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To find:
The rate law and units of the rate constant (by using the units M for concentration and s for time) for the given reactions.
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Answer to Problem 13.49QA
Solution:
a) The reaction of oxygen atoms with NO2 is first order in both reactants.
Rate law is Rate=k[O][NO2]
Unit of rate constant is M-1s-1
b) The reaction between NO and Cl2 is second order in NO and first order in Cl2
Rate law is Rate=k[NO2]2[Cl2]
Unit of rate constant is M-2s-1
c) The reaction between Cl2 and chloroform CHCl3 is first order in CHCl3 and one half order in Cl2.
Rate law is Rate=k[CHCl3][Cl2]1/2
Unit of rate constant is M-1/2s-1
d) The decomposition of ozone (O3) to O2 is second order in O3 and an order of -1 in O atoms.
Rate law is Rate=k[O3]2[O]-1
Unit of rate constant is s-1
Explanation of Solution
1) Concept:
i. Rate law:
Therefore,
Rate ∝[reactant]m
Hence rate law will be,
Rate=k[reactant]m….. (equation 1)
where k is the rate constant, and m is the order of reaction with respect to the reactant.
ii. Unit of reaction rate:
Rate is change in concentration per unit time, so the unit for rate is M/s(or M s-1)
Here unit for concentration is M(molarity) and time is s(second).
.
iii. Unit of rate constant k:
From equation 1,
k=Rate[reactant]m
Units of rate are M s-1 and that of concentration is M. Therefore, units of rate constant are:
k=M s-1Mm=M1-ms-1
2) Calculations:
a. The reaction of oxygen atoms with NO2 is first order in both reactants.
Rate law:
The reaction is first order in both reactants. Therefore, the exponents of concentration of both reactants is 1, and the rate law is:
Rate=k[O][NO2]
Units of rate constant k:
Rearranging the rate law for rate constant, we get:
k=Rate[O][NO2]
k=M s-1M×M
k=s-1M
k=M-1s-1
b. The reaction between NO and Cl2 is second order in NO and first order in Cl2.
Rate law:
The reaction is second order in NO and first order in Cl2. Therefore, the exponents of concentrations of NO and of Cl2 are 2 and 1 respectively.
Therefore, the rate law is:
Rate=k[NO2]2[Cl2]
Unit of rate constant k:
Rearranging this rate law for rate constant, we get:
k=Rate[NO2]2[Cl2]
k=M s-1M2×M
k= s-1M2
k=M-2s-1
c. The reaction between Cl2 and chloroform CHCl3 is first order in CHCl3 and one half order in Cl2.
Rate law:
The reaction is first order in CHCl3 and one half order in Cl2. Therefore, the exponents of concentrations of CHCl3 and Cl2 are 1 and ½ respectively and the rate law is:
Rate=k[CHCl3][Cl2]1/2
Units of rate constant k:
Rearranging the rate equation for rate constant, we get:
k=Rate [CHCl3][Cl2]1/2
k=M s-1 M×M1/2
k= s-1 M1/2
k=M-1/2s-1
d. The decomposition of ozone (O3) to O2 is second order in O3 and an order of -1 in O atoms.
Rate law:
The reaction is second order in O3 and -1 order in O atoms, i.e., the exponents of concentrations of O3 and O atoms are 2 and -1 respectively, and the rate law is
Rate=k[O3]2[O]-1
Units of rate constant k:
Rearranging the rate equation for rate constant, we get:
k= Rate [O3]2[O]-1
k=M s-1 M2×M-1
k=M×M s-1 M×M
k=s-1
Conclusion:
Rate law determines the relation between the concentration of reactants and the rate of reaction. Order with respect to the reactants is the exponent of each reactant in the rate law.k, the constant of proportionality in the rate law, is called the rate constant. The units of k can be found from the rate law.
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Chapter 13 Solutions
Chemistry: An Atoms-Focused Approach (Second Edition)
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