Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30 and the other a gas of molar mass 60, both at the same temperature. The pressure in flask A is x atm, and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5x atm, and the mass of gas in that flask is 1.2 g. Which flask contains the gas of molar mass 30, and which contains the gas of molar mass 60?

검증된 단계별 안내

Calculate the number of moles of gas in each flask using the formula: number of moles (n) = mass (g) / molar mass (g/mol).

Apply the Ideal Gas Law, PV = nRT, to each flask to find the relationship between the pressure and the number of moles. Since the volume (V) and temperature (T) are constant and the same for both flasks, and R is a constant, focus on how P varies with n.

For Flask A, substitute the calculated moles from step 1 into the Ideal Gas Law rearranged as P = (nRT)/V, and note that R, T, and V are constants.

Repeat step 3 for Flask B, using the moles calculated for Flask B and noting that the pressure is 0.5x atm.

Compare the calculated pressures relative to the moles of gas in each flask to determine which flask must contain the gas with the molar mass of 30 g/mol and which contains the gas with the molar mass of 60 g/mol.

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주요 개념

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Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law allows us to understand how gases behave under different conditions and is essential for solving problems involving gas properties, such as pressure and molar mass.

Molar Mass and Density

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). The density of a gas can be calculated using its molar mass and the Ideal Gas Law, which helps in determining the relationship between mass, volume, and pressure of gases in different flasks.

Relationship Between Pressure and Molar Mass

For gases at the same temperature and volume, the pressure is inversely related to the molar mass when the mass of the gas is constant. This means that a gas with a lower molar mass will exert a higher pressure compared to a gas with a higher molar mass, allowing us to deduce which flask contains which gas based on their pressures.