Final answer:
The mass of methane in a 250.0 L tank at 28.0 °C and 5572.0 kPa pressure can be determined by using the Ideal Gas Law, converting given values to appropriate units, and calculating the number of moles and then the mass using the molar mass of methane.
Step-by-step explanation:
To find the mass of methane (CH4) in a 250.0 L tank at 28.0 °C and 5572.0 kPa pressure, we'll use the Ideal Gas Law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
- Convert the temperature from Celsius to Kelvin: T = 28.0 °C + 273.15 = 301.15 K
- Convert pressure from kPa to atm since the ideal gas constant is often given in these units: P = 5572.0 kPa / 101.325 = 55.0 atm (rounded to two significant figures as final answer should be).
- Use the ideal gas constant R = 0.0821 atm·L/mol·K for these units.
- Calculate the number of moles of methane: n = PV / RT
- Substitute the values into the equation: n = (55.0 atm × 250.0 L) / (0.0821 atm·L/mol·K × 301.15 K)
- Calculate the mass of methane by multiplying the number of moles by the molar mass of CH4 (16.04 g/mol): mass = n × 16.04 g/mol
By following these steps, we can determine the mass of the methane in the tank.