Question

In a container, a gas mixture consists of 320 mg of methane, 175 mg of argon, and 225 mg of neon. The partial pressure of neon at 300K is 8.87 kPa. Calculate the volume of the container and determine the total pressure of the gas mixture. Hint: The molar mass of neon is 20.18 g/mol, the molar mass of methane is 16.04 g/mol, and the molar mass of argon is 39.95 g/mol. The gas constant is 8.314 dm3 kPa/K mole.

Answer 1

To calculate the volume of the container, the ideal gas law is applied using the molar mass of neon and its partial pressure to find that the volume is 2.808 L. The total pressure of the gas mixture is then determined by finding the moles of each gas using their respective molar masses and summing them up, resulting in a total pressure of 29.95 kPa.

Step-by-step explanation:

To find the volume of the container and the total pressure of a gas mixture, we will apply the ideal gas law: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. To find the mole of neon, we use its molar mass and the given mass to calculate n = mass / molar mass = 225 mg / (20.18 g/mol * 1000 mg/g) = 0.01115 mol. Using the ideal gas law, the volume V of the container is V = nRT / PNeon = (0.01115 mol * 8.314 dm3 kPa/K mol * 300 K) / 8.87 kPa = 2.808 dm3 or 2.808 L.

To find the total pressure, we need to determine the number of moles of each gas using their molar masses similarly. For methane: n = 320 mg / (16.04 g/mol * 1000 mg/g) = 0.01995 mol, and for argon: n = 175 mg / (39.95 g/mol * 1000 mg/g) = 0.00438 mol. Total moles of gas mixture, ntotal = nNeon + nMethane + nArgon = 0.01115 mol + 0.01995 mol + 0.00438 mol = 0.03548 mol. Therefore, the total pressure Ptotal is Ptotal = ntotalRT / V = (0.03548 mol * 8.314 dm3 kPa/K mol * 300 K) / 2.808 L = 29.95 kPa.