A 60.0 mL sample of #CO_2# gas is collected over water at 70.0° and 101.3 kPa. What is the volume of the dry gas at STP?
The important thing to remember about gases that are being collected over water is that the total pressure measured includes the vapor pressure of water at that given temperature.
In this case, the collection tube will hold a gaseous mixture that contains molecules of carbon dioxide,
This means that you can use Dalton's Law of Partial Pressures to determine the partial pressure of carbon dioxide in this mixture.
#color(blue)(P_"total" = sum_i P_i)" "#, where
In this case, the vapor pressure of water at
This means that you have
#P_"total" = P_(CO_2) + P_(H_2O)#
#P_(CO_2) = "101.3 kPa" - "31.09 kPa" = "70.21 kPa"#
Now, STP conditions imply a temperature of
#color(blue)((P_1V_1)/T_1 = (P_2V_2)/T_2)" "#, where
Plug in your values and solve for
#V_2 = P_1/P_2 * T_2/T_1 * V_1#
#V_2 = (70.21 color(red)(cancel(color(black)("kPa"))))/(100.0color(red)(cancel(color(black)("kPa")))) * ( (273.15 + 0)color(red)(cancel(color(black)("K"))))/((273.15 + 70.0)color(red)(cancel(color(black)("K")))) * "60.0 mL"#
#V_2 = color(green)("33.5 mL")#
The answer is rounded to three sig figs.