Question

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

Short answer

At the same conditions of pressure and temperature, ammonia gas is less dense than air because its molar mass (17.04 g/mol) is lower than the molar masses of nitrogen (28.02 g/mol) and oxygen (32.00 g/mol), which are the main components of air. Since density is directly proportional to molar mass, ammonia's lower molar mass results in a lower density compared to air.

Step-by-step solution

Define density

Density is a measure of mass per unit volume. Mathematically, it can be defined as: $density=\frac{mass}{volume}$ For a gas, density can also be described using the Ideal Gas Law given as: $PV=nRT$ Where: P = Pressure of the gas V = Volume of the gas n = Number of moles of the gas R = Ideal Gas constant T = Temperature of the gas in Kelvin Rearranging the Ideal Gas Law formula in terms of n/V, we have $\frac{n}{V}=\frac{P}{RT}$ Multiplying both left and right side of the equation by the molar mass (M) of the gas: $density=\frac{nM}{V}=\frac{MP}{RT}$ From this equation, we understand that at the same conditions of pressure and temperature (P and T), the density of a gas is directly proportional to its molar mass.

Determine the molar masses of ammonia, nitrogen, and oxygen

Next, we need to find the molar masses of ammonia (NH3), nitrogen (N2), and oxygen (O2). We can find the molar mass by summing the atomic masses of the elements in each molecule. - Ammonia (NH3): one nitrogen atom and three hydrogen atoms M(NH3) = 1 * M(N) + 3 * M(H) = 1 * 14.01 + 3 * 1.01 = 17.04 g/mol - Nitrogen (N2): two nitrogen atoms M(N2) = 2 * M(N) = 2 * 14.01 = 28.02 g/mol - Oxygen (O2): two oxygen atoms M(O2) = 2 * M(O) = 2 * 16.00 = 32.00 g/mol

Compare the molar masses to explain density

Now that we have the molar masses of ammonia, nitrogen, and oxygen, we can compare them in relation to their densities at the same pressure and temperature. According to the density formula from Step 1, the density of a gas is directly proportional to its molar mass. Since ammonia (NH3) has a lower molar mass (17.04 g/mol) than nitrogen (N2, 28.02 g/mol) and oxygen (O2, 32.00 g/mol)—the main components of air—, its density is lower than the density of air under the same conditions of pressure and temperature. Therefore, ammonia gas is less dense than air.