Dr. I. M. A. Brightguy adds 0.1727 g of an unknown gas to a 125-mL flask. If Dr. B finds the pressure to be 736 torr at 20.0°C, is the gas likely to be methane, CH₄, nitrogen, N₂, oxygen, O₂, neon, Ne, or argon, Ar? A)CH ₄ B)N ₂ C)Ne D)Ar E)O ₂

Question

Quizplus · Accepted Answer

To determine the identity of the gas, we can use the ideal gas law: PV = nRT. We can rearrange this equation to solve for moles of gas: n = PV/RT. We know the pressure (736 torr), volume (125 mL), and temperature (20.0°C = 293 K). We can also calculate the number of moles of gas added: n = m/M, where m is the mass (0.1727 g) and M is the molar mass of the gas. We can use the periodic table to find the molar masses: - CH₄: (12.01 + 1.01 + 14.01) + 4(1.01) = 16.05 g/mol - N₂: 14.01 g/mol - O₂: 2(16.00) = 32.00 g/mol - Ne: 20.18 g/mol - Ar: 39.95 g/mol Calculating the number of moles for each gas: - CH₄: n = (736 torr)(0.125 L)/(0.0821 L*atm/mol*K)(293 K) = 0.00467 mol - N₂: n = (736 torr)(0.125 L)/(0.0821 L*atm/mol*K)(293 K) = 0.00467 mol - O₂: n = (736 torr)(0.125 L)/(0.0821 L*atm/mol*K)(293 K) = 0.00467 mol - Ne: n = (736 torr)(0.125 L)/(0.0821 L*atm/mol*K)(293 K) = 0.00467 mol - Ar: n = (736 torr)(0.125 L)/(0.0821 L*atm/mol*K)(293 K) = 0.00467 mol Since all the gases have the same number of moles, we cannot determine the identity of the gas based on the amount added. However, the molar mass of the gas can help us identify it. The molar mass of the gas must be close to 32.00 g/mol (the molar mass of O2) since the pressure is only 736 torr. This rules out Ne and Ar, which have much larger molar masses. CH₄ and N₂ have molar masses close to 16.05 g/mol (the molar mass of CH4), which is too light to produce a pressure of 736 torr. The only remaining gas is O₂, which has a molar mass close to 32.00 g/mol and could produce the observed pressure. Therefore, the gas is likely to be oxygen (O2).

Dr I M A M