A chemist collects 156 mL of carbon dioxide gas at 25°C and 790 torr. What would the volume of the carbon dioxide be at STP?

Mar 5, 2016

The volume would be 150 mL.

Explanation:

This is a problem involving the Combined Gas Law.

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

P_1 = 790 color(red)(cancel(color(black)("torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("torr")))) = "1.039 atm"

STP is defined as 0 °C and 1 bar, so we must express our pressures in bars.

P_1 = 1.039 color(red)(cancel(color(black)("atm"))) × "1.0132 bar"/(1 color(red)(cancel(color(black)("atm")))) = "1.053 bar"

Hence, our data are:

${P}_{1} = \text{1.053 bar"; V_1 = "156 mL"; T_1 = "(25 + 273.15) K = 298.15 K}$
${P}_{2} = \text{1 bar"; color(white)(mm)V_2 = "?"; color(white)(mmm)T_2 = "(0 + 273.15) K = 273.15 K}$

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

V_2 = V_1 × P_1/P_2 × T_2/T_1 = "156 mL" × (1.053 color(red)(cancel(color(black)("bar"))))/(1 color(red)(cancel(color(black)("bar")))) × (273.15 color(red)(cancel(color(black)("K"))))/(298.15 color(red)(cancel(color(black)("K")))) = "150 mL"