Chemistry: Basic Gas Laws and Partial Pressure

Question

In 1783, Jacques Charles launched his first balloon filled with hydrogen gas, which he chose because it was lighter than air. The balloon had a volume of 31,000 L when it reached an altitude of 1000 m, where the pressure was 658 mmHg and the temperature was -8 degrees Celsius.

How many kilograms of hydrogen were used to fill the balloon at STP?

Through multiple ways I try to solve this problem I continue to get a rounded answer of 2.8 and 2.4 which are both incorrect. Please help me solve this problem.

Answer 1

In 1783, Jacques Charles launched his first balloon filled with hydrogen gas, which he chose because it was lighter than air. The balloon had a volume of 31,000 L when it reached an altitude of 1000 m, where the pressure was 658 mmHg and the temperature was -8 degrees Celsius.

How many kilograms of hydrogen were used to fill the balloon at STP?

P=658mmHg, 658/760=0.865789 atm

V=31000L

n=? mol

R=0.08206 Latm/molK

T= -8^oC +273.15=265.15 K

solve for n, moles

PV=nRT

n=PV/RT

n=(0.865789(31000))/(0.08206(265.15))

n=1233.532549 mol of H₂(g)

molar mass: 1 mol H2=2.016 g/mol

1233.532549 mol (2.016 g/ 1mol)=2486.801618784 g H2

10³g=1kg

2.486801618784 kg H₂