KEY2CHEM

Ratio of Elements in a Compound

Atoms are the smallest building blocks of matter that retain a specific property. A substance that contains only one type of atoms is called an element. For example, the element sodium ($$\require{mhchem}\ce{Na}$$ on the periodic table) is composed of only sodium atoms. Chemical compounds are substances made up of two or more types of atoms. For example, the compound carbon dioxide ($$\require{mhchem}\ce{CO2}$$) is made up of carbon atoms and oxygen atoms. Each molecule (or unit) of $$\require{mhchem}\ce{CO2}$$contains exactly one carbon atom and two oxygen atoms. Conversely, a molecule with a different ratio of carbon to oxygen atoms, such as one carbon and one oxygen atom, would be a different chemical substance with different chemical and physical properties.

Example 1.

A $$100.0 \text{ g}$$ sample of compound $$\require{mhchem}\ce{XY}$$ contains $$50.0 \text{ g}$$ of $$\require{mhchem}\ce{X}$$ and $$50.0 \text{ g}$$ of $$\require{mhchem}\ce{Y}$$. How many grams of $$\require{mhchem}\ce{X}$$ does a $$10.0 \text{ g}$$ sample of compound $$\require{mhchem}\ce{XY}$$ contain?

A. $$0.500 \text{ g}$$

B. $$10.0 \text{ g}$$

C. $$5.00 \text{ g}$$

Solution

C. $$5.00 \text{ g}$$ of element X

The ratio of masses of elements in a compound is always the same for a given compound. If there are $$50.0 \text{ g}$$ of element $$\require{mhchem}\ce{X}$$ in a $$100.0 \text{ g}$$ sample of compound $$\require{mhchem}\ce{XY}$$, then there will be $$5.00 \text{ g}$$ of element $$\require{mhchem}\ce{X}$$ in a $$10.0 \text{ g}$$ sample of compound $$\require{mhchem}\ce{XY}$$, since the ratio masses of the constituent elements in any pure sample of that compound is always the same.

Example 2.

Which is a pure substance?

A. tea

B. pure water

C. ocean water

Solution

B. pure water

A pure sample contains particles (or units) of one specific atom or molecule; a mixture contains particles (or units) of more than one specific atom or molecule. Both tea and ocean water are examples of mixtures, as they contain many substances in varying proportions. In pure water ($$\require{mhchem}\ce{H2O}$$), the elements hydrogen and oxygen are present in a consistent mass ratio.

Example 3.

Two samples of sodium chloride are decomposed into their elements. The first sample was found to contain $$16.8\text{ g}$$ of sodium and $$25.9\text{ g}$$ chlorine. If the second sample contains $$12.6\text{ mg}$$ of chlorine, how many mg of sodium does it contain?

A. $$19.4\text{ mg}$$

B. $$8.17\text{ mg}$$

C. $$34.5\text{ mg}$$

Solution

B. $$8.17\text{ mg}$$

Since the two samples are the same chemical compound, the ratio of the masses of their elements is the same. This can be determined using cross multiplication. $$\frac{16.8\text{ g }\require{mhchem}\ce{ Na}}{25.9\text{ g }\require{mhchem}\ce{ Cl}} = \frac{ x\text{ mg }\require{mhchem}\ce{ Na}}{12.6\text{ mg }\require{mhchem}\ce{ Cl}}$$