Chemistry
Chemistry
4th Edition
ISBN: 9780078021527
Author: Julia Burdge
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 14, Problem 22QP

The following gas-phase reaction was studied at 290°C by observing the change in pressure as a function of time in a constant-volume vessel:

ClCO 2 CCl 3 ( g ) 2 COCl 2 ( g )

Determine the order of the reaction and the rate constant based on the following data.

Time (s)

P(mmHg)

0

15.76

181

18.88

513

22.79

1164

27.08

where P is the total pressure.

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation:

The order of the reaction and the rate constant, based on the given data, areto be determined.

Concept introduction:

The power of the concentration of reactants is called the order of the reaction.

According to the Arrheniusequation, the rate that is dependent on a given temperature is called the rate constant.

Answer to Problem 22QP

Solution: The order of the reaction is first order and the rate constant is 1.08×103.

Explanation of Solution

Given information: The following gas phase reaction was studied at a temperature of 290°C by observing the change in pressure as a function of time in a constant-volume vessel.

The reaction is as follows:

ClCO2CCl3(g)2COCl2(g)

The given data is as follows:

t(s)                  P(mmHg)            _0                       15.76            181                    18.88            513                    22.79             1164                  27.08            

Consider P0 as the pressure of the reactant in the above reaction when the time (t) is 0 and x is considered as the pressure decrease after t. In the abovereaction, if ClCO2CCl3 loses one atmosphere, two atmospheres of COCl2 areformed.

The reaction is as follows:

ClCO2CCl3(g)2COCl2(g)

The pressure data is represented below.

Time        [ClCO2CCl3]            [COCl2]_t=0                P0                             0t=t                P0x                       2x

Therefore, the pressure increases, and the change in pressure (ΔP) is as follows:

(2xx)=x

The data is represented as follows:

t(s)    P(mmHg)   1PClCO2CCl3        ΔP=x        PClCO2CCl3         ln PClCO2CCl3        _0          15.76            0.00              15.76           2.757            0.0635181      18.88             3.12              12.64           2.537            0.0791513      22.79             7.03              8.73             2.167            0.1151164    27.08            11.32             4.44             1.491            0.225

The plot of lnPClCO2CCl3 vs. t will be in a linear form, if the reaction is of the first order. The plot of 1PClCO2CCl3 vs. t will be linear, if the reaction is of the second order.

The plot of lnPClCO2CCl3 vs. t is as follows:

Chemistry, Chapter 14, Problem 22QP , additional homework tip  1

The plot of 1PClCO2CCl3 vs. t is as follows:

Chemistry, Chapter 14, Problem 22QP , additional homework tip  2

The rate constant for the first-order reaction is as follows:

slope=y2y1x2x1=(2.7571.4911164)=(1.2661164)=0.00108 or 1.08×103

The reaction is a first-order reaction, as can be interpreted from the graph. The slope for a first-order reaction is equal to the rate constant (k).

Conclusion

The order of reaction is first order and rate constant is 1.08×103.

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Chapter 14 Solutions

Chemistry

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