geometry than the capped octahedral and capped trigonal prismatic geometries, the difference is small, and the three structures are often close in energy. As a result the structure observed is often dependent on ligand-based constraints, crystal packing, and solvent effects that preference one geometry over the others.
Heptacyano complexes are often pentagonal bipyramidal. Examples include [Mo(CN) 7 ] 3- , [W(CN) 7 ] 3- , and [Os(CN) 7 ] 3- . Seven-coordinate complexes containing oxo ligands commonly are pentagonal bipyramidal with the oxo ligand(s) in the less sterically hindered axial position. Examples include [NbOF 6 ] 3- and, for the inner transition metals, [UO 2 F 5 ] 3- . Ligands that have been used to promote formation of seven-coordinate species include 15-crown-5 and 2,2':6',2'':6'',2'''-quaterpyridine. Representative complexes are given in Figure \(\sf{\PageIndex{17}}\).
Capped trigonal prismatic geometries are common for complexes of the early transition metals. Examples include [NbF 7 ] 2- ,[TaF 7 ] 2- , and [ZrF 7 ] 3- in (NH 4 ) 3 [ZrF 7 ].
Capped octahedral geometries are found in [MoMe 7 ] - , [WMe 7 ] - , and [WBr 3 (CO) 4 ], which contains three pairs of trans -Br and CO with the final CO capping the octahedron's (CO) 3 face, as shown in Figure \(\sf{\PageIndex{18}}\).
In seven- and higher-coordinate complexes, ligand and crystal packing effects frequently give distorted coordination geometries. These geometries are intermediate between two or more of the idealized seven coordinate geometries, making it difficult to tell exactly which structure they are a distortion of (Figure \(\sf{\PageIndex{19}}\)).
Coordination Number 8
Eight-coordinate complexes are rare and occurs in discrete molecules and ions only for the relatively large early transition metals, lanthanides, and actinides. The three common eight-coordinate geometries are square antiprismatic, dodecahedral, and bicapped trigonal prismatic. In contrast, the cubic coordination geometry is only found in ionic lattices like that of CsCl and in complexes of the inner transition metals such as Na 3 [UF 8 ].
As with other high-coordinate structures, the energy difference between these eightfold coordination geometries is small enough that packing effects can significantly influence the observed structure. For example, octacyanomolybdates commonly adopt a square antiprismatic coordination geometry but depending on the counterions present can give dodecahedral or bicapped trigonal prismatic complexes. Examples are given in Figure \(\sf{\PageIndex{21}}\).
Coordination Number 9
Again, nine-coordinate complexes typically require larger transition metals, lanthanides, and actinides. Coordination geometries are typically either tricapped trigonal prismatic or idiosyncratically determined by the ligands. Simple examples include the aqua complexes [Sc(H 2 O) 9 ] 3+ , [Y(H 2 O) 9 ] 3+ , and [La(H 2 O) 9 ] 3+ , as well as [TcH 9 ] 2- and [ReH 9 ] 2- .
Coordination Numbers 10-16
Coordination numbers higher than nine are extremely rare for compounds that bind in \(\kappa\) fashion (form conventional metal-ligand bonds) 14 and usually involve some combination of large metals, sterically undemanding ligands, and special ligand structures that promote higher coordination. Noteworthy examples include
- Twelve-coordinate [Hf(BH 4 ) 4 ], which illustrates how small multidentate ligands promote higher coordination numbers. As shown in Figure \(\sf{\PageIndex{23}}\), [Hf(BH 4 ) 4 ] has a cubooctahedral structure in which BH 4 - acts as a tridentate ligand, with BH 3 units occupying triangular faces of the cubooctahedron to give a tetrahedron of BH 4 - ligands around the Hf.
- Twelve-coordinate [Ce(NO 3 ) 6 ] 2- , in which the nitrate oxygens define an icosahedral coordination geometry as shown in Figure \(\sf{\PageIndex{24}}\). The nitrates in the structure bind the Ce center in bidentate fashion in an octahedral array.
- Fifteen-coordinate [Th(H 3 BNMe 2 BH 3 ) 4 ], which also uses bridging H-B-H units that occupy little of the coordination sphere. In [Th(H 3 BNMe 2 BH 3 ) 4 ], three of the four H 3 BNMe 2 BH 3 ligands bind in \(\kappa\) 4 fashion and one binds \(\kappa\) 3 , giving the fifteen fold coordination. 16
- Sixteen-coordinate [CoB 16 ] − , which possesses the highest coordination number yet observed. Its structure is given in Figure \(\sf{\PageIndex{25}}\). The coordination geometry is an octahedral antiprism, and the complex should be considered to involve a Co center in the midst of a B 16 - "molecular drum" held together by cluster bonds.
References
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- The structures are rendered from cif data reported in the following publications: (A) square antiprismatic [Mo(CN) 8 ] 3- : Wen-Yan Liu, Hu Zhou, Ai-Hua Yuan, Acta Crystallographica Section E: Structure Reports Online , 2008, 64, m1151, (B) dodecahedral [Mo(CN) 8 ] 4- : B.J.Corden, J.A.Cunningham, R.Eisenberg, Inorganic Chemistry , 1970, 9, 356.
- The structure of ReH 9 2 - is rendered from the structure reported in Abrahams, S.C.; Ginsberg, A.P.; Knox, K. Transition metal-hydrogen compounds. II. The crystal and molecular structure of potassium rhenium hydride, K 2 ReH 9 Inorganic Chemistry , 1964 , 3 , 558-567.
- There are other complexes in which a metal may be said to interact with more than sixteen "ligand atoms", but these are not usually considered to possess a higher coordination number. For example, in some \(\pi\) complexes like \(\eta\) 5 -Cp 4 U, technically there are 20 C atoms fastened to the U, but these complexes are better considered as 12-coordinate than twenty (since each cyclopentadienyl ring is isolobal with a fac -coordinated set of 3 L ligands), while the metal centers in endohedral fullerene species like La@C 60 do not interact with all sixty carbon atoms at once, and so are better thought of as a metal trapped in a spacious sixty-carbon cage.
- Zalkin, A.; Forrester, J.D.; Templeton, D.H. Crystal structure of cerium magnesium nitrate hydrate Journal of Chemical Physics , 1963 , 39 , 2881-2891.
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- Popov, I., Jian, T., Lopez, G., Boldyrev, A. I.; Wang, L-S. Cobalt-centred boron molecular drums with the highest coordination number in the CoB 16 − cluster. Nat Commun 6, 8654 (2015).