What pressure is exerted by 0.442 mol of hydrogen gas in a 4.71 L container at 39◦C?

Question

answer in units of atm.

Answer 1

Step 1: List the values that are known

T = 39°C

V = 4.71L

n = 0.442 mol H₂ (hydrogen gas)

Use the following equation to solve for P

PV = nRT

Rearrange the equation

P = nRT / V

Plug in the known from above

• = x = multiply

P = 0.442 mol H₂ • R • 39°C

-------------------------------------

4.71L

Select the appropriate R to cancel all units out to be left with P in units of atm

0.0821

L.atm.K-1.mol-1

You need to convert temperature in units of K

39°C + 273 = 312K

Replace this in the equation and R with atm. Your equation should look like this now.

P = 0.442 mol • 0.0821 L atm • 312K • 1

------------- ------------------ --------- ------------

1 mol K 4.71L

All units should cancel out except for atm

P = 0.442 mol • 0.0821 L atm • 312K • 1

------------ ------------------ --------- ------------

1 mol K 1 4.71L

P = 2.41 atm

Answer 2

For this problem, we want to use the ideal gas law equation and this is because we know the number of moles, the volume and the temperature, so the unknown is the pressure. This also means we need to isolate the pressure in the equation in order to solve for it:

PV = nRT

P = (nRT) / V

P = [(0.442) (0.08206) (312.15)] / 4.71

P = 11.32 / 4.71

P = 2.40 atm

Notes:

1. R in this equation is the gas constant, which is 0.08206
2. The temperature (T) must be in kelvin which is why it was converted
3. The answer should have 3 significant figures (SFs) as the value with the least SFs in the question has 3.
4. You can check to make sure this is correct by plugging the numbers back into the equation; if both sides are equal (or very close) you know you are correct.
5. I have done this and both sides are equal to 11.3, so we know 2.40 atm is correct.