# Hydrogen is collected over water at 19C and 785 mmHg of pressure. THe total volume of the sample was 1.93L How do you calculate the volume of hydrogen at STP?

Jun 1, 2016

The volume of hydrogen is 1.84 L.

#### Explanation:

This is an example of a Combined Gas Laws problem.

color(blue)(|bar(ul((P_1V_1)/T_1 = (P_2V_2)/T_2|)

We can rearrange this formula to get

V_2 = V_1 × P_1/P_2 × T_2/T_1

The vapour pressure of water at 19 °C = 16.5 mmHg.

∴ The pressure of the dry hydrogen is given by

${P}_{\text{H₂" = P_"atm" -P_"H₂O" = "785 mmHg" - "16.5 mmHg" = 768.5 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg")))) = "1.011 atm}}$

${P}_{1} = \text{1.011 atm"; V_1 = "1.93 L"; T_1 = "(19 + 273.15) K" ="292.15 K}$
P_2 = 1 color(red)(cancel(color(black)("bar"))) × "1 atm"/(1.013 color(red)(cancel(color(black)("bar")))) = "0.9872 atm"; V_2 = "?"; T_2 = "273.15 K"
V_2 = V_1 × P_1/P_2 × T_2/T_1 = "1.93 L" × (1.011 color(red)(cancel(color(black)("atm"))))/(0.9872 color(red)(cancel(color(black)("atm")))) × (273.15 color(red)(cancel(color(black)("K"))))/(293.15 color(red)(cancel(color(black)("K")))) = "1.84 L"