According to Graham's law, how does the rate of effusion of NH_3 compare to that of He under identical conditions?

• A. NH_3 effuses slower than He because its molar mass is greater.
• B. NH_3 and He effuse at the same rate because they are both gases.
• C. NH_3 effuses faster than He because it is a compound.
• D. NH_3 effuses faster than He because its molar mass is smaller.

Answer: (A)

Verified step by step guidance

1. Recall Graham's law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, this is expressed as: \[\text{Rate} \propto \frac{1}{\sqrt{M}}\] where \(M\) is the molar mass of the gas.
2. Write the ratio of the rates of effusion for NH\(_3\) and He using Graham's law: \[\frac{\text{Rate}_{\text{NH}_3}}{\text{Rate}_{\text{He}}} = \sqrt{\frac{M_{\text{He}}}{M_{\text{NH}_3}}}\]
3. Determine the molar masses of NH\(_3\) and He: - For NH\(_3\), calculate by adding the atomic masses of 1 nitrogen (N) and 3 hydrogens (H). - For He, use the atomic mass of helium.
4. Substitute the molar masses into the ratio expression to compare the rates of effusion. Since NH\(_3\) has a larger molar mass than He, the square root ratio will be less than 1, indicating NH\(_3\) effuses slower.
5. Conclude that NH\(_3\) effuses slower than He because its molar mass is greater, consistent with Graham's law.