Math

Question10) Identify the molecule that effuses the fastest. A) Ar B) CH4\mathrm{CH}_{4} C) CO2\mathrm{CO}_{2} D) CO

Studdy Solution

STEP 1

1. We are comparing the rates of effusion of different gases.
2. The rate of effusion is inversely proportional to the square root of the molar mass of the gas (Graham's law of effusion).

STEP 2

1. Understand Graham's law of effusion.
2. Calculate the molar masses of the given molecules.
3. Determine which molecule has the smallest molar mass.
4. Conclude which molecule effuses the fastest.

STEP 3

Graham's law of effusion 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:
Rate of effusion1Molar mass\text{Rate of effusion} \propto \frac{1}{\sqrt{\text{Molar mass}}}

STEP 4

Calculate the molar mass of each molecule:
- A) Ar (Argon): The molar mass of Ar is approximately 39.95 g/mol. - B) CH4\mathrm{CH}_{4} (Methane): The molar mass is 12.01+4×1.01=16.0512.01 + 4 \times 1.01 = 16.05 g/mol. - C) CO2\mathrm{CO}_{2} (Carbon dioxide): The molar mass is 12.01+2×16.00=44.0112.01 + 2 \times 16.00 = 44.01 g/mol. - D) CO (Carbon monoxide): The molar mass is 12.01+16.00=28.0112.01 + 16.00 = 28.01 g/mol.

STEP 5

Identify the molecule with the smallest molar mass:
- Ar: 39.95 g/mol - CH4\mathrm{CH}_{4}: 16.05 g/mol - CO2\mathrm{CO}_{2}: 44.01 g/mol - CO: 28.01 g/mol
The molecule CH4\mathrm{CH}_{4} has the smallest molar mass.

STEP 6

According to Graham's law, the molecule with the smallest molar mass effuses the fastest. Therefore, CH4\mathrm{CH}_{4} effuses the fastest.
The molecule that effuses the fastest is:
CH4 \boxed{\mathrm{CH}_{4}}

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