Final answer:
To calculate the mass of hydrogen sulfide gas that occupies 57.5 L at 450 kPa and 85.0 °C, convert units to Pa, m³, and K and use the Ideal Gas Law. After finding the number of moles using PV=nRT, multiply moles by the molecular weight of H2S to get the mass.
Step-by-step explanation:
To find the mass of hydrogen sulfide gas (H2S) that would occupy a volume of 57.5 L at a pressure of 450 kPa and a temperature of 85.0 °C, we can use the Ideal Gas Law, which is PV = nRT. First, we need to make sure all our units are consistent with the universal gas constant (R). The pressure must be in pascals (Pa), the volume in cubic meters (m3), and the temperature in Kelvin (K).
The first step is to convert the known values to the appropriate units:
- Pressure: 450 kPa = 450,000 Pa
- Volume: 57.5 L = 0.0575 m3 (since 1 L = 0.001 m3)
- Temperature: 85.0 °C = 358.15 K (since K = °C + 273.15)
Now we can use the Ideal Gas Law:
PV = nRT
450,000 Pa × 0.0575 m3 = n × 8.3145 J/mol·K × 358.15 K
After calculating the above equation, we get the number of moles (n) of H2S gas.
To find the mass of H2S, we multiply the moles by the molecular weight of H2S:
Molar mass of H2S = 2(1.008 g/mol for H) + 32.065 g/mol for S = 34.081 g/mol
Finally, mass = n × molar mass of H2S, giving us the mass in grams.