Problem 16 - Chemistry An Atoms First Approach

Question

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

Step-by-Step Solution

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 1: 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: \[ Density = \frac{Mass}{Volume} \]

Step 2: 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.

Step 3: 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.

Step 4: 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.

Step 5: 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.