Suppose you are given two flasks at the same temperature, one of volume 2 L and the other of volume 3 L. The 2-L flask contains 4.8 g of gas, and the gas pressure is x atm. The 3-L flask contains 0.36 g of gas, and the gas pressure is 0.1x. Do the two gases have the same molar mass? If not, which contains the gas of higher molar mass?

검증된 단계별 안내

Determine the number of moles of gas in each flask using the ideal gas law equation, PV = nRT. Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Since the temperature and R are constants and not provided, you can simplify the equation to n = PV/RT for each flask.

Calculate the molar mass of the gas in each flask. Molar mass (M) is given by the formula M = mass of gas (g) / number of moles of gas (n). Use the mass of gas provided for each flask and the number of moles calculated in the previous step.

Compare the molar masses calculated for the gases in the two flasks. The gas with the higher molar mass will have a greater mass per mole.

Identify which flask contains the gas with the higher molar mass based on the comparison done in the previous step.

Conclude whether the gases in the two flasks have the same molar mass or not based on the molar mass values calculated.

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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 calculating the number of moles from given mass and molar mass.

Molar Mass

Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by dividing the mass of the gas by the number of moles present. Understanding molar mass is crucial for comparing the properties of different gases in the question.

Density of Gases

The density of a gas can be determined using the formula density = mass/volume. In this context, comparing the densities of the gases in the two flasks will help in determining their molar masses, as gases with higher molar masses will generally have higher densities at the same temperature and pressure.