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

To determine the reason behind the difference in densities, we need to compare the molecular masses of ammonia and air. Ammonia (NH₃) is composed of one nitrogen atom and three hydrogen atoms. The molecular mass of nitrogen is 14 u (atomic mass units) and the molecular mass of hydrogen is 1 u. The molecular mass of ammonia (NH₃) can be calculated as follows: Molecular mass of NH₃ = Molecular mass of N + 3 × Molecular mass of H Molecular mass of NH₃ = 14 u + 3 × 1 u = 17 u Air is primarily composed of nitrogen gas (N₂) and oxygen gas (O₂), with molecular masses of 28 u and 32 u, respectively. As air is not a single molecule but a mixture of gases, we consider the average molecular mass of the main components to have a general comparison.

The Ideal Gas Law equation is given by: \[ PV = nRT \] Where: P - Pressure V - Volume n - Number of moles R - Ideal gas constant (8.31 J/mol·K) T - Temperature Now, using the relation between moles and mass, we can rewrite the equation as follows: \[ PV = \frac{m}{M} RT \] Where: m - Mass of the gas M - Molecular mass of the gas Rearranging the equation to find the density (ρ = mass/volume) of the gas, we get: \[ ρ = \frac{m}{V} = \frac{PM}{RT} \] From this equation, we can observe that the density (ρ) of a gas is directly proportional to its molecular mass (M) when pressure and temperature are constant.

Since the molecular mass of ammonia gas (17 u) is less than the average molecular mass of the main components of air (approximately 29 u, considering nitrogen and oxygen gases), according to the relation derived in Step 2, the density of ammonia gas will also be lower than that of air under the same temperature and pressure conditions. Therefore, ammonia gas is less dense than air because of its lower molecular mass.