# A sample of diatomic gas A has three times the mass of an equal volume of gas B under the same conditions. What is the ratio of the atomic mass of A to that of B?

Mar 15, 2017

The atomic mass of $\text{A}$ is 1.5 times the atomic mass of $\text{B}$.

#### Explanation:

Let's say that the formula of Gas A is ${\text{A}}_{2}$ and the formula of Gas B is $\text{B}$.

Avogadro's Law tells us that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Thus, if Gas A has three times the mass of an equal volume of Gas B, a molecule of Gas A must have three times the mass of an atom of Gas B.

But a molecule of Gas A contains two atoms of $\text{A}$.

Hence each atom of $\text{A}$ has $\frac{3}{2} = 1.5$ times the mass of an atom of $\text{B}$.