Question

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?

Answer 1

The volume would be 150 mL.

Explanation:

This is a problem involving the Combined Gas Law.

`(P_1V_1)/T_1 = (P_2V_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 = "1.053 bar"; V_1 = "156 mL"; T_1 = "(25 + 273.15) K = 298.15 K"`
`P_2 = "1 bar"; color(white)(mm)V_2 = "?"; color(white)(mmm)T_2 = "(0 + 273.15) K = 273.15 K"`

`(P_1V_1)/T_1 = (P_2V_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"`