At constant volume and temperature conditions, the rates of...

At constant volume and temperature conditions, the rates of diffusion $D_{A}$ and $D_{B}$ of gases $A$ and $B$ having densities $\rho_{A}$ and $\rho_{B}$ are related by the expression: (a) $\mathrm{D}_{\mathrm{A}}=\left[\mathrm{D}_{\mathrm{B}} \rho_{A} / \rho_{\mathrm{B}}\right]^{1 / 2}$ (b) $\mathrm{D}_{\mathrm{A}}=\left[\mathrm{D}_{\mathrm{B}} \rho_{\mathrm{B}} / \rho_{\mathrm{A}}\right]^{1 / 2}$ (c) $\mathrm{D}_{\mathrm{A}}=\mathrm{D}_{\mathrm{B}}\left[\rho_{A} / \rho_{\mathrm{B}}\right]^{1 / 2}$ (d) $\mathrm{D}_{\mathrm{A}}=\mathrm{D}_{\mathrm{B}}\left[\rho_{\mathrm{B}} / \rho_{\mathrm{A}}\right]^{1 / 2}$

At constant volume and temperature conditions, the rates of diffusion $D_{A}$ and $D_{B}$ of gases $A$ and $B$ having densities $\rho_{A}$ and $\rho_{B}$ are related by the expression:
(a) $\mathrm{D}_{\mathrm{A}}=\left[\mathrm{D}_{\mathrm{B}} \rho_{A} / \rho_{\mathrm{B}}\right]^{1 / 2}$
(b) $\mathrm{D}_{\mathrm{A}}=\left[\mathrm{D}_{\mathrm{B}} \rho_{\mathrm{B}} / \rho_{\mathrm{A}}\right]^{1 / 2}$
(c) $\mathrm{D}_{\mathrm{A}}=\mathrm{D}_{\mathrm{B}}\left[\rho_{A} / \rho_{\mathrm{B}}\right]^{1 / 2}$
(d) $\mathrm{D}_{\mathrm{A}}=\mathrm{D}_{\mathrm{B}}\left[\rho_{\mathrm{B}} / \rho_{\mathrm{A}}\right]^{1 / 2}$

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Key Concepts

Graham's Law

Graham's Law states that under constant temperature and pressure, the rate of gas diffusion is inversely proportional to the square root of its molar mass. This principle explains why lighter gases diffuse faster than heavier ones and forms the basis for comparing the diffusion rates of different gases.

Diffusion of Gases

Gas diffusion refers to the spontaneous mixing process where gas molecules move from areas of higher concentration to areas of lower concentration. This movement is driven by the random thermal motion of the molecules.

Density and Diffusion Rate Relationship

The relationship between a gas's density and its rate of diffusion is rooted in kinetic theory. Since density is related to the mass of the gas molecules, the rate of diffusion is inversely proportional to the square root of the density, meaning that gases with lower densities tend to diffuse faster than those with higher densities.

Constant Volume and Temperature Conditions

Maintaining constant volume and temperature ensures that other influencing factors such as pressure and thermal energy remain uniform. This allows a direct comparison of diffusion rates based solely on intrinsic properties like density or molecular mass, which is critical for applying principles such as Graham's Law accurately.

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