A 226.4-L cylinder contains 65.5% He(g) and 34.5% Kr(g) by mass at 27.0°C and 1.40 atm total pressure. What is the mass of He in this container?

Question

Quizplus · Accepted Answer

To find the mass of He in the container, we first calculate the total mass of the gas mixture. Using the ideal gas law, PV = nRT, where P is the pressure (1.40 atm), V is the volume (226.4 L), R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin (27.0°C + 273 = 300K). Rearranging the formula to solve for n (the total moles of gas), we get n = PV/RT. Substituting the given values, we find n = (1.40 atm * 226.4 L) / (0.0821 L·atm/mol·K * 300K) = 12.8 moles of gas. Since the question asks for mass and we have the percentage composition by mass, we need to find the total mass of the gas mixture. The percentage composition doesn't directly help in finding the moles or mass of He without knowing the total mass of the gas mixture. However, the approach described initially is incorrect for this problem because it mistakenly attempts to use the ideal gas law to find moles and then convert to mass using percentage composition, which is not directly applicable without knowing the molar mass of the gas mixture or using the gas law in this context. The correct approach involves directly calculating the mass of He based on the percentage given and the total mass of the gas mixture, which we initially don't have. Since the question directly asks for the mass of He and provides the percentage composition by mass, we need to focus on finding the total mass of the gas mixture first. Without the total mass or a direct way to calculate it from the given information (pressure, volume, temperature), we cannot accurately calculate the mass of He using the ideal gas law alone. The correct approach should involve using the mass percentage directly once the total mass is known, but the provided solution skips the step of finding or using the total mass correctly. Therefore, the explanation provided initially is incorrect because it misapplies the ideal gas law for this specific question's requirements. The correct method to find the mass of He involves directly using the mass percentages and the total mass of the gas mixture, which needs to be determined or given. Given the percentages, if we knew the total mass, we could simply calculate the mass of He by taking 65.5% of the total mass. Without additional information or a correct interpretation of the problem's requirements, the solution path is mistaken. The correct answer involves recognizing the error in the application of the ideal gas law for calculating mass from the given percentages and conditions.

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