Chapter 16, Problem 89A

Create a table of concentrations, starting with 0.100Mconcentrations of all reactants, that you would proposein order to establish the rate law for the reaction $aA+bB+cD\to products$ using the method ofinitial rates.

Interpretation Introduction

Interpretation:

A table of concentrations starting with 0.100 M concentrations of all reactants needs to be constructed in order to establish the rate law for the reaction $aA+bB+cD\to \text{products}$ using the method of initial rates.

Concept introduction:

The rate law for a reaction, $aA\to \text{products}$ is given by the formula,

$rate=k{\left[A\right]}^m$

Where, [A] is the concentration of reactant A, k is the specific rate constant and exponent m is the order of the reactant.

Answer to Problem 89A

A table of concentrations, starting with 0.100 M concentrations of all reactants, in order to establish the rate law for the reaction $aA+bB+cD\to \text{products}$ using the method of initial rates is given below.

Trial	Initial [A] ( M)	Initial [B] ( M)	Initial [C] ( M)
1	0.100 M	0.100 M	0.100 M
2	0.200 M	0.100 M	0.100 M
3	0.200 M	0.200 M	0.100 M
4	0.200 M	0.200 M	0.200 M

Explanation of Solution

The rate law for the reaction, $aA+bB+cD\to \text{products}$ is given by $rate=k{\left[A\right]}^m{\left[B\right]}^n{\left[C\right]}^l$ Here, [A] is the concentration of reactant A, [B] is the concentration of reactant B, [C] is the concentration of reactant C. k is the specific rate constant and m, n, l are the orders corresponding to their reactants.

Initial rate method is used in order to establish the rate law for the reaction experimentally.

With 3 reactants combined in a successive trail, the initial method uses a minimum of 4 trails having different initial amounts of the reactant A and B to study the effect of each reactant has on the reaction rate.

A table of concentrations, starting with 0.100 M concentrations of all reactants, in order to establish the rate law for the reaction $aA+bB+cD\to \text{products}$ using the method of initial rates is given below.

Trial	Initial [A] ( M)	Initial [B] ( M)	Initial [C] ( M)
1	0.100 M	0.100 M	0.100 M
2	0.200 M	0.100 M	0.100 M
3	0.200 M	0.200 M	0.100 M
4	0.200 M	0.200 M	0.200 M

From the above trials, if trial 1 has a reaction rate of $1\times {10}^{-3}M/s$ while trial 2 has a reaction rate of $4\times {10}^{-3}M/s$, then, the order of A would be 2 because withing the given reaction rate, ${\left[\text{2A}\right]}^{\text{2}}\text{=}\text{4}\left[\text{A}\right]$

Conclusion

A table of concentrations, establishing the rate law for the reaction using the method of initial rates is given below.

Trial	Initial [A] ( M)	Initial [B] ( M)	Initial [C] ( M)
1	0.100 M	0.100 M	0.100 M
2	0.200 M	0.100 M	0.100 M
3	0.200 M	0.200 M	0.100 M
4	0.200 M	0.200 M	0.200 M