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?

1 Answer
Ernest Z.
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_"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"#

Your data are then:

#P_1 = "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"#

The volume is 1.84 L.

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