Answered: Because of their different molar…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

Because of their different molar masses, H₂ and D₂ effuse at different rates . (a) If it takes 16.5 min for 0.10 mol of H₂ to effuse, how long does it take for 0.10 mol of D₂ to do so in the same apparatus at the same T and P? (b) Howmany effusion steps does it take to separate an equimolar mix-ture of D₂ and H₂ to 99 mol % purity?

Expert Solution

Step 1

(a)

Given data contains,

Moles of H₂ is $0.10 m o l$ .

Time taken for effusion of H₂ is $16.5 m i n$ .

Moles of D₂ is $0.10 m o l$ .

Molar mass of H₂ is $2.016 g / m o l$ .

Molar mass of D₂ is $4.00 g / m o l$ .

Step 2

The rate of effusion is calculated as,

$\frac{R a t e o f H}{R a t e o f D} = \sqrt{\frac{M o l a r m a s s o f D}{M o l a r m a s s o f H}} \frac{R a t e o f H}{R a t e o f D} = \sqrt{\frac{4.00 g / m o l}{2.016 g / m o l}} \frac{R a t e o f H}{R a t e o f D} = 1.40859$

The time taken is calculated as,

$T i m e D_{2} = (1.40859) (16.5 m i n) T i m e D_{2} = 23.2417 m i n T i m e D_{2} = 23.2 m i n$

The time taken for 0.10 mol of D₂ is $23.2 m i n$ .

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