5.1.2H: Applied Body Language
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Learning Objectives
- Discuss the importance of body language as a means of social communication and give specific examples of body language
Body language is a form of human non-verbal communication, which consists of body posture, gestures, facial expressions, and eye movements. Humans send and interpret such signals almost entirely subconsciously. It is impossible for social scientists to study body language in any manner that is not applied. Indeed, social scientists are interested in body language precisely because of what it conveys about social interactions and the relationship between nonverbal interlocutors. This dynamic can only be studied in applied contexts.
Research has suggested that between 60 and 70 percent of all meaning is derived from nonverbal behavior, making body language a crucial part of social interaction. Body language may provide clues as to the attitude or state of mind of a person. For example, it may indicate aggression, attentiveness, boredom, relaxed state, pleasure, amusement, and intoxication, among many other clues.
One of the most basic and powerful body language signals is when a person crosses his or her arms across the chest. This can indicate that a person is putting up an unconscious barrier between themselves and others. However, it can also indicate that the person’s arms are cold, which would be clarified by rubbing the arms or huddling. When the overall situation is amicable, it can mean that a person is thinking deeply about what is being discussed, but in a serious or confrontational situation, it can mean that a person is expressing opposition. This is especially so if the person is leaning away from the speaker. A harsh or blank facial expression often indicates outright hostility.
Another obvious example of expressive body language used in everyday life is flirting. Flirting is a playful activity involving verbal communication and also body language to indicate an interest in a deeper romantic or sexual relationship. Flirting usually involves speaking and behaving in a way that suggests a mildly greater level of intimacy than the actual relationship between parties would justify, though within the rules of social etiquette, which generally frown upon a direct expression of sexual interest. Body language may include flicking one’s hair, eye contact, brief touching, open stances, and close proximity between partners. Thus, by watching two individuals, one can tell if they are flirting.
Flirting Instruction : This video is a how-to on how to flirt. Note the significant attention paid to body language.
Key Points
- Research has suggested that between 60 and 70 percent of all meaning is derived from nonverbal behavior.
- One basic body- language signal is when a person crosses his or her arms. When the overall situation is amicable, it can mean that a person is thinking deeply about what is being discussed, but in a serious or confrontational situation, it can mean that a person is expressing opposition.
- Flirting is an example of applied body language. Sexual or romantic interest is primarily communicated through body language, which may include flicking one’s hair, eye contact, brief touching, open stances, and close proximity between partners.
Key Terms
- Flirting : It is a playful activity involving verbal communication and also body language to indicate an interest in a deeper romantic or sexual relationship.
- body language : Nonverbal communication by means of facial expressions, eye behavior, gestures, posture, and the like; often thought to be involuntary.
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13.5: Analysis
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Situla Art and Writing at Iron Age Este: Use, ritual, and display
At Este, material supports for situla art included elaborate bronze belt plaques and lozenge-shaped belts, knife scabbards, large drinking and/or high-handled cups and situlae (Capuis and Chieco Bianchi 1992). Sympotic (i.e. related to the ritual consumption of sophisticated beverages, presumably including alcohol) implements such as situlae and drinking cups were also occasionally inscribed, although never when decorated with situla art, as discussed below. All the artefact types listed above acted as status symbols highly appreciated by the local elites, as their widespread deposition in prominent graves testifies. Moreover, the most luxurious drinking vessels, weaponry and belts were often exotic products, either as directly imported items or local reproductions of foreign models, a characteristic which probably increased their worth. The high symbolic value of these artefacts is further attested by the fact that they were not only used to carry the decoration but were also portrayed among the decorative motifs of situla art, thus constituting part of the situla art ‘language’ itself.
For example, situlae are commonly depicted on Venetic and non-Venetic situla art products as key components of highly ritualised elite activities such as processions and libations ( Arte Situle 1961; Frey 1969). Although soon integrated into Venetic material culture, they were originally vessels of exotic origin with a widespread geographical distribution, from Continental Europe to Central Italy. Their employment at elite banquets highlights the ‘international’ rituality of alcohol consumption, whose role in promoting commensality, hospitality and power dynamics in late prehistory is well-acknowledged (e.g. Dietler 1990; Iaia 2005: 207–219; 2006; for Veneto see Perego 2010; 2012 a ). Not surprisingly, therefore, practices of ritual drinking are often represented on situla art objects, which allow us to glimpse the lost language of the ritualised gestures constituting the ritual banquet.
The diffusion of situlae in Veneto relates to the adoption by the local elites of sophisticated practices of consumption which often featured exotic components and were integrated into a larger spectrum of ritual technologies of status construction and expression. The same must have been true of other practices represented on situla art, and bearing strong elite overtones, such as hunting, weaving, sacrificing animals, playing games and conducting warfare. Notably, many artefacts usually appearing in Veneto in wealthy graves (e.g. axes, weaponry, weaving tools, and arrows) relate closely to these practices. Within the tomb, these items were also often accompanied by bronze banqueting equipment, situla art products and, more rarely and mainly from the late Iron Age, inscribed artefacts. As Riva (2010) argues for Orientalising Etruria, the introduction of new food technologies in the elite context is not only to be related to the creation of new modes of political negotiation via the ritual banquet, but also to the promotion of novel practices of embodiment which altered the construction and perception of the elite individual’s self. As such, the specialised equipment for ritual food preparation and consumption may have acted as a metaphorical extension of the elite person him/herself while signalling group belonging (Perego 2012 a ). In Veneto, for example, the intimate relationship between the situla and the self was reinforced by the occasional adoption of the situla vessel shape for elite funerary urns. This close association of situlae with the elite body was taken even further through the practice of the anthopomorphisation of the urn, which has been identified so far only in the case of wealthy graves. This was achieved by wrapping the situla-urn in a cloth or dress and/or by embellishing- ing it with ornaments and belts employed to re-create the lost integrity of the cremated body. Interestingly, this practice is also well-known from Etruscan and Centro-Italian funerary contexts (e.g. von Eles 2002), and may have been adopted by the Veneto elite alongside the other foreign practices described in this chapter.
The Early Iron Age
One of the earliest Este graves signalling the elaboration by prominent local groups of a shared ritual language in use until the 3rd century is Ricovero tomb 236, a multiple grave of exceptional wealth and ritual complexity dating to the 8th century (Iaia 2006; Chieco Bianchi and Calzavara Capuis 1985: 300–312). The most prestigious urn in the grave was a bronze situla either imported from Continental Europe or produced locally by imitating an exotic vessel shape. While the bones of the deceased have been lost, the weaponry possibly imported from the eastern Alpine region and the pins usually associated with male depositions indicate a male burial. The latter may have been accompanied by a female individual, as suggested by the presence inside the situla of ornaments generally associated with women. The second urn in the grave, a ceramic vessel, yielded rich female ornaments. Apart from weaponry, ornaments and pins, the bronze situla-urn contained a sympotic service for the preparation and distribution of an indeterminate beverage, possibly wine or beer. This sympotic equipment included two different handled containers probably employed to carry the main beverage (e.g. alcohol) and any additional components (e.g. water), while the three strainers might have been used to filter the residuals generally found in ancient fermented beverages. Finally, the high-handled cups were probably used to remove the liquid from the ‘krater’ — the larger vessel in which alcohol was mixed with water. The ‘krater’ was possibly represented in this case by the situla-urn itself. These sympotic implements bear evidence of burning and may have burnt with the dead. The deposition of a sympotic set on the pyre and later in the urn was an extremely rare practice at Este, where banqueting vessels were usually placed unburned in the grave outside the urn. The close connection between the sympotic set from tomb 236 and the dead buried in the bronze situla seems intended to reinforce the vessels’ pertinence to the elite individual(s) buried here, who may have been in charge of the intoxicating beverage’s preparation. The grave assemblage also included an exceptionally sophisticated ceramic drinking and dining set. Part of this service was found in the tomb container and part was placed intentionally broken on the tomb’s covering slab. The ceramic drinking set included numerous high-handled cups possibly used by the deceased’s fellow diners, either in their everyday life or during the funeral (Iaia 2006). The latter may have been allowed to drink, but not to manipulate the precious intoxicant — a prerogative possibly belonging to the person(s) buried in the situla-urn with the bronze set for beverage preparation and consumption. Two other implements interpreted as incense burners seem to recall practices of purification common at the Graeco-Etruscan banquet/symposium: their presence reinforces the idea that the Venetic elite were constructing their social identity in part through the adoption of foreign rituals.
Although pre-dating the spread of both situla art and writing in Veneto, Ricovero tomb 236 proves that the channels of cultural transmission were already established at this stage. The Venetic elites exhibited their openness towards non-local practices of consumption and their ability to adapt diverse cultural influences to their needs. The emphasis granted to the ingestion of sophisticated beverages, presumably alcohol, demonstrates that the ritual techniques of formal drinking later associated with situla art and writing were already a medium adopted to advertise the elites’ status. Significantly, many of the ritual practices adopted in this grave remained in use at Este until the 3 rd century bc, often in tombs containing situla art and inscribed objects, as exemplified by the graves described below.
Benvenuti tombs 122, 124, and 126 were erected near each other between c. 625 and 550 bc. These yielded grave goods bearing some of the most ancient and most sophisticated — in terms of compositional complexity — situla art objects from the Ricovero-Benvenuti cemetery. The exceptional wealth and close proximity of the tombs suggest they belonged to an elite group. The rare and exotic grave goods found within indicate that the tomb owners, or their living kin or associates, might have been able to monopolise the production and / or acquisition of prestigious bronze status symbols (Chieco Bianchi and Calzavara Capuis 2006: 46). The most ancient grave, Benvenuti 122, contained two urns dating to c. 625–600 bc and probably belonging to women (Chieco Bianchi and Calzavara Capuis 2006: 267–276). The most ancient urn consisted of a bronze situla embellished with a complex decoration of dots, studs and stylised birds of Central European inspiration. This vessel was covered by a bronze drinking cup whose Central European geometric ornamentation is accompanied by vegetal and animal motifs in the manner of the earliest Bolognese situla art style. An influence from Etruria and Bologna is also visible in the luxurious ornaments from the urns. In the case of Benvenuti tomb 126, the famous Benvenuti situla was re-used as a container for a small ceramic urn containing the remains of a 1- to 3-year old child (Chieco Bianchi and Calzavara Capuis 2006: 320–331). The urn was adorned with luxurious ornaments and wrapped in a cloth giving the cinerary human-like qualities. The theme of drinking was evoked not only by the situla itself, but also by the scenes of ritual drinking embossed on the vase and described above. The presence of three high-handled cups in the tomb further emphasised this possible reference to alcohol consumption.
The third tomb of the group, Benvenuti 124, dates to c. 550 bc (Chieco Bianchi and Calzavara Capuis 2006: 294–301) and yielded three ceramic urns with the remains of three adults and two children. One of the urns was placed inside a bronze situla, whose lid bore a situla art motif of animals and geometric dots. The grave also yielded a sophisticated bronze drinking set, two bone and bronze distaffs, rich ornaments, a knife from the Adriatic koinè and an axe. A bronze belt plaque and two fibulae were from Lombardy.
As for the earlier Ricovero tomb 236, these graves reveal a clear intersection of diverse cultural influences incorporated into the material culture and lifestyle of the Este elite. Drinking still features as a fundamental means of social promotion and self-expression, while situla art is adopted as a novel status symbol promoting new ways of elite self-representation. In the case of the Benvenuti situla, which featured images of aristocrats involved in socially distinctive activities, the impact of the new technology over the elite individual’s self-perception must have been considerable. In a cultural context in which representations of human beings were possibly rare or absent at this early stage, the Benvenuti situla’s owners, perhaps for the very first time, were able to ideally project themselves and their world on the new medium, like in a mirror.
From the 6 th Century to the Late Iron Age
The production of elaborate situla art motifs on large bronze containers seems to vanish at Este during the 6th century. This has been related to the social changes brought about by the incipient urbanisation, which may have altered the consumption habits of previous situla art commissioners or even wiped out the previous elite groups (Capuis 2001). At Este, this time-span was also characterised by the development of the first local sanctuaries as new loci of public display and political negotiation (Ruta Serafini 2002). It was at that moment that writing presumably appeared in Veneto as a novel technique of status expression, possibly favoured by the new proto-urban elites. The latter, however, also maintained older practices of status construction, including ritual drinking. Significantly, one of the most ancient Venetic inscriptions presently known was inscribed on a bronze cup of Etruscan form, the kantharos from Lozzo near Este (Locatelli and Marinetti 2002). Kantharoi were widely employed at the Etruscan elite banquet and exported. The Lozzo cup dates between c. 625–575 bc although the inscription may have been added later. The area of discovery was occupied in Roman times by a sanctuary. The Venetic inscription is probably votive in nature, suggesting that a cult was already established at Lozzo during the Iron Age. The kantharos must have been a valuable item in many respects. Apart from the exceptional value attributed by the Este elite to bronze containers, its exoticism due to its Etruscan shape and its reference to privileged drinking practices relate it to prominent individuals. The emphasis granted to the donors through the inscription of their personal names on the vessel testifies of new forms of expressing the elite individuals’ self and social role in a novel context of display — the sanctuary — via the novel technology of writing.
The Lozzo kantharos embodied a close relationship between three of the main aspects of the elite ‘language’ which I have sketched out so far, namely writing, drinking and the acquisition of exotica. A similar relationship between drinking, the adoption of foreign rituals and, in this case, situla art is evidenced by a belt plaque from Este Carceri tomb 48 (500–450 bc). This belt plaque features a single situla art scene which appears to reproduce the reclined symposium of Graeco- Etruscan inspiration (Capuis and Chieco Bianchi 1992: 95): a woman wrapped in a veil is represented about to serve a man reclining on a couch. The ideology of the reclined symposium may have spread into Veneto from the 6th–5th century bc alongside the importation of Greek drinking vessel shapes and possibly wine. It is unclear, however, when and to what extent the Venetic elites came to imitate the complex ritual practices of the reclined Graeco-Etruscan symposium. This uncertainty is compounded by the extreme selectivity exhibited by the inhabitants of Veneto in the choice of imported vessel types, as they adopted only a restricted number of the whole range of sympotic vessels available in Greece and Etruria. The widespread deposition of local ware even within the wealthiest Venetic graves further suggests the persistence of localised modes of consumption. The ambivalent reaction of Venetic elites towards the new sympotic practice is revealed by the Carceri plaque itself, where the woman holds a jug clearly resembling an Etruscan schna-belkanne . This beaked jug shape — albeit widely attested in regions such as Etruria, Lombardy and Continental Europe — was extremely rare in Veneto. Jugs of any type remained uncommon here until the 3rd century. Their rarity, set against the still widespread use of high-handled cups to serve beverages, further suggests the persistence of traditional drinking practices. It is significant, therefore, that in the case of the Carceri belt plaque a new and possibly uncommon ritual practice — the reclined symposium featuring the employment of a rare vessel shape, the schnabelkanne — was related to a medium, situla art, whose distinctive social value has been already emphasised. These associations reinforce the special nature of both the practice and the medium and emphasise the sophistication of these privileged modes of self-expression.
It is also worth emphasising again the exceptional value attributed in Veneto to elaborate bronze belts and belt plaques, as both status symbols and ceremonial artefacts. Due to their social value and proximity to the body, belts probably constituted important vehicles for communicating an individual’s elevated status, as testified by both their deposition in wealthy graves and their display in sanctuaries as prestigious miniature offerings or depictions on laminas (Capuis and Chieco Bianchi 1992: 84, 97). The importance of belts and belt-elements in the funerary context is emphasised by the wide range of ritual manipulations undergone by these artefacts, including deliberate fragmentation, burning, and deposition around the urn to promote the latter’s identification with the elite body. Este Nazari tomb 161 (400–350 bc) provides an example of this kind of ritual (Tirelli 1981). In this wealthy grave, two bronze situlae contained a ceramic urn each. The largest situla was wrapped in cloth. A lozenge-shaped belt decorated with situla art motifs was fastened around this vessel, apparently to give human-like qualities to the urn-container. This deposition emphasises again the symbolic link elaborated over the centuries between situla art itself, sophis- ticated practices of ‘humanisation’ of the urn and the employment of situlae as urns in elite graves. The grave also yielded a rich service for drinking and for food preparation, including meat roast- ing. This emphasis on the preparation of solid foodstuff via the deposition of roasting spits, fire- dogs, knives and slices is characteristic of wealthy graves from the 4th century and suggests the spread of new elite habits of display and consumption. Not surprisingly, the interment of these implements was often accompanied by the deposition of situla art objects and inscribed vessels (e.g. Capuis and Chieco Bianchi 1992: 86–87).
Evidence enabling the clearest synthesis of the ritual practices described above is offered by finds unearthed in Ricovero tomb 23/1984, 300–250 bc (Chieco Bianchi 1987). This grave of exceptional wealth displays both an intentional ritual conservatism going back to the 8th century and an extraordinary openness towards contemporaneous cultural influences especially from Etruria and the international port-of-trade of Adria, located on the Adriatic Sea slightly south of the main Venetic area. The urn found in the grave was a skyphos containing the remains of an unsexed individual. The skyphos was placed within a bronze situla incised with the name of the deceased, a woman called Nerka Trostiaia. The situla was also wrapped in cloth embellished with rich ornaments probably pinned or sewn on it, again intended to evoke the human body. The importance of alcohol consumption was also emphasised via the deposition of an extremely rich banqueting set at the bottom of the grave, which included several imported items. An Attic red-figure krater was found broken on the tomb’s covering slab, possibly indicating the continuation of a ritual practice that is already attested 500 years earlier in Ricovero tomb 236. Importantly, this grave featured the latest example of situla art presently known at Este, the bronze model of a piece of furniture decorated with animal images.
Mutually Exclusive Spheres?
It is noteworthy that in Veneto, despite the adoption of writing and situla art within the same social milieu and often in connection with exotica, foreign ritual practices and sympotic rituals, inscriptions have never been found to date on objects bearing situla art. This is true for the vast majority of the entire situla art corpus presently known, with only a couple of exceptions (Zaghetto 2007: 180). An obvious explanation for this pattern is that situla art and writing were different communicative systems. The former was a non-linguistic symbol-based system spread over a vast area inhabited by different ethnic groups and possibly developed to facilitate interaction between people unable to speak the same language. The latter was the written form of languages (e.g. Venetic) presumably spoken in the more restricted area where the related inscriptions have emerged. This important observation, however, does not explain why the receivers/owners of situla art items, who may have been exposed to, or even taken control of, writing as well, decided not to inscribe their possessions (or have them inscribed), for example in gift- exchange with people speaking the same language or at the funeral, by putting the deceased’s name on a decorated situla-urn. For the Veneto, this ‘otherness’ between the two ‘languages’ seems compounded by the fact that the interment of both written items and situla art objects in the same grave seems to have been uncommon, with some exceptions such as Nerka ’s tomb. As suggested by Whitehouse (pers. comm.), a possible explanation is that few Venetic inhabitants were ‘bilingual’ in the two ‘languages’. It is worth noting, however, that this pattern may partially relate to the limited number of intact wealthy graves dating between the 5 th and 3 rd centuries BC. It is also possible that inscriptions were written on perishable materials now vanished. Another possible explanation for this pattern, however, may reside in the uses to which writing was put after its introduction in Veneto. Although writing may have spread in Veneto as early as the late 7 th or 6 th century bc, at Este the presence of inscriptions inside the grave (i.e. the context in which situla art items are found) is extremely rare before the late 4 th – early 3 rd century bc. One possible exception is a male name inscribed on a bronze tripod or cup buried in a grave dating to the 5 th or 4 th century bc (Marinetti 1992: 138). The practice of inscribing the deceased’s name on urns started in the 3rd century and became more common in the following centuries, especially from c. 75–25 bc. The epitaph inscribed on Nerka ’s situla is one of the earliest examples of this practice. A similar epitaph is incised on a contemporary situla-urn buried in a wealthy multiple grave, namely Benvenuti tomb 123 (Chieco Bianchi and Calzavara Capuis 2006: 276–294). This tomb yielded several items comparable with Nerka ’s grave goods, including lavish ornaments, a bronze model of a loom, three axes and a skyphos . Again, the inscribed situla-urn was possibly wrapped in a cloth. Interestingly, no situla art product comes from this grave, although this may relate to the several re-openings the tomb underwent.
Before 325–300 bc writing was generally adopted in cemetery contexts to mark the gravestones ascribing the ownership of tombs and/or burial plots to prestigious individuals and families. The individuals mentioned on tombstones were 75% male. In the mortuary context, therefore, writing was mainly associated with the male individual and the monumentality, visibility and durability of funerary monuments erected outside the grave. A possible shift in the function and values accorded to writing may have taken place around 300 bc with the spread of ‘hidden’ and more intimate dedications on small, portable items buried in the grave, such as urns and vessels which bore male and female names in a similar proportion. Inscriptions on small objects were not unknown at Este before, but mainly appeared on votive offerings dedicated in sanctuaries, entail- ing different ways of constructing and expressing personal and social identities. This shift towards a ‘hidden’ funerary literacy took place when situla art seems to disappear. The deposition of situla art products and written objects in the same grave was therefore limited to c. 325–250 BC, when the two ‘languages’ were briefly in use in the same context at the same time. Later, the progressive erosion of the previous prominent groups’ social identity in favour of novel forms of display and consumption probably led to the disappearance of situla art — a language which had lost its significance in the new social setting. Before c. 325, I cannot exclude the possibility that writing and situla art were used contemporaneously in the same context outside the grave. However, it seems that, despite their common pertinence to the elite ‘language’ outlined above, their final destination was different, and entailed a diverse conceptualisation of the two media, due to complex social motivations which are not presently identifiable.


1.1.11: Activity Coefficients
In descriptions of the properties of the components of liquid mixtures, rational activity coefficients are given the symbols \(\mathrm{f}_{1}, \mathrm{f}_{2}, \mathrm{f}_{3} \ldots\). With reference to solvents their thermodynamic properties are described by rational activity coefficients \(\mathrm{f}_{1}, \mathrm{f}_{2}, \mathrm{f}_{3} \ldots\) and (practical) osmotic coefficient, \(\phi\). The properties of solutes in solutions are described using activity coefficients which are linked to the descriptions of the composition of solutions: molality scale, \(\gamma_{j}\); concentration scale \(\gamma_{j}\); mole fraction scale \(\mathrm{f}_{\mathrm{j}}^{*}\).
These coefficients are intimately related to the concept of activity . Their significance is clarified by equations relating chemical potentials to the composition of a given system; e.g.
- components in liquid mixtures,
- solvents in solutions and
- solutes in solutions.
In all cases they summarise the extent to which the thermodynamic properties of liquid mixtures and solutions are not ideal. The challenge for chemists is to understand in terms of molecular properties why the thermodynamic properties of real systems are not ideal. It has to be admitted that activity coefficients have a ‘bad press’ as far as most chemists are concerned. All too often their importance is ignored. But ‘learn to love activity coefficients! Perhaps the importance of activity coefficients can be understood in the following terms.
The chemical potential of urea as a solute in aqueous solutions, \(\mu_{j}(\mathrm{aq})\) at temperature \(\mathrm{T}\) and pressure \(p\) ( \(\approx\) the standard pressure \(p^{0}\)) is related to the molality of urea \(\mathrm{m}_{j}\) using equation (a).
\[\begin{aligned}
&\mu_{\mathrm{j}}(\mathrm{aq} ; \mathrm{T}, \mathrm{p})=\\
&\mu_{\mathrm{j}}^{0}\left(\mathrm{aq} ; \mathrm{T}, \mathrm{p}, \mathrm{m}_{\mathrm{j}}=1 \mathrm{~mol} \mathrm{~kg} \mathrm{~kg}^{-1}\right)+\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{m}_{\mathrm{j}} / \mathrm{m}^{0}\right)+\mathrm{R} \, \mathrm{T} \, \ln \left(\gamma_{\mathrm{j}}\right)
\end{aligned} \nonumber \]
The term \(\mu_{\mathrm{j}}^{0}\left(\mathrm{aq} ; \mathrm{T}, \mathrm{p}, \mathrm{m}_{\mathrm{j}}=1 \mathrm{~mol} \mathrm{\textrm {kg } ^ { - 1 } )}\right.\) describes the chemical potential of solute, urea in an aqueous solution having unit molality where there are no urea - urea (i.e. solute – solute) interactions. Each urea molecule in these terms is unaware of the presence of other urea molecules in the aqueous solution. In a solution having ideal thermodynamic properties \(\mu_{j}(\mathrm{aq} ; \mathrm{T}, \mathrm{p} ; \mathrm{id})\) depends on the molality of solute mj. Thus the osmotic pressure of this solution is a function of the molality of urea. For such an ideal solution there are no urea-urea interactions although there are important urea-water interactions, the hydration of urea. But in a real solution there are also solute-solute interactions. Each solute molecule ‘knows’ there are other solute molecules in the solution. Indeed the extent to which \(\mu_{j}(\mathrm{aq} ; \mathrm{T}, \mathrm{p})\) differs from \(\mu_{j}(\mathrm{aq} ; \mathrm{T}, \mathrm{p} ; \mathrm{id})\) is a function of the molality of the solute, \(\mathrm{m}_{j}\).


15.8: Development of Sexual Identity
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Dating and Romantic Relationships
Adolescence is the developmental period during which romantic relationships typically first emerge. By the end of adolescence, most American teens have dated others and have had at least one romantic relationship (Dolgin, 2011). However, culture does play a role as Asian Americans and Latinas are less likely to date than other ethnic groups (Connolly, Craig, Goldberg, & Pepler, 2004). Dating serves many purposes for teens, including having fun, companionship, status, socialization, intimacy, sexual experimentation, and partner selection for those in late adolescence (Dolgin, 2011). There are several stages in the dating process, beginning with engaging in mixed-sex group activities in early adolescence (Dolgin, 2011).
| Age | Relationship |
|---|---|
| Early Adolescence | Romantic relationships often form in the context of these mixed-sex peer groups (Connolly, Furman, & Konarski, 2000). Interacting in mixed-sex groups is easier for teens as they are among a supportive group of friends, can observe others interacting, and are kept safe from becoming intimate too soon. |
| Middle Adolescence | By middle adolescence, teens are engaging in brief, casual dating, or in group dating with other couples (Dolgin, 2011). |
| Late Adolescence | In late adolescence, dating involves exclusive, intense relationships that are short-lived or are long-term committed partnerships, either way their importance should not be minimized. Adolescents spend a great deal of time focused on romantic relationships or lack thereof. Their positive and negative emotions are tied to this intense interest more than they are to friendships, family relationships, or school (Furman & Shaffer, 2003). |
Furthermore, romantic relationships are centrally connected to adolescents’ emerging sexuality. Parents, policymakers, and researchers have devoted a great deal of attention to adolescents’ sexuality, in large part because of concerns related to sexual intercourse, contraception, and preventing teen pregnancies. However, sexuality involves more than this narrow focus, for example, adolescence is often when individuals who are lesbian, gay, bisexual, or transgender come to understand and define what their sexual identity is (Russell, Clarke, & Clary, 2009). Thus, romantic relationships are a domain in which adolescents experiment with new behaviors and identities. 53
Violence by Someone You Know
Violence can be committed against someone that the victim knows well, referred to as an intimate, in many ways: an intimate can hit with their fists, slap with an open hand, throw an object, push or shove, or use or threaten to use a weapon. While we can never be certain of the exact number of intimates that are attacked, the U.S. Department of Justice estimates from its National Crime Victimization Survey that almost 600,000 acts of violence (2008 data) are committed annually by one intimate against another intimate. 55
According to a fact sheet from the National Coalition Against Domestic Violence that compiled the results of several studies:
- In 2013, 35% of 10th graders reported that they had been physically or verbally abused and 31% reported having perpetrated such abuse
- In 2014, 10% of teenage students in dating relationships reported being coerced into sexual intercourse in the previous year
- In 2015, 20.9% of female and 13.4% of male high school students reported being physically or sexually assaulted by a dating partner
- But only 33% of teenage dating abuse victims reported having ever told anyone about it (according to a 2005 study) 56
A 2010 report by the CDC shows the larger pictures of intimate partner violence
- 1 in 3 women and 1 in 4 women have been victims of some form of physical violence by an intimate partner in their lifetime
- 1 in 7 women and 1 in 18 men have been stalked by an intimate partner to the point that they were fearful for their safety 57
This topic is an important one because “domestic violence is prevalent in every community, and affects all people regardless of age, socio-economic status, sexual orientation, gender, race, religion, or nationality. Physical violence is often accompanied by emotionally abusive and controlling behavior as part of a much larger, systematic pattern of dominance and control. Domestic violence can result in physical injury, psychological trauma, and even death.   According to the American Psychological Association (APA) (2016), sexual orientation also refers to a person's sense of identity based on those attractions, related behaviors, and membership in a community of others who share those attractions. Some specific orientation is defined in many ways, including heterosexuality (attraction to the opposite sex/gender), same-sex attraction (previously referred to as homosexuality , which is an outdated term that many people find offensive because it was previously classified as a mental illness), bisexuality , polysexuality , or pansexuality (attraction to two, multiple, or all sexes/genders respectively), and asexuality (no sexual attraction to any sex/gender).
Sexual Orientation on a Continuum
Sexuality researcher Alfred Kinsey was among the first to conceptualize sexuality as a continuum rather than a strict dichotomy of gay or straight. To classify this continuum of heterosexuality and homosexuality, Kinsey et al. (1948) created a seven-point rating scale that ranged from exclusively heterosexual to exclusively homosexual. Research done over several decades has supported this idea that sexual orientation ranges along a continuum, from exclusive attraction to the opposite sex/gender to exclusive attraction to the same sex/gender (Carroll, 2016).
 A closer examination of The Genderbread Person v2.0 introduced earlier in the chapter illustrates this:
Development of Sexual Orientation
According to current scientific understanding, individuals are usually aware of their sexual orientation between middle childhood and early adolescence. However, this is not always the case, and some do not become aware of their sexual orientation until much later in life. It is not necessary to participate in sexual activity to be aware of these emotional, romantic, and physical attractions; people can be celibate and still recognize their sexual orientation. Some researchers argue that sexual orientation is not static and inborn, but is instead fluid and changeable throughout the lifespan.
There is no scientific consensus regarding the exact reasons why an individual holds a particular sexual orientation. Research has examined possible biological, developmental, social, and cultural influences on sexual orientation, but there has been no evidence that links sexual orientation to one factor (APA, 2016). Biological explanations, that include genetics, hormones, and birth order, will be explored further.  One-third of females exposed to abnormal amounts of prenatal androgens, a condition called congenital adrenal hyperplasia (CAH), identify as bisexual or lesbian (Cohen-Bendahan, van de Beek, & Berenbaum, 2005).
Sexual Orientation Discrimination : The United States is heteronormative , meaning that society supports heterosexuality as the norm. Consider, for example, that homosexuals are often asked, "When did you know you were gay?" but heterosexuals are rarely asked, "When did you know you were straight?" (Ryle, 2011). Living in a culture that privileges heterosexuality has a significant impact on the ways in which non-heterosexual people are able to develop and express their sexuality.
Understanding the Acronyms: LGBT, LGBTQ, LGBTQ+
The letters LGBT refer to a group of individuals that identify as Lesbian, Gay, Bisexual, and Transgender. This community includes a diverse group of people from all backgrounds, races, ethnicities, ages, and socioeconomic statuses.
A Little History LGB was used to replace the term, “Gay,” in the mid-1980s, but the acronym LGBT became common in the 1990s. However, recently the term has evolved with the preferred acronym to LGBTQ. The added “Q” means Questioning or Queer. The addition of “Q” as a term of questioning includes people that are in the process of exploring their gender or sexual orientation.
Additionally, the term, “Queer,” can be used as an umbrella term, as the community has accepted this word to represent anything outside of the dominant narrative. Queer is not specific to sexual orientation or gender identity and can be used to refer to the community as a whole. While Queer was used as a derogatory term for decades, it was reclaimed by the LGBTQ community in the 1990s with the rise of an organization called Queer Nation. As an activist group out of New York, Queer Nation opposed discrimination of the LGBTQ community and rejected the heteronormative ideals of society.
What does the plus sign mean? Recently LGBTQ is also used as LGBTQ+. The plus sign, “+” accounts for many additional identifications in the community, including transsexual, two-spirit, intersex, asexual, pansexual, and gender queer. Gender Queer is an umbrella term that can be used for all gender identities not exclusive to masculine or feminine, including gender fluid, agender, bigender, pan gender, gender free, genderless, gender variant, and gender non-conforming. The plus also includes allies or people in support of the LGBTQ community.
While LGBTQ+ or Queer are currently the most common terms, additionally the term, Rainbow Community, may be used. The important takeaway is that the community will continue to evolve, and the terminology will evolve with it. 62
Open identification of one's sexual orientation may be hindered by homophobia , which encompasses a range of negative attitudes and feelings toward homosexuality or people who are identified or perceived as being lesbian, gay, bisexual, or transgender (LGBT). It can be expressed as antipathy, contempt, prejudice, aversion, or hatred; it may be based on irrational fear and is sometimes related to religious beliefs (Carroll, 2016). Homophobia is observable in critical and hostile behavior, such as discrimination and violence on the basis of sexual orientations that are non- heterosexual. Recognized types of homophobia include institutionalized homophobia , such as religious and state-sponsored homophobia, and internalized homophobia in which people with same-sex attractions internalize, or believe, society's negative views and/or hatred of themselves.
 Research has shown that gay, lesbian, and bisexual teenagers are at a higher risk of depression and suicide due to exclusion from social groups, rejection from peers and family, and negative media portrayals of homosexuals (Bauermeister et al., 2010). Discrimination can occur in the workplace, in housing, at schools, and in numerous public settings. Much of this discrimination is based on stereotypes and misinformation.  Sexuality may be experienced and expressed in a variety of ways, including thoughts, fantasies, desires, beliefs, attitudes, values, behaviors, practices, roles, and relationships. These may manifest themselves in biological, physical, emotional, social, or spiritual aspects. The biological and physical aspects of sexuality largely concern the human reproductive functions, including the human sexual-response cycle and the basic biological drive that exists in all species. Emotional aspects of sexuality include bonds between individuals that are expressed through profound feelings or physical manifestations of love, trust, and care. Social aspects deal with the effects of human society on one's sexuality, while spirituality concerns an individual's spiritual connection with others through sexuality. Sexuality also impacts, and is impacted by cultural, political, legal, philosophical, moral, ethical, and religious aspects of life.
 This motivation is determined by biological, psychological, and social factors.  However, sex hormones do not directly regulate the ability to have sexual intercourse or to copulate in primates (including humans); rather, they are only one influence on the motivation to engage in sexual behaviors. Social factors, such as work and family also have an impact, as do internal psychological factors like personality and stress. Sex drive may also be affected by hormones, medical conditions, medications, lifestyle stress, pregnancy, and relationship issues.
 According to Kinsey, Pomeroy, and Martin (1948), the cycle consists of four phases: excitement, plateau, orgasm, and resolution.
| Phase | Description |
|---|---|
| Excitement Phase | the phase in which the intrinsic (inner) motivation to pursue sex arises |
| Plateau Phase | the period of sexual excitement with increased heart rate and circulation that sets the stage for orgasm |
| Orgasm Phase | the climax |
| Resolution Phase | the un-arousal state before the cycle begins again |
Societal Views on Sexuality: Society's views on sexuality are influenced by everything from religion to philosophy, and they have changed throughout history and are continuously evolving. Historically, religion has been the greatest influence on sexual behavior in the United States; however, in more recent years, peers and the media have emerged as two of the strongest influences, particularly among American teens (Potard, Courtois, & Rusch, 2008).
Media Influences on Sexuality: Media in the form of television, magazines, movies, music, online, etc., continues to shape what is deemed appropriate or normal sexuality, targeting everything from body image to products meant to enhance sex appeal.
Cultural Differences with Sexuality: In the West, premarital sex is normative by the late teens, more than a decade before most people enter marriage. In the United States and Canada, and in northern and Eastern Europe, cohabitation is also normative; most people have at least one cohabiting partnership before marriage. In southern Europe, cohabiting is still taboo, but premarital sex is tolerated in emerging adulthood. In contrast, both premarital sex and cohabitation remain rare and forbidden throughout Asia. Even dating is discouraged until the late twenties, when it would be a prelude to a serious relationship leading to marriage. In cross-cultural comparisons, about three fourths of emerging adults in the United States and Europe report having had premarital sexual relations by age 20, versus less than one fifth in Japan and South Korea (Hatfield & Rapson, 2006). 65
Contributors and Attributions
53. Lifespan Development: A Psychological Perspective by Martha Lally and Suzanne Valentine-French is licensed under CC BY-NC-SA 3.0 ; Lifespan Development – Module 7: Adolescence by Lumen Learning is licensed under CC BY 4.0
55. Lifespan Development: A Psychological Perspective by Martha Lally and Suzanne Valentine-French is licensed under CC BY-NC-SA 3.0
Lifespan Development – Module 7: Adolescence by Lumen Learning is licensed under CC BY 4.0
56. Dating Abuse and Teen Violence (n.d.). Retrieved from https://www.speakcdn.com/assets/2497/dating_abuse_and_teen_violence_ncadv.pdf
57. Who is Doing What to Whom? Determining the Core Aggressor in Relationships Where Domestic Violence Exists. (n.d.). Retrieved from https://www.speakcdn.com/assets/2497/who_is_doing_what_to_whom.pdf
59. National Child Traumatic Stress Network. (n.d.). National Domestic Violence Awareness Month . Retrieved from https://www.nctsn.org/resources/public-awareness/national-domestic-violence-awareness-month
62. Understanding the Acronyms: LGBT, LGBTQ, LGBTQ+. (2019). Retrieved from https://www.horizon-health.org/blog/2019/01/understanding-the-acronym-lgbtq/ .
63. Lifespan Development: A Psychological Perspective by Martha Lally and Suzanne Valentine-French is licensed under CC BY-NC-SA 3.0
Boundless Psychology - Gender and Sexuality references Curation and Revision by Boundless Psychology, which is licensed under CC BY-SA 4.0
65. Lifespan Development: A Psychological Perspective by Martha Lally and Suzanne Valentine-French is licensed under CC BY-NC-SA 3.0


8.3: Solve Equations Using the Division and Multiplication Properties of Equality
- Solve equations using the Division and Multiplication Properties of Equality
- Solve equations that need to be simplified
Before you get started, take this readiness quiz.
- Simplify: −7\(\left(\dfrac{1}{−7}\right)\). If you missed this problem, review Example 4.3.10 .
- What is the reciprocal of \(− \dfrac{3}{8}\)? If you missed this problem, review Example 4.4.11 .
- Evaluate 9x + 2 when x = −3. If you missed this problem, review Example 3.8.10 .
Solve Equations Using the Division and Multiplication Properties of Equality
We introduced the Multiplication and Division Properties of Equality in Solve Equations Using Integers; The Division Property of Equality and Solve Equations with Fractions . We modeled how these properties worked using envelopes and counters and then applied them to solving equations (See Solve Equations Using Integers; The Division Property of Equality ). We restate them again here as we prepare to use these properties again.
Division Property of Equality: For all real numbers a, b, c, and c ≠ 0, if a = b, then \(\dfrac{a}{c} = \dfrac{b}{c}\).
Multiplication Property of Equality: For all real numbers a, b, c, if a = b, then ac = bc.
When you divide or multiply both sides of an equation by the same quantity, you still have equality.
Let’s review how these properties of equality can be applied in order to solve equations. Remember, the goal is to ‘undo’ the operation on the variable. In the example below the variable is multiplied by 4, so we will divide both sides by 4 to ‘undo’ the multiplication.
Solve: 4x = −28.
Solution
We use the Division Property of Equality to divide both sides by 4.
| Divide both sides by 4 to undo the multiplication. | $$\dfrac{4x}{\textcolor{red}{4}} = \dfrac{-28}{\textcolor{red}{4}}$$ |
| Simplify. | $$x = -7$$ |
| Check your answer. Let x = −7. | $$\begin{split} 4x &= -28 \\ 4(\textcolor{red}{-7}) &\stackrel{?}{=} -28 \\ -28 &= -28\; \checkmark \end{split}$$ |
Since this is a true statement, x = −7 is a solution to 4x = −28.
Solve: 3y = −48.
- Answer
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y = -16
Solve: 4z = −52.
- Answer
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z = -13
In the previous example, to ‘undo’ multiplication, we divided. How do you think we ‘undo’ division?
Solve: \(\dfrac{a}{−7}\) = −42.
Solution
Here a is divided by −7. We can multiply both sides by −7 to isolate a.
| Multiply both sides by −7. | $$\textcolor{red}{-7} \left(\dfrac{a}{-7}\right) = \textcolor{red}{7} (-42)$$ |
| Simplify. | $$a = 294$$ |
| Check your answer. Let a = 294. | $$\begin{split} \dfrac{a}{-7} &= -42 \\ \dfrac{\textcolor{red}{294}}{-7} &\stackrel{?}{=} -42 \\ -42 &= -42\; \checkmark \end{split}$$ |
Solve: \(\dfrac{b}{−6}\) = −24.
- Answer
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b = 144
Solve: \(\dfrac{c}{−8}\) = −16.
- Answer
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c = 128
Solve: −r = 2.
Solution
Remember −r is equivalent to −1r.
| Rewrite −r as −1r. | $$-1r = 2$$ |
| Divide both sides by −1. | $$\dfrac{-1r}{\textcolor{red}{-1}} = \dfrac{2}{\textcolor{red}{-1}}$$ |
Check.
| Substitute r = −2. | $$-r = 2$$ |
| Simplify. | $$\begin{split} -(\textcolor{red}{-2}) &\stackrel{?}{=} 2 \\ 2 &= 2\; \checkmark \end{split}$$ |
In Solve Equations with Fractions , we saw that there are two other ways to solve −r = 2.
- We could multiply both sides by −1.
- We could take the opposite of both sides.
Solve: −k = 8.
- Answer
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k = -8
Solve: −g = 3.
- Answer
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g = -3
Solve: \(\dfrac{2}{3}\)x = 18.
Solution
Since the product of a number and its reciprocal is 1, our strategy will be to isolate x by multiplying by the reciprocal of \(\dfrac{2}{3}\).
| Multiply by the reciprocal of \(\dfrac{2}{3}\). | $$\textcolor{red}{\dfrac{3}{2}} \cdot \dfrac{2}{3} x = \textcolor{red}{\dfrac{3}{2}} \cdot 18$$ |
| Reciprocals multiply to one. | $$1x = \dfrac{3}{2} \cdot \dfrac{18}{1}$$ |
| Multiply. | $$x = 27$$ |
| Check your answer. Let x = 27. | $$\begin{split} \dfrac{2}{3} x &= 18 \\ \dfrac{2}{3} \cdot \textcolor{red}{27} &\stackrel{?}{=} 18 \\ 18 &= 18\; \checkmark \end{split}$$ |
Notice that we could have divided both sides of the equation \(\dfrac{2}{3}\)x = 18 by \(\dfrac{2}{3}\) to isolate x. While this would work, multiplying by the reciprocal requires fewer steps.
Solve: \(\dfrac{2}{5}\)n = 14.
- Answer
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n = 35
Solve: \(\dfrac{5}{6}\)y = 15.
- Answer
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y = 18
Solve Equations That Need to be Simplified
Many equations start out more complicated than the ones we’ve just solved. First, we need to simplify both sides of the equation as much as possible.
Solve: 8x + 9x − 5x = −3 + 15.
Solution
Start by combining like terms to simplify each side.
| Combine like terms. | $$12x = 12$$ |
| Divide both sides by 12 to isolate x. | $$\dfrac{12x}{\textcolor{red}{12}} = \dfrac{12}{\textcolor{red}{12}}$$ |
| Simplify. | $$x = 1$$ |
| Check your answer. Let x = 1. | $$\begin{split} 8x + 9x - 5x &= -3 + 15 \\ 8 \cdot \textcolor{red}{1} + 9 \cdot \textcolor{red}{1} - 5 \cdot \textcolor{red}{1} &\stackrel{?}{=} -3 + 15 \\ 12 &= 12\; \checkmark \end{split}$$ |
Solve: 7x + 6x − 4x = −8 + 26.
- Answer
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x = 2
Solve: 11n − 3n − 6n = 7 − 17.
- Answer
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n = -5
Solve: 11 − 20 = 17y − 8y − 6y.
Solution
Simplify each side by combining like terms.
| Simplify each side. | $$-9 = 3y$$ |
| Divide both sides by 3 to isolate y. | $$\dfrac{-9}{\textcolor{red}{3}} = \dfrac{3y}{\textcolor{red}{3}}$$ |
| Simplify. | $$-3 = y$$ |
| Check your answer. Let y = −3. | $$\begin{split} 11 - 20 &= 17y - 8y - 6y \\ 11 - 20 &\stackrel{?}{=} 17(\textcolor{red}{-3}) -8(\textcolor{red}{-3}) -6(\textcolor{red}{-3}) \\ 11 - 20 &\stackrel{?}{=} -51 + 24 + 18 \\ -9 &\stackrel{?}{=} -9\; \checkmark \end{split}$$ |
Notice that the variable ended up on the right side of the equal sign when we solved the equation. You may prefer to take one more step to write the solution with the variable on the left side of the equal sign.
Solve: 18 − 27 = 15c − 9c − 3c.
- Answer
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c = -3
Solve: 18 − 22 = 12x − x − 4x.
- Answer
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\(x = -\frac{4}{7}\)
Solve: −3(n − 2) − 6 = 21.
Solution
Remember—always simplify each side first.
| Distribute. | $$−3n + 6 = 21$$ |
| Simplify. | $$-3x = 21$$ |
| Divide both sides by -3 to isolate n. | $$\begin{split} \dfrac{-3n}{\textcolor{red}{-3}} &= \dfrac{21}{\textcolor{red}{-3}} \\ n &= -7 \end{split}$$ |
| Check your answer. Let n = −7. | $$\begin{split} −3(n − 2) − 6 &= 21 \\ -3(\textcolor{red}{-7} - 2) - 6 &\stackrel{?}{=} 21 \\ -3(-9) - 6 &\stackrel{?}{=} 21 \\ 27 - 6 &\stackrel{?}{=} 21 \\ 21 &= 21\; \checkmark \end{split}$$ |
Solve: −4(n − 2) − 8 = 24.
- Answer
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n = -6
Solve: −6(n − 2) − 12 = 30.
- Answer
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n = -5
Solving One Step Equation by Mult/Div. Integers (Var on Left)
Solving One Step Equation by Mult/Div. Integers (Var on Right)
Solving One Step Equation in the Form: −x = −a
Practice Makes Perfect
Solve Equations Using the Division and Multiplication Properties of Equality
In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.
- 8x = 32
- 7p = 63
- −5c = 55
- −9x = −27
- −90 = 6y
- −72 = 12y
- −16p = −64
- −8m = −56
- 0.25z = 3.25
- 0.75a = 11.25
- −3x = 0
- 4x = 0
In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.
- \(\dfrac{x}{4}\) = 15
- \(\dfrac{z}{2}\) = 14
- −20 = \(\dfrac{q}{−5}\)
- \(\dfrac{c}{−3}\) = −12
- \(\dfrac{y}{9}\) = −6
- \(\dfrac{q}{6}\) = −8
- \(\dfrac{m}{−12}\) = 5
- −4 = \(\dfrac{p}{−20}\)
- \(\dfrac{2}{3}\)y = 18
- \(\dfrac{3}{5}\)r = 15
- \(− \dfrac{5}{8}\)w = 40
- 24 = \(− \dfrac{3}{4}\)x
- \(− \dfrac{2}{5} = \dfrac{1}{10} a\)
- \(− \dfrac{1}{3} q = − \dfrac{5}{6}\)
Solve Equations That Need to be Simplified
In the following exercises, solve the equation.
- 8a + 3a − 6a = −17 + 27
- 6y − 3y + 12y = −43 + 28
- −9x − 9x + 2x = 50 − 2
- −5m + 7m − 8m = −6 + 36
- 100 − 16 = 4p − 10p − p
- −18 − 7 = 5t − 9t − 6t
- \(\dfrac{7}{8} n − \dfrac{3}{4} n\) = 9 + 2
- \(\dfrac{5}{12} q + \dfrac{1}{2} q\) = 25 − 3
- 0.25d + 0.10d = 6 − 0.75
- 0.05p − 0.01p = 2 + 0.24
Everyday Math
- Balloons Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. Find the number of balloons in each bunch, b, by solving the equation 3b = 18.
- Teaching Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. Find the number of children in each group, g, by solving the equation 4g = 24.
- Ticket price Daria paid $36.25 for 5 children’s tickets at the ice skating rink. Find the price of each ticket, p, by solving the equation 5p = 36.25.
- Unit price Nishant paid $12.96 for a pack of 12 juice bottles. Find the price of each bottle, b, by solving the equation 12b = 12.96.
- Fuel economy Tania’s SUV gets half as many miles per gallon (mpg) as her husband’s hybrid car. The SUV gets 18 mpg. Find the miles per gallons, m, of the hybrid car, by solving the equation \(\dfrac{1}{2}\)m = 18.
- Fabric The drill team used 14 yards of fabric to make flags for one-third of the members. Find how much fabric, f, they would need to make flags for the whole team by solving the equation \(\dfrac{1}{3}\)f = 14.
Writing Exercises
- Frida started to solve the equation −3x = 36 by adding 3 to both sides. Explain why Frida’s method will result in the correct solution.
- Emiliano thinks x = 40 is the solution to the equation \(\dfrac{1}{2}\)x = 80. Explain why he is wrong.
Self Check
(a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
(b) After reviewing this checklist, what will you do to become confident for all objectives?
Contributors and Attributions
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Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at<EMAIL_ADDRESS>."


5.1: Characteristics of Gases
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Learning Objectives
- To describe the characteristics of a gas.
The three common phases (or states) of matter are gases, liquids, and solids. Gases have the lowest density of the three, are highly compressible, and completely fill any container in which they are placed. Gases behave this way because their intermolecular forces are relatively weak, so their molecules are constantly moving independently of the other molecules present. Solids, in contrast, are relatively dense, rigid, and incompressible because their intermolecular forces are so strong that the molecules are essentially locked in place. Liquids are relatively dense and incompressible, like solids, but they flow readily to adapt to the shape of their containers, like gases. We can therefore conclude that the sum of the intermolecular forces in liquids are between those of gases and solids. Figure \(\PageIndex{1}\) compares the three states of matter and illustrates the differences at the molecular level.
The state of a given substance depends strongly on conditions. For example, H 2 O is commonly found in all three states: solid ice, liquid water, and water vapor (its gaseous form). Under most conditions, we encounter water as the liquid that is essential for life; we drink it, cook with it, and bathe in it. When the temperature is cold enough to transform the liquid to ice, we can ski or skate on it, pack it into a snowball or snow cone, and even build dwellings with it. Water vapor ( the term vapor refers to the gaseous form of a substance that is a liquid or a solid under normal conditions so nitrogen (N 2 ) and oxygen (O 2 ) are referred to as gases, but gaseous water in the atmosphere is called water vapor) is a component of the air we breathe, and it is produced whenever we heat water for cooking food or making coffee or tea. Water vapor at temperatures greater than 100°C is called steam. Steam is used to drive large machinery, including turbines that generate electricity. The properties of the three states of water are summarized in Table 10.1.
| Temperature | State | Density (g/cm3) |
|---|---|---|
| ≤0°C | solid (ice) | 0.9167 (at 0.0°C) |
| 0°C–100°C | liquid (water) | 0.9997 (at 4.0°C) |
| ≥100°C | vapor (steam) | 0.005476 (at 127°C) |
The geometric structure and the physical and chemical properties of atoms, ions, and molecules usually do not depend on their physical state; the individual water molecules in ice, liquid water, and steam, for example, are all identical. In contrast, the macroscopic properties of a substance depend strongly on its physical state, which is determined by intermolecular forces and conditions such as temperature and pressure.
Figure \(\PageIndex{2}\) shows the locations in the periodic table of those elements that are commonly found in the gaseous, liquid, and solid states. Except for hydrogen, the elements that occur naturally as gases are on the right side of the periodic table. Of these, all the noble gases (group 18) are monatomic gases, whereas the other gaseous elements are diatomic molecules ( H 2 , N 2 , O 2 , F 2 , and Cl 2 ). Oxygen can also form a second allotrope, the highly reactive triatomic molecule ozone ( O 3 ), which is also a gas. In contrast, bromine (as Br 2 ) and mercury (Hg) are liquids under normal conditions (25°C and 1.0 atm, commonly referred to as “room temperature and pressure”). Gallium (Ga), which melts at only 29.76°C, can be converted to a liquid simply by holding a container of it in your hand or keeping it in a non-air-conditioned room on a hot summer day. The rest of the elements are all solids under normal conditions.
All of the gaseous elements (other than the monatomic noble gases) are molecules. W ithin the same group (1, 15, 16 and 17), the lightest elements are gases. All gaseous substances are characterized by weak interactions between the constituent molecules or atoms.
Summary
Bulk matter can exist in three states: gas, liquid, and solid. Gases have the lowest density of the three, are highly compressible, and fill their containers completely. Elements that exist as gases at room temperature and pressure are clustered on the right side of the periodic table; they occur as either monatomic gases (the noble gases) or diatomic molecules (some halogens, N 2 , O 2 ).


12.4A: Structure of a Nerve
A nerve is the primary structure of the peripheral nervous system and is composed of bundles of axons.
- Describe the structure of nerves
Key Points
- A nerve is the primary structure of the peripheral nervous system (PNS) that encloses the axons of peripheral neurons.
- A nerve provides a structured pathway that supports neuron function.
- A nerve consists of many structures including axons, glycocalyx, endoneurial fluid, endoneurium, perineurium, and epineurium.
- The axons are bundled together into groups called fascicles, and each fascicle is wrapped in a layer of connective tissue called the perineurium.
- Magnetic resonsance neurography is a technology used to detect nerve damage.
Key Terms
- endoneurial fluid : A low protein liquid that is the peripheral nervous system equivalent to cerebrospinal fluid in the central nervous system.
- perineurium : A protective sheath covering nerve fascicles.
- glycocalyx : A glycoprotein-polysaccharide covering that surrounds cell membranes.
- endoneurium : A layer of connective tissue that surrounds axons.
- fascicles : A small bundle of nerve fibers enclosed by the perineurium.
- epineurium : The outermost layer of dense, irregular connective tissue surrounding a peripheral nerve.
Nerve Anatomy
Nerves : An illustration of the main nerves of the arm.
A nerve is an enclosed, cable-like bundle of axons (the projections of neurons) in the peripheral nervous system (PNS). A nerve provides a structured pathway that supports the electrochemical nerve impulses transmitted along each of the axons.
In the central nervous system, the analogous structures are known as tracts. Neurons are sometimes referred to as nerve cells, although this term is misleading since many neurons do not occupy nerves, and nerves also include non-neuronal support cells (glial cells) that contribute to the health of enclosed neurons.
Each nerve contains many axons that are sometimes referred to as fibers. Within a nerve, each axon is surrounded by a layer of connective tissue called the endoneurium. The axons are bundled together into groups called fascicles. Each fascicle is wrapped in a layer of connective tissue called the perineurium.
Finally, the entire nerve is wrapped in a layer of connective tissue called the epineurium. See the following illustrations of these structures.
The endoneurium consists of an inner sleeve of material called the glycocalyx and a mesh of collagen. Nerves are bundled along with blood vessels, which provide essential nutrients and energy to the enclosed, and metabolically demanding, neurons.
Within the endoneurium, individual nerve fibers are surrounded by a liquid called the endoneurial fluid. The endoneurium has properties analogous to the blood–brain barrier. It prevents certain molecules from crossing from the blood into the endoneurial fluid.
In this respect, endoneurial fluid is similar to cerebrospinal fluid in the central nervous system. During nerve irritation or injury, the amount of endoneurial fluid may increase at the site of damage. This increase in fluid can be visualized using magnetic resonance neurography to diagnose nerve damage.
(a) Anatomy of a nerve and (b) Cross-section of a nerve: The primary structures of a nerve. An illustration of a cross-section of a nerve highlighting the epineurium and perineurium. Individual axons can also be seen as tiny circles within each perineurium.
Basic Function
A nerve conveys information in the form of electrochemical impulses (known as nerve impulses or action potentials) carried by the individual neurons that make up the nerve. These impulses are extremely fast, with some myelinated neurons conducting at speeds up to 120 m/s. The impulses travel from one neuron to another by crossing a synapse, and the message is converted from electrical to chemical and then back to electrical.
Nerves can be categorized into two groups based on function:
- Sensory nerves conduct sensory information from their receptors to the central nervous system, where the information is then processed. Thus they are synonymous with afferent nerves.
- Motor nerves conduct signals from the central nervous system to muscles. Thus they are synonymous with efferent nerves.
Neurologists usually diagnose disorders of the nerves by a physical examination, including the testing of reflexes, walking and other directed movements, muscle weakness, proprioception, and the sense of touch. This initial exam can be followed with tests such as nerve conduction study, electromyography, or computed tomography.