Final answer:
The density of N₂O gas at 45.2°C and 1.53 atm is calculated using the Ideal Gas Law, with the equation rearranged to solve for density as ρ = (P*M)/(R*T), where the variables represent pressure, molar mass, ideal gas constant, and temperature respectively.
Step-by-step explanation:
To calculate the density of N₂O gas at a specific temperature and pressure, we can use the Ideal Gas Law, which relates the pressure, volume, temperature, and number of moles of a gas.
The Ideal Gas Law is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, convert the temperature to Kelvin: T = 45.2°C + 273 = 318.2 K.
Next, use the Ideal Gas Law rearranged to solve for the density (ρ) of the gas: ρ = (P*M)/(R*T) where M is the molar mass.
Given:
Pressure (P) = 1.53 atm,
Temperature (T) = 318.2 K,
The molar mass of N₂O (M) = 44.0 g/mol,
The ideal gas constant (R) = 0.0821 L.atm.mol⁻¹.K⁻¹.
Substituting the values into the density equation, we get:
ρ = (1.53 atm * 44.0 g/mol) / (0.0821 L.atm.mol⁻¹.K⁻¹ * 318.2 K).
Calculating the density yields the final value.