Question

What is the temperature of the gas inside a 750 ml balloon filled with 0.30 g hydrogen gas? The pressure of the balloon is 1.2 atm.

Answer 1

Use the ideal gas law: PV = nRT, and solve for T,

T = PV/nR.

We should convert any of our parameters to units that would be easy to use with a known R value. One option would be to have the pressure in atm, volume in L, and convert the mass of the hydrogen gas to moles:

P = 1.2 atm
V = 750 mL = 0.750 L
n = (0.30 g H2)/(2.0159 g/mol) = 0.1488 mol H2
R = 0.0821 L•atm/mol•K.

Solving for T,

T = (1.2 atm)(0.750 L)/(0.1488 mol H2)(0.0821 L•atm/mol•K) = 73.671 K.

If you opt to leave your temperature in Kelvin, I would go with 74 K, as that has two significant figures like the rest of the values.

If you opt to go with Celsius, then the answer would be a bit awkward if you had to follow two sig figs: 73.671 - 273.15 = -199.49 ≈ -2.0 × 10² °C.

Pick your poison, I suppose.