Problem 81 - Chemistry: An Atoms-Focused Approach

Question

How does the density of a gas sample change when (a) its pressure is increased and (b) its temperature is decreased?

Step-by-Step Solution

Answer

Answer: When the pressure of a gas sample is increased, its density increases. When the temperature of a gas sample is decreased, its density also increases.

Step 1: Density of a gas equation

Since P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin, let's define "m" as the mass of the gas and "M" as its molar mass. Then, the density of the gas (ρ) can be given as: ρ = m/V As mass (m) can be represented as nM, where n is the number of moles and M is the molar mass, we have: ρ = nM/V Now, let's rewrite the Ideal Gas Law equation PV = nRT in terms of the number of moles (n): n = PV/RT Substitute this equation into our density equation: ρ = (PV/RT)M

Step 2: Analyze the impact of pressure increase on density

Now we need to study the relationship between the density (ρ) and pressure (P), while keeping the other variables constant. From ρ = (PV/RT)M, we can see that if the pressure increases, the density of the gas will also increase, while the temperature and molar mass remain constant. Thus, when the pressure of the gas sample is increased, its density will increase.

Step 3: Analyze the impact of temperature decrease on density

Now we need to study the relationship between the density (ρ) and temperature (T), while keeping the other variables constant. From ρ = (PV/RT)M, we can see that if the temperature decreases, the density of the gas will increase, while the pressure and the molar mass remain constant. Thus, when the temperature of the gas sample is decreased, its density will increase. In conclusion: a) When the pressure of a gas sample is increased, its density increases. b) When the temperature of a gas sample is decreased, its density increases.