The balanced chemical equation for the combustion of hydrogen gas is:
2H2(g) + O2(g) → 2H2O(g)
From the equation, we see that 2 moles of water are produced for every 2 moles of hydrogen gas burned. Therefore, the number of moles of water produced can be calculated as:
moles of H2O = moles of H2/2
To find the number of moles of hydrogen gas, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Rearranging this equation, we get:
n = PV/RT
Plugging in the given values, we get:
n = (20.0 atm * 150.0 L) / (0.0821 L·atm/(mol·K) * 298 K) = 123.1 mol
Therefore, the number of moles of water produced is:
moles of H2O = 123.1 mol / 2 = 61.6 mol
Finally, we can convert the number of moles of water to mass using the molar mass of water:
mass of H2O = moles of H2O * molar mass of H2O
mass of H2O = 61.6 mol * 18.015 g/mol = 1109.98 g
Rounding to two decimal places, the mass of water vapor produced is 1110.00 g.