Answer :
Final answer:
By converting the given temperature to Kelvin and the pressure to Pascal, substituting these into the modified ideal gas law ρ = PM/(RT) along with R and the molar mass of air, one calculates that the density is approximately 1.195 kg/m³, which corresponds to option b).
Explanation:
To calculate the density (ρ) of a gas given the pressure and temperature, we can use the ideal gas equation PV = nRT. We need to first convert the given temperature from Celsius to Kelvin, which would be 22 °C + 273.15 = 295.15 K. Next, we'll solve the equation for ρ, which is the mass (m) divided by the volume (V), or ρ = m/V. The molar mass (M) of air is approximately 28.97 g/mol or 0.02897 kg/mol. Now, we can use the modified ideal gas equation ρ = PM/(RT).
Substituting the given pressure, which is 101.2 kPa (and converting it to Pa by multiplying by 1000), and the molar mass of air into the equation, and using the value for R (8.314 J/(mol·K)), we get ρ = (101.2 x 10³ Pa)(0.02897 kg/mol) / ((8.314 J/(mol·K))(295.15 K)). After calculating the values, we find the density to be approximately 1.195 kg/m³, which corresponds to option b).
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