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Which gas has the smallest rate of diffusion?

Chemistry

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To determine which gas has the smallest rate of diffusion, we use Graham's Law of Diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. This means the gas with the largest molar mass will have the smallest rate of diffusion.

  1. Identify the chemical formula for each gas.

    • A. Hydrogen: H2\text{H}_2
    • B. Ammonia: NH3\text{NH}_3
    • C. Carbon dioxide: CO2\text{CO}_2
    • D. Chlorine: Cl2\text{Cl}_2
  2. Calculate the molar mass for each gas.

    • A. Molar mass of H2=2×1.008 g/mol=2.016 g/mol\text{H}_2 = 2 \times 1.008 \text{ g/mol} = 2.016 \text{ g/mol}
    • B. Molar mass of NH3=14.01 g/mol+(3×1.008 g/mol)=17.034 g/mol\text{NH}_3 = 14.01 \text{ g/mol} + (3 \times 1.008 \text{ g/mol}) = 17.034 \text{ g/mol}
    • C. Molar mass of CO2=12.01 g/mol+(2×16.00 g/mol)=44.01 g/mol\text{CO}_2 = 12.01 \text{ g/mol} + (2 \times 16.00 \text{ g/mol}) = 44.01 \text{ g/mol}
    • D. Molar mass of Cl2=2×35.45 g/mol=70.90 g/mol\text{Cl}_2 = 2 \times 35.45 \text{ g/mol} = 70.90 \text{ g/mol}
  3. Compare the molar masses.

    The molar masses are:

    • Hydrogen: 2.016 g/mol2.016 \text{ g/mol}
    • Ammonia: 17.034 g/mol17.034 \text{ g/mol}
    • Carbon dioxide: 44.01 g/mol44.01 \text{ g/mol}
    • Chlorine: 70.90 g/mol70.90 \text{ g/mol}

    Chlorine (Cl2\text{Cl}_2) has the largest molar mass (70.90 g/mol70.90 \text{ g/mol}).

  4. Conclude which gas has the smallest rate of diffusion.

    According to Graham's Law, the gas with the largest molar mass will have the smallest rate of diffusion. Therefore, chlorine has the smallest rate of diffusion.

    The final answer is D\boxed{\text{D}}.

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