Suppose you are given two 2 -L flasks and told that one contains a gas of molar mass 28 , the other a gas of molar mass 56 , both at the same temperature and pressure. The mass of gas in the flask \(A\) is $1.0 \mathrm{~g}\( and the mass of gas in the flask \)\mathrm{B}\( is \)2.0 \mathrm{~g}$. Which flask contains the gas of molar mass 28 , and which contains the gas of molar mass 56 ?

We are given the following information: - Flask A contains 1.0 g of gas - Flask B contains 2.0 g of gas - Molar mass of gas 1 = 28 g/mol - Molar mass of gas 2 = 56 g/mol - Both flasks have the same temperature and pressure

Using the given mass and molar mass, we can calculate the number of moles for each flask. Let's denote gas 1 as the gas with molar mass 28 and gas 2 as the gas with molar mass 56. For Flask A, let the number of moles be \(n_A\), we have: \(n_A = \frac{mass_A}{molar \: mass \: of \: gas}\) For Flask B, let the number of moles be \(n_B\), we have: \(n_B = \frac{mass_B}{molar \: mass \: of \: gas}\) We will calculate these values assuming both possibilities, i.e., Flask A contains gas 1 and Flask B contains gas 2 and vice versa.

Now, we will calculate and compare the number of moles in both possibilities: Case 1 - Flask A contains gas 1 and Flask B contains gas 2: - For Flask A: \(n_A = \frac{1.0 g}{28\: g/mol} = 0.0357\: mol\) - For Flask B: \(n_B = \frac{2.0 g}{56\: g/mol} = 0.0357\: mol\) Case 2 - Flask A contains gas 2 and Flask B contains gas 1: - For Flask A: \(n_A = \frac{1.0 g}{56\: g/mol} = 0.0179\: mol\) - For Flask B: \(n_B = \frac{2.0 g}{28\: g/mol} = 0.0714\: mol\)

From the ideal gas law, we know that the number of moles of gas present in a container depends on the pressure, volume, and temperature of the system. Since both flasks have the same temperature and pressure, the flask containing more gas molecules (higher number of moles) will have lower molar mass. From the calculations in Step 3, we can infer the following: - In Case 1, Flask A and Flask B have the same number of moles (0.0357 mol), which is not possible since one flask contains gas with a molar mass of 28, and the other contains gas with a molar mass of 56. - In Case 2, Flask B contains more gas molecules (0.0714 mol) than Flask A (0.0179 mol). Given the higher number of moles in Flask B, it must contain the gas with the lower molar mass, making Flask B the flask that contains the gas of molar mass 28, and Flask A the flask containing the gas of molar mass 56.

Flask A contains the gas of molar mass 56, and Flask B contains the gas of molar mass 28.