Chapter 3, Problem 104A

Interpretation Introduction

Interpretation : The number of grams of strontium obtained from one cubic meter of seawater is to be calculated.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. The dimensional analysis is an effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another.

Answer to Problem 104A

The number of grams of strontium obtained from one cubic meter of seawater is $8.0{\text{g/m}}^3$ .

Explanation of Solution

Given information :

The seawater contains $8.0\times {10}^{-1}\text{cg}$ .

It is known that $\text{1}\text{g}\text{=}{10}^2\text{cg}$ , $\text{1}\text{kg}\text{=}{10}^3\text{g}$ , $\text{1}{\text{m}}^3\text{=}{10}^6{\text{cm}}^3$ and $\text{1}\text{g}\text{=}1{\text{cm}}^3$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is $\text{cg/kg}\to {\text{g/m}}^3$ .

The conversion of the units is given as:

  $\begin{array}{c}8.0\times {10}^{-1}\text{cg/kg}=\frac{8.0\times {10}^{-1}\cancel{\text{cg}}}{1\cancel{\text{kg}}}\times \frac{1\cancel{\text{kg}}}{{10}^3\cancel{\text{g}}}\times \frac{\text{1}\text{.0}\cancel{\text{g}}}{1\cancel{{\text{cm}}^3}}\times \frac{{10}^6\cancel{{\text{cm}}^3}}{1{\text{m}}^3}\times \frac{1\text{g}}{{10}^2\cancel{\text{cg}}}\\ =8.0{\text{g/m}}^3\end{array}$

The gram of Strontium is $8.0{\text{g/m}}^3$ .