Multiple Choice
According to Graham's law, what is the ratio of the rate of effusion of F_2 gas to Cl_2 gas?
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7. Gases
Effusion
Multiple Choice
According to Graham's law of effusion, how many times faster do ammonia (NH_3) molecules effuse compared to carbon monoxide (CO) molecules?
A
1.37 times faster
B
2.00 times faster
C
1.00 times faster
D
0.73 times faster
Verified step by step guidance1
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:
\[\frac{\text{rate}_1}{\text{rate}_2} = \sqrt{\frac{M_2}{M_1}}\]
where \(\text{rate}_1\) and \(\text{rate}_2\) are the effusion rates of gases 1 and 2, and \(M_1\) and \(M_2\) are their molar masses.
Identify the gases involved: ammonia (NH\(_3\)) and carbon monoxide (CO). Assign ammonia as gas 1 and carbon monoxide as gas 2 for the formula.
Calculate the molar masses of each gas:
- For NH\(_3\): Nitrogen (N) has an atomic mass of approximately 14 g/mol, and Hydrogen (H) has about 1 g/mol. So, \(M_{NH_3} = 14 + 3 \times 1 = 17\) g/mol.
- For CO: Carbon (C) is about 12 g/mol, Oxygen (O) is about 16 g/mol. So, \(M_{CO} = 12 + 16 = 28\) g/mol.
Substitute the molar masses into Graham's law formula to find the relative rate of effusion of ammonia compared to carbon monoxide:
\[\frac{\text{rate}_{NH_3}}{\text{rate}_{CO}} = \sqrt{\frac{28}{17}}\]
Evaluate the square root expression to determine how many times faster ammonia effuses compared to carbon monoxide. This value will tell you the relative speed of effusion.
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