Chapter 16, Problem 74A

Interpretation Introduction

Interpretation:

To write down the rate law for the decay of strontium-90.

Concept introduction:

In a chemical reaction, the reactants are written on the left side of the equation and the product is written on the right side.

The average rate of a reaction can be given by the formula,

Average reaction rate $\text{=}-\frac{\text{Δ}\left[\text{reactant}\right]}{\text{Δt}}$

Here, $\text{Δ}\left[\text{reactant}\right]$ = change in the concentration of the reactant

Answer to Problem 74A

The rate law for the decay of the element strontium-90 is $\text{rate}=k{\left[{}^{90}\text{Sr}\right]}^m$

Explanation of Solution

Radioactive isotope strontium-90 decays to yttrium-90 and a beta particle. The rate law for strontium-90 is $\text{rate=}k{\left[\text{A}\right]}^m$, here, [A] is the concentration of reactant A, exponent m is the order of the reactant and k is the specific rate constant.

If we consider strontium-90 $\left({}^{\text{90}}\text{Sr}\right)$, the order is m = 1, but the value of k is unknown. We can use these values to calculate the rate law of the reaction.

$\begin{array}{l}\text{rate}=k{\left[\text{A}\right]}^m\\ \text{rate}=k{\left[{}^{90}\text{Sr}\right]}^1=k{\left[{}^{90}\text{Sr}\right]}^m\end{array}$

There, the rate law for the decay of the element strontium-90 is $\text{rate}=k{\left[{}^{90}\text{Sr}\right]}^m$

Conclusion

The rate law for the decay of the element strontium-90 is given as,

$\text{rate}=k{\left[{}^{90}\text{Sr}\right]}^m$