Chapter 16, Problem 102A

Interpretation Introduction

Interpretation:

The instantaneous rate of reaction needs to be determined when the concentration of phenolphthalein is 0.0025 M and the rate constant of the reaction is $\text{1}\text{.0}\text{×}{\text{10}}^{-\text{2}}{\text{s}}^{-\text{1}}$

Concept introduction:

The rate law for a reaction, $aA\to \text{products}$ id 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 102A

The instantaneous rate of reaction when the concentration of phenolphthalein is 0.0025 M is $2.5\times {10}^{-5}\frac{\text{mol}}{\text{L}\text{.s}}$

Explanation of Solution

We consider table 16.6 to know the value of concentration of phenolphthalein with time.

Concentration of phenolphthalein (M)	Time (s)
0.0050	0.0
0.0040	22.3
0.0020	91.6
0.0010	160.9
0.00050	230.3
0.00015	350.7

The given rate law is $\text{rate}=k{\left[\text{phenolpthalein}\right]}^1$, here, the rate constant is $k=1.0\times {10}^{-2}{\text{s}}^{\text{-1}}$

Using this value, we calculate the rate of the reaction.

$\text{rate}=k{\left[\text{phenolpthalein}\right]}^1$

$\begin{array}{l}=(1.0\times {10}^{-2}{\text{s}}^{\text{-1}}){\left(0.0025M\right)}^1\\ =\left(1.0\times {10}^{-2}\frac{1}{\text{s}}\right)\left(0.0025\frac{\text{mol}}{\text{L}}\right)\\ =\left(1.0\times {10}^{-2}\times 0.0025\right)\frac{\text{mol}}{\text{L}\text{.s}}\\ =2.5\times {10}^{-5}\frac{\text{mol}}{\text{L}\text{.s}}\end{array}$

Conclusion

The rate of the reaction is $2.5\times {10}^{-5}\frac{\text{mol}}{\text{L}\text{.s}}$