Final answer:
To calculate the mass of air in the living room, multiply the volume of the room by the mass of one cubic meter of air.
Step-by-step explanation:
To calculate the mass of the air in an apartment's living room with dimensions of 2.9m x 3.9m x 6.5m at a temperature of 24°C and a pressure of 1.01 x 10⁵ Pa, we use the ideal gas law and the known composition of air. Air is mostly composed of nitrogen (N₂) and oxygen (O₂), with an average molar mass (M) of 28.8 g/mol. The room's volume is 2.9m x 3.9m x 6.5m = 73.485 m³. The density (ρ) of air at the given conditions can be found using the equation ρ = PM/RT, where P is the pressure, R is the universal gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin (297K). After calculating the density, we find the mass by multiplying the room's volume by the density of the air.
Given the rounded density of air is approximately 1.28 kg/m³, the mass of air (μ) inside the living room is calculated as μ = volume x density. Plugging in the known values, μ = 73.485 m³ x 1.28 kg/m³ = 94.061 kg. Since the question asks for the mass in grams, we convert kilograms to grams (1 kg = 1000 g), resulting in a total mass of 94,061 grams.