Question

Hydrogen gas holds promise as an alternative fuel to gasoline. Calculate the mass of H

2
​
gas in a 30.7 L fuel tank at a pressure of 1.53×10
4
mmHg and a temperature of 33.2
∘
C

Answer 1

To calculate the mass of hydrogen gas in a given volume, pressure, and temperature, we use the Ideal Gas Law. First, we convert the provided values to compatible units (Kelvin for temperature and atm for pressure), then use the Ideal Gas Law to solve for the number of moles, and finally multiply by the molar mass of hydrogen to get the mass.

Step-by-step explanation:

To calculate the mass of H2 gas in a 30.7 L fuel tank at a pressure of 1.53×104 mmHg and a temperature of 33.2 °C, we can use the Ideal Gas Law, which is PV = nRT. For the calculation, we need to convert pressure to atm by dividing by 760 mmHg/atm, and temperature must be converted to Kelvin by adding 273.15.

First, we convert the temperature to Kelvin:
33.2 °C + 273.15 = 306.35 K

Next, we convert the pressure to atm:
1.53×104 mmHg / 760 mmHg/atm = 20.125 atm

Now, we use the Ideal Gas Law with R = 0.0821 L·atm/(mol·K):
(20.125 atm) × (30.7 L) = n × (0.0821 L·atm/(mol·K)) × (306.35 K)

Solve for n (number of moles of H2):
n = (20.125 atm × 30.7 L) / (0.0821 L·atm/(mol·K) × 306.35 K)

Once we have the moles, we can find the mass by multiplying moles by the molar mass of H2 (2.016 g/mol):
Mass of H2 = n × 2.016 g/mol