Answered: A gas mixture with the same number of…

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

A gas mixture with the same number of moles of CO₂ and H₂ was prepared and heated to 700K where the initial total pressure was 12 Atm. The equilibrium constant for the reaction:

CO₂ (g) + H₂ (g) ⇄ CO(g) + H₂O(g) is 23 at 700 K.

What is the CO partial pressure after equilibrium is established?

Expert Solution

Step 1

Recall the given reaction and find expression of K_p

$C O_{2} (g) + H_{2} (g) \to C O (g) + H_{2} O (g) K_{p} = \frac{(P_{C O}) \times (P_{H_{2} O})}{(P_{C O_{2}}) \times (P_{H_{2}})} K_{p} f o r t h i s r e a c t i o n i s 23 a t 700 K$

$A s i n i t i a l t o t a l p r e s s u r e i s 12 a t m a n d m o l e s o f e a c h r e a c \tan t i s s a m e . S o i t i s e v i d e n t t h a t i n i t i a l p r e s s u r e o f C O_{2} i s 6 a t m a n d i n i t i a l p r e s s u r e o f H_{2} i s 6 a t m$

Step 2

Construct ICE table

$C O_{2} (g) + H_{2} (g) \to C O (g) + H_{2} O (g) I n i t i a l p r e s s u r e 6 6 0 0 (a t m) P r e s s u r e - x - x x x C h a n g e (a t m) E q u i l i b r i u m (6 - x) (6 - x) x x P r e s s u r e (a t m) F i n d p a r t i a l p r e s s u r e o f a l l r e a c \tan t s a n d p r o d u c t s P_{C O_{2}} = (6 - x), P_{H_{2}} (6 - x), P_{C O} = x, P_{H_{2} O} = x S u b s t i t u t e e x p r e s s i o n o f K_{p} w i t h t h i s v a l u e s \frac{{(x)}^{2}}{{(6 - x)}^{2}} = 23 o r, \frac{x}{6 - x} = 4.796 x = 4.964 S o p a r t i a l p r e s s u r e o f C O i s 4.964 a t m$

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