Collection by Water Displacement - a problem

Here is a typical problem involving a gas collected over water (by water displacement)
34.94 mL of hydrogen gas are collected over water at an atmospheric pressure of 0.982 atm and a temperature of 36.9 ^oC. What would the volume be if the pressure of the gas was 1.00 atm and if the temperature was decreased to exactly 0 ^oC?
(the vapor pressure of water at 36.9^oC is 47.1 mm Hg) 

This looks like (and is) an IF problem – it has initial conditions and final conditions. The IF chart would initially look like this:

	initial	final
pressure	unclear	1.00 atm
volume	34.94 mL	?
temperature	36.9oC	0oC

The initial pressure is unclear, because the pressure of the hydrogen was not given in the problem. The temperature also needs to be dealt with. Converting the temperatures (to Kelvin) would give us this:

	initial	final
pressure	unclear	1.00 atm
volume	34.94 mL	?
temperature	310.1 K	273.15 K

To find the initial pressure of the hydrogen, we must use Dalton's Law.

We know that the pressure of the atmosphere is equal to the pressure of the hydrogen plus the pressure of the water vapor

P atmosphere = P hydrogen + P water vapor 

and that therefore the pressure of the hydrogen is equal to the atmospheric pressure minus the pressure of the water vapor.

P hydrogen = P atmosphere - P water vapor

That gives us:

P hydrogen = 0.982 atm – 47.1 mm Hg 

To make that subtraction problem work, we need to fix the units:

So, the pressure of the hydrogen gas  = 0.982 atm – 0.0620 atm = 0.920 atm

Now, we can actually solve the IF problem.

Here's the updated IF table:

	initial	final
pressure	0.920 atm	1.00 atm
volume	34.94 mL	?
temperature	310.1 K	273.15 K

We can solve this either logically or algebraically
Logically, the problem would set up like this:

Algebraically, the problem would set up like this: