# Question #542e5

May 30, 2017

Here's what I got.

#### Explanation:

The idea here is that the volume of a gas is directly proportional to its temperature when the number of moles of gas and the pressure of the gas are kept constant $\to$ this is known as Charles' Law.

In other words, when pressure and the number of moles of gas are kept constant, decreasing the temperature by a factor $f$ will cause its volume to decrease by the same factor $f$.

In your case, the volume decreased

$\text{240 mL " -> " 180 mL}$

which implies that the temperature decreased as well

$\text{270 K " -> " ? K}$

Now, the volume decreased by a factor

$\left(240 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{mL"))))/(180color(red)(cancel(color(black)("mL}}}}\right) = \textcolor{b l u e}{\frac{4}{3}}$

You can thus say that the temperature of the gas decreased by a factor of $\textcolor{b l u e}{\frac{4}{3}}$ as well, so

$f = \text{270 K"/"final temperature}$

which means that

$\text{final temperature" = "270 K"/color(blue)(4/3) = "202.5 K}$

Rounded to two sig figs, the answer will be

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{final temperature" = 2.0 * 10^2color(white)(.)"K}}}}$