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# Mass Ratio Calculation

## The mass ratio of an element discusses the mass of an element in combination with another element. Learn these important chemistry building blocks.

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Mass Ratio Calculation

Credit: Laura Guerin
Source: CK-12 Foundation

#### What are the similarities and differences between these two equations?

One of the fundamental laws of chemistry deals with the fact that we cannot (using chemical means) create or destroy matter.  When a reaction is run, the number of atoms of each specific type must be the same on both sides of the equation.  For some materials, it turns out that one element can combine with a second element in more than one ratio.  Carrying out mass ratio calculations helped establish the law of multiple proportions.

### Mass Ratio Calculations

Copper reacts with chlorine to form two compounds.  Compound A consists of 4.08 g of copper for every 2.28 g of chlorine.  Compound B consists of 7.53 g of copper for every 8.40 g of chlorine.  What is the lowest whole number mass ratio of copper that combines with a given mass of chlorine?

Step 1:  List the known quantities and plan the problem.

Known

Compound A = 4.08 g Cu and 2.28 g Cl

Compound B = 7.53 g Cu and 8.40 g Cl

Apply the law of multiple proportions to the two compounds.  For each compound, find the grams of copper that combine with 1.00 g of chlorine by dividing the mass of copper by the mass of chlorine.  Then, find the ratio of the masses of copper in the two compounds by dividing the larger value by the smaller value.

Step 2:  Calculate.

Compound A  \begin{align*}\frac{4.08 \ \text{g Cu}}{2.28 \ \text{g Cl}}=\frac{1.79 \ \text{g Cu}}{1.00 \ \text{g Cl}}\end{align*}

Compound B  \begin{align*}\frac{7.53 \ \text{g Cu}}{8.40 \ \text{g Cl}}=\frac{0.896 \ \text{g Cu}}{1.00 \ \text{g Cl}}\end{align*}

Compare the masses of copper per gram of chlorine in the two samples.

\begin{align*}\frac{1.79 \ \text{g Cu (in compound A)}}{0.896 \ \text{g Cu (in compound B)}}=\frac{2.00}{1}=2:1\end{align*}

The mass ratio of copper per gram of chlorine in the two compounds is 2:1.

The ratio is a small whole-number ratio.  For a given mass of chlorine, compound A contains twice the mass of copper as does compound B.

Credit: User:Chemicalinterest/Wikimedia Commons
Source: http://commons.wikimedia.org/wiki/File:Copper_chloride_crystals.JPG

CuCl2.[Figure2]

### Summary

• The mass ratio gives the mass of an element that is found in combination with another element.

### Review

1. What does the mass ratio tell us?
2. In the compound CH4, what is the carbon:hydrogen mass ratio?
3. Methane is CH4 and ethane is C2H6. What is the mass ratio of carbon per gram of hydrogen in the two compounds?

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