The answer to Question 56 follows from the answer to...

The answer to Question 56 follows from the answer to Question 55. Answer Question 55 first. Labels have become detached from cylinders of two gases, one of which is known to be propane, $\mathrm{C}_{3} \mathrm{H}_{8}$, and the other butane, $\mathrm{C}_{4} \mathrm{H}_{10} .$ The densities of the two gases are compared at the same temperature and pressure. The density of gas $A$ is $1.37 \mathrm{g} / \mathrm{L},$ and the density of gas $\mathbf{B}$ is higher. Which gas is A and which is B? What is the density of B?

The answer to Question 56 follows from the answer to Question
55. Answer Question 55 first.
Labels have become detached from cylinders of two gases, one of which is known to be propane, $\mathrm{C}_{3} \mathrm{H}_{8}$, and the other butane, $\mathrm{C}_{4} \mathrm{H}_{10} .$ The densities of the two gases are compared at the same temperature and pressure. The density of gas $A$ is $1.37 \mathrm{g} / \mathrm{L},$ and the density of gas $\mathbf{B}$ is higher. Which gas is A and which is B? What is the density of B?

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Key Concepts

Molar Mass Calculation

Calculating the molar mass of a molecule involves summing the atomic masses of its constituent atoms. This calculation is crucial for predicting the relative densities of gases, as the one with the larger molar mass is expected to be denser when measured under the same conditions.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) governs the behavior of gases under various conditions. When rearranged in terms of density, it shows that, for a given temperature and pressure, a gas's density is directly proportional to its molar mass. This concept is fundamental for comparing the densities of different gases under the same conditions.

Density-Molar Mass Relationship

Under constant temperature and pressure, the density of a gas is determined by its molar mass. A gas with a higher molar mass will have a higher density than a gas with a lower molar mass. This relationship allows us to infer which gas is which by comparing their densities.

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