A 350 mL sample of air collected at 35°C has a pressure of 550 torr. What pressure will the air exert if it is allowed to expand to 425 mL at 57°C?

Jun 17, 2017

$485$ $\text{torr}$

Explanation:

We can solve this equation using the combined gas law:

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

Remember, always use the absolute (Kelvin) temperature when working with gas equations.

The temperature conversions are

T_1 = ""^"o""C" + 273 = 35^"o" + 273 = color(red)(308 color(red)("K"

T_2 = 57^"o""C" + 273 = color(green)(330 color(green)("K"

Since we're trying to find the final pressure, let's rearrange this equation to solve for ${P}_{2}$:

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

Our known values:

${P}_{1} = 550$ $\text{torr}$

${V}_{1} = 350$ $\text{mL}$

T_1 = color(red)(308 color(red)("K"

${V}_{2} = 425$ "mL"

T_2 = color(green)(330 color(green)("K"

Let's plug these into the equation to find the final pressure:

P_2 = ((550"torr")(350cancel("mL"))(330cancel("K")))/((308cancel("K"))(425cancel("mL"))) = color(blue)(485 color(blue)("torr"

The final pressure after it is subjected to these changes is thus color(blue)(485 sfcolor(blue)("torr".