Chapter 7.2, Problem 37PPE

To determine

To find: The number of molecules that river discharges every minute and also the use of unit analysis and properties to find the solution and making calculation easier.

Answer to Problem 37PPE

The number of molecules that river discharges every minute are $3.\text{417}\times {10}^{34}\text{molecules}$ and the property to be used for make the calculation easier in scientific notation is the exponential property of multiplication.

Explanation of Solution

Given information:

The number of molecules in one liter is $3.35\times {10}^{25}$ and the amount of water discharges every second is $1.7\times {10}^7\text{L}$ .

Calculation:

Formula for exponential property of multiplication is:

  $a^m\times a^n=a^{m+n}$

The given amount of water discharges by Mississippi river in liter per second is:

  $\frac{1.7\times {10}^7\text{L}}{\text{1}\text{sec}}$

Formula to convert liter per second into liter per minute is:

  $1\frac{\text{L}}{\sec }=60\frac{\text{L}}{\min }$

Multiply $1.7\times {10}^7$ to both sides in the above expression.

  $\begin{array}{c}1.7\times {10}^7\times 1\frac{\text{L}}{\text{sec}}=1.7\times {10}^7\times 60\frac{\text{L}}{\text{min}}\\ =1.7\times {10}^7\times 6\times 10\frac{\text{L}}{\text{min}}\\ =10.2\times {10}^{7+1}\frac{\text{L}}{\text{min}}\\ =10.2\times {10}^8\frac{\text{L}}{\text{min}}\end{array}$

The given number of molecules in one liter is:

  $1\text{L}=3.35\times {10}^{25}\text{molecules}$

To determine the number of molecules in $10.2\times {10}^8\text{L}$ , multiply the both sides of the above expression by $10.2\times {10}^8$ .

  $\begin{array}{c}10.2\times {10}^8\times 1\text{L}=10.2\times {\text{10}}^{\text{8}}\times 3.35\times {10}^{25}\text{molecules}\\ \text{=10}\text{.2}\times \text{3}\text{.35}\times {\text{10}}^{\text{8}}\times {10}^{25}\text{molecules}\\ =34.17\times {\text{10}}^{\text{8}}\times {10}^{25}\text{molecules}\\ =3.417\times 10\times {\text{10}}^{\text{8}}\times {10}^{25}\text{molecules}\end{array}$

Apply the exponential property of multiplication in the above expression.

  $\begin{array}{c}10.2\times {10}^8\times 1\text{L}=3.417\times {10}^1\times {\text{10}}^{\text{8}}\times {10}^{25}\text{molecules}\\ =3.417\times {10}^{1+8+25}\text{molecules}\\ =3.\text{417}\times {10}^{34}\text{molecules}\end{array}$

Therefore, the number of molecules that river discharges every minute are $3.\text{417}\times {10}^{34}\text{molecules}$ and the property to be used for make the calculation easier in scientific notation is the exponential property of multiplication.