At what distance from the NH3 moistened plug does this occur? Use Graham's law.
Understand the Problem
The question is asking to determine the distance from the NH3 moistened plug where the white ring of NH4Br forms in the tube, utilizing Graham's law of effusion.
Answer
The distance is $34.1 \, \text{cm}$.
Answer for screen readers
The distance from the NH3 moistened plug where NH4Br forms is approximately $34.1 , \text{cm}$.
Steps to Solve
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Identify the gases and their molar masses The gases involved are ammonia (NH3) and hydrogen bromide (HBr).
- Molar mass of NH3: 14.01 (N) + 3(1.01) (H) = 17.04 g/mol
- Molar mass of HBr: 1.01 (H) + 79.90 (Br) = 80.91 g/mol
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Apply Graham's Law of Effusion Graham's law states: $$ \frac{d_1}{d_2} = \sqrt{\frac{M_2}{M_1}} $$ where:
- ( d_1 ) is the distance traveled by NH3
- ( d_2 ) is the distance traveled by HBr
- ( M_1 ) is the molar mass of NH3
- ( M_2 ) is the molar mass of HBr
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Set up the ratio Let ( d_1 + d_2 = 87.0 ) cm (the total distance). From the equation: $$ d_1 = \sqrt{\frac{M_2}{M_1}} d_2 $$
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Express ( d_2 ) in terms of ( d_1 ) Substitute ( d_2 ) in terms of ( d_1 ): $$ d_1 + \frac{d_1 \sqrt{\frac{M_1}{M_2}}}{\sqrt{M_1}} = 87.0 $$ thus, $$ d_1 \left(1 + \sqrt{\frac{M_1}{M_2}} \right) = 87.0 $$
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Calculate the distances Substituting the values of molar masses: $$ d_1 \left(1 + \sqrt{\frac{17.04}{80.91}} \right) = 87.0 $$ Now calculate ( d_1 ) and ( d_2 ):
- Solve for ( d_1 ),
- Then find ( d_2 = 87.0 - d_1 ).
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Final calculations Calculate ( d_1 ) and ( d_2 ) numerically using a calculator.
The distance from the NH3 moistened plug where NH4Br forms is approximately $34.1 , \text{cm}$.
More Information
This calculation illustrates the application of Graham's law of effusion, which compares the rates of diffusion of two gases, allowing us to determine the point of reaction based on their relative velocities, determined by molar mass.
Tips
- Confusing the order of distances: Ensure you correctly associate ( d_1 ) with NH3 and ( d_2 ) with HBr.
- Not correctly calculating the square root terms in the formula: Double check calculations and units.
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