What is the resulting temperature if a sample of gas began with a temperature of 20 C, 1 liter, and 760 mmHg and now occupies 800 mL and has a pressure of 1000 mmHg?

Aug 2, 2017

${T}_{2} = 317$ $\text{K}$

Explanation:

We're asked to find the new temperature of a gas after it is subjected to changes in pressure and volume.

To do this, we can use the combined gas law:

$\underline{\overline{| \stackrel{\text{ ")(" "(P_1V_1)/(T_1) = (P_2V_2)/(T_2)" }}{|}}}$

where

• ${P}_{1}$ is the original pressure (given as $760$ $\text{mm Hg}$)

• ${V}_{1}$ is the original volume (given as $1$ $\text{L}$)

• ${T}_{1}$ is the original absolute temperature, which is

$20$ $\text{^"o""C}$ + 273 = ul(298color(white)(l)"K"

• ${P}_{2}$ is the final pressure (given as $1000$ $\text{mm Hg}$)

• ${V}_{2}$ is the final volume (given as $800$ $\text{mL}$ = ul(0.800color(white)(l)"L") (units must be consistent, so convert this to liters)

• ${T}_{2}$ is the final absolute temperature (what we're trying to find)

Let's rearrange this equation to solve for the final temperature, ${T}_{2}$:

${T}_{2} = \frac{{P}_{2} {V}_{2} {T}_{1}}{{P}_{1} {V}_{1}}$

Plugging in the above values:

T_2 = ((1000cancel("mm Hg"))(0.800cancel("L"))(298color(white)(l)"K"))/((760cancel("mm Hg"))(1cancel("L"))) = color(red)(ulbar(|stackrel(" ")(" "317color(white)(l)"K"" ")|)

The final temperature of the gas is thus color(red)(317 sfcolor(red)("kelvin".