If 9.69 moles of an ideal gas has a pressure of 3.10 atm, and a volume of 64.51 L, what is the temperature of the sample?

Dec 21, 2016

$\text{251 K}$

Explanation:

All you have to do here is use the ideal gas law equation, which looks like this

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{P V = n R T}}}$

Here

• $P$ is the pressure of the gas
• $V$ is the volume it occupies
• $n$ is the number of moles of gas present in the sample
• $R$ is the universal gas constant, equal to $0.0821 \left(\text{atm L")/("mol K}\right)$
• $T$ is the absolute temperature of the gas

Rearrange the equation to solve for $T$

$P V = n R T \implies T = \frac{P V}{n R}$

Before plugging in your values, make sure that the units given to you match those used in the expression of the universal gas constant.

In this case, the volume is given in liters and the pressure in atmospheres, so you're good to go.

Plug in your values to find

T = (3.10 color(red)(cancel(color(black)("atm"))) * 64.51 color(red)(cancel(color(black)("L"))))/(9.69 color(red)(cancel(color(black)("moles"))) * 0.0821 (color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * "K"))

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{T = \text{251 K}}}}$

The answer is rounded to three sig figs.