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A solution of 62 g of ethylene glycol in 250 g of water is cooled to $-10°$C. If $K_f(\text{water}) = 1.86\ \text{K kg mol}^{-1}$, what mass of water (in g) separates out as ice?
Molar mass of ethylene glycol (C$_2$H$_6$O$_2$) $= 62\ \text{g mol}^{-1}$
Moles of glycol $= \dfrac{62}{62} = 1\ \text{mol}$
Let $w$ g of water freeze. Remaining water = $(250 - w)\ \text{g}$.
At $-10°$C: $\Delta T_f = 10$
$m = \dfrac{1}{(250-w)/1000} = \dfrac{1000}{250-w}$
$10 = 1.86 \times \dfrac{1000}{250-w}$
$250 - w = \dfrac{1860}{10} = 186$
$w = 250 - 186 = \mathbf{64\ \text{g}}$
Wait — that gives 64 g (option C, index 2). Let me recheck: $250-w=186$, $w=64$. Official answer is 48 g. Using $w=48$: $250-48=202$, molality $=1000/202=4.95$, $\Delta T_f=1.86\times4.95=9.2\neq10$. The correct answer is indeed 64 g (index 2).
The question of why humans make and respond to music is among the most perplexing in evolutionary biology. Unlike language, tool use, or social cooperation — cognitive capacities whose adaptive advantages are relatively straightforward to theorize — music appears, on the surface, to be a costly activity that confers no obvious survival benefit. Charles Darwin himself acknowledged the puzzle, noting that "as neither the enjoyment nor the capacity of producing musical notes are faculties of the least use to man in reference to his daily habits of life, they must be ranked amongst the most mysterious with which he is endowed."
One prominent evolutionary hypothesis, associated with Geoffrey Miller, proposes that music is best understood as a form of sexual selection — a costly display that signals genetic fitness in the manner of a peacock's tail. On this view, musical virtuosity, like physical beauty or athletic prowess, functions as an honest signal of underlying cognitive and physical quality, and musical preference in potential mates represents an adaptive mechanism for identifying high-quality partners. The hypothesis has the virtue of explaining why musical performance is disproportionately a young adult phenomenon and why the capacity for musical improvisation correlates with general cognitive flexibility.
Critics of the sexual selection hypothesis argue that it fails to account for music's pervasiveness across contexts that have nothing to do with mate attraction — religious ritual, military coordination, infant soothing, collective labor. An alternative hypothesis holds that music is primarily a mechanism for social bonding and group cohesion: the synchronization of movement and vocalization in communal musical activity produces neurochemical effects (including oxytocin release) that reinforce social ties. On this view, music is adaptive not because it signals individual fitness but because it strengthens the cooperative bonds on which collective survival depends.
A third possibility, perhaps the most unsatisfying to committed adaptationist thinkers, is that music is primarily a byproduct of other adaptive capacities — language, fine motor control, pattern recognition — rather than an adaptation in its own right. On this view, dubbed the "auditory cheesecake" hypothesis by Steven Pinker, music exploits the brain's pre-existing reward systems without having been selected for its own functional role. The persistence of music across human cultures would then reflect not its adaptive value but the depth of the neural architectures it hijacks.
Sub-Questions:
Acetic acid can be prepared by hydrolysis of:
Hydrolysis of methyl cyanide (acetonitrile, CH₃CN) yields acetic acid: \(\mathrm{CH_3CN + 2H_2O \rightarrow CH_3COOH + NH_3}\).
These two types of advertising serve very different purposes:
- Informational Advertising: Used when a new product is first being introduced. The primary goal is to make consumers aware of the product's existence, name, features, and uses. Example: When SUVs were first introduced, manufacturers ran informational ads explaining what they were and why consumers might want one.
- Institutional Advertising: Takes a broader view, promoting the benefits, concept, idea, or philosophy of a particular company or industry — not a specific product. It focuses on building a positive corporate image. Example: A lumber company running ads about its tree-replanting programme to project an environmentally responsible image.
Institutional advertising is closely related to public relations, as both aim to shape public perception of the organisation rather than drive immediate product sales.
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