Question

At the same conditions of pressure and temperature, ammonia gas is less dense than air. Why is this true?

Short answer

Under the same pressure and temperature conditions, ammonia gas is less dense than air because its molar mass (17 g/mol) is lower than the average molar mass of air (29 g/mol). According to Avogadro's principle, equal volumes of gases have the same number of molecules, so a given volume of ammonia will have a lower mass compared to the same volume of air. Hence, its density, which is defined as mass per unit volume, is lower than that of air.

Step-by-step solution

Recall the definition and formula of density

Density is a property that describes how much mass is present in a given volume. It is defined as mass per unit volume and can be expressed using the formula: \[ Density = \frac{Mass}{Volume} \]

Analyze the composition of air and ammonia

In order to understand the density of air and ammonia, it is necessary to know their compositions. Air is a mixture of gases, mainly nitrogen (N2, 78%), oxygen (O2, 21%), and traces of other gases, including argon and carbon dioxide. The average molar mass of air is approximately 29 g/mol. Ammonia (NH3) is a compound made of one nitrogen atom and three hydrogen atoms. The molar mass of ammonia is 17 g/mol.

Compare the molar masses of air and ammonia

Comparing the molar masses, we can observe that the molar mass of ammonia (17 g/mol) is less than the average molar mass of air (29 g/mol). If the mass of ammonia molecules is less than that of air molecules, it would mean that under identical conditions of temperature and pressure, a specific volume of ammonia will contain fewer molecules and thus, have lower mass compared to the same volume of air.

Apply Avogadro's principle

Under the same conditions of pressure and temperature, equal volumes of gases contain the same number of molecules (Avogadro's principle). So, for a given volume, the mass of ammonia will be lower than the mass of air since its molar mass is lower, meaning a lighter composition.

Explain the difference in density

As we established in Step 1, density is mass per unit volume. Since the mass of ammonia is lower than that of air for a given volume under the same pressure and temperature conditions, ammonia will be less dense than air. This is the reason why ammonia gas is less dense compared to air.