Question

Solve for x, where M is molar and s is seconds. x=(7.4×10^3M^−2s^−1)(0.29M)^3

Answer 1

x = 1.8 x 10² Ms⁻¹.

Step-by-step explanation:

First, let's see the expression of x:

`x=(7.4\cdot10^3M^(-2)s^(-1))\cdot(0.29M)^3.`

Let's eliminate the parenthesis:

`x=7.4\cdot10^3M^(-2)s^(-1)\cdot0.29^3M^3.`

We can 'cancel' the M (molar) term. Remember that we have the following exponent law:

`a^ma^n=a^(m+n).`

So we can apply this to M: we have to sum -2 and 3 to obtain 1 (-2+3 = 1):

`x=7.4\cdot10^3Ms^(-1)\cdot0.29^3.`

And finally, we just have to multiply 7.4 x 10³ by 0.29³ using the correct units that we already know (Ms⁻¹), as follows:

`x=180.48Ms^(-1)\approx1.8\cdot10^2Ms^(-1).`

As we have to give the answer with 2 significant figures, the answer would be x = 1.8 x 10² Ms⁻¹.