To identify a diatomic gas (X_{2}), a researcher carried out the following experiment: She weighed an empty 5.4-L bulb, then filled it with the gas at 1.10 atm and 28.0 °C and weighed it again. The difference in mass was 6.7 g. Identify the gas.

Express your answer as a chemical formula.

Pressure and temperature affect the amount of space between gas molecules, which affects the volume and, therefore, the density of the gas since

$\mathbf{density}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{volume}}$

The molar mass of a substance, however, is a constant and can be used to identify an unknown gas sample. Molar mass is found by dividing the mass of a sample (in grams) by the number of moles in that sample. The number of moles of gas can be calculated using the ideal gas law

$\mathbf{PV}\mathbf{=}\mathbf{nRT}$

which can be rearranged as

$\mathbf{n}\mathbf{=}\frac{\mathbf{PV}}{\mathbf{RT}}$

Given the number of moles of a gas and its molar mass, you can calculate the mass of the gas. Since density is equal to the ratio of the mass and volume, you can then divide by the volume to find density.

Alternatively, you can use the ratio n/V from the ideal gas equation where *n* is the number of moles and *V* is the volume, and convert from moles per unit volume to grams per unit volume using molar mass.

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