Chapter 9.5, Problem 52LC

Interpretation Introduction

Interpretation: Whether the compounds A and B are the same or not is to be predicted and the lowest whole-number mass ratio of copper in the two compounds is to be stated.

Concept Introduction : According to the law of multiple proportions, the two elements form more compounds, than the ratios of the second element’s masses, which combines with the fixed first’s element mass will always be ratios of small whole numbers.

Answer to Problem 52LC

Both compounds A and B are different as copper and chlorine are present in different ratios. The lowest whole-number mass ratio of copper in the two compounds is 2:1.

Explanation of Solution

It is given that copper forms two compounds with chlorine. One contains 32.10 g of copper and 17.90 g of chlorine. The other contains 23.64 g of copper and 26.37 g of chlorine.

The ratio of copper and oxygen in both compounds is:

  $\begin{array}{l}\text{Compound}\text{A}=\frac{32.10\text{g}\text{Cu}}{\text{17}\text{.90}\text{g}\text{Cl}}=1.8\\ \text{Compound}\text{B}=\frac{23.64\text{g}\text{Cu}}{\text{26}\text{.37}\text{g}\text{Cl}}=0.9\end{array}$

The ratio is different so both compounds are different. The ratio of copper in both compounds is calculated as follows:

The denominator of each compound is to be made 1. So,

  $\begin{array}{l}\text{Compound}\text{A}=\frac{32.10\text{g}\text{Cu}}{\text{17}\text{.90}\text{g}\text{Cl}}=\frac{\frac{32.10\text{g}\text{Cu}}{\text{17}\text{.90}}}{\frac{\text{17}\text{.90}\text{g}\text{Cl}}{\text{17}\text{.90}}}=\frac{1.79\text{g}\text{Cu}}{1\text{g}\text{Cl}}\\ \text{Compound}\text{B}=\frac{23.64\text{g}\text{Cu}}{\text{26}\text{.37}\text{g}\text{Cl}}=\frac{\frac{23.64\text{g}\text{Cu}}{\text{26}\text{.37}}}{\frac{\text{26}\text{.37}\text{g}\text{Cl}}{\text{26}\text{.37}}}=\frac{0.90\text{g}\text{Cu}}{1\text{g}\text{Cl}}\end{array}$

Now, compound the mass of each copper separately.

  $\begin{array}{c}\text{Ratio}=\frac{1.79\text{g}\text{Cu}}{0.90\text{g}\text{Cu}}\\ =2:1\end{array}$

Therefore, the lowest whole-number mass ratio of copper in the two compounds is 2:1.