Q1: Assuming that CO₂ obeys perfect gas law, calculate the density of CO₂ (in kg/m³) at 263°C and 2 atm.

ANS:B - 2

To calculate the density (𝜌ρ) of carbon dioxide (CO2) at 263°C and 2 atm pressure, we can use the ideal gas law equation: 𝑃𝑉=𝑛𝑅𝑇PV=nRT Where:

• 𝑃P is the pressure (in atm)
• 𝑉V is the volume (in liters)
• 𝑛n is the number of moles of the gas
• 𝑅R is the gas constant (0.0821 L.atm/mol.K)
• 𝑇T is the temperature (in Kelvin)

We need to find the number of moles of CO2 first and then use it to calculate the density using the formula: 𝜌=𝑚𝑉ρ=Vm​ Where:

• 𝑚m is the mass of CO2 (in kg)
• 𝑉V is the volume (in m^3)

Given:

• Temperature, 𝑇=263°𝐶=263+273.15=536.15T=263°C=263+273.15=536.15 K
• Pressure, 𝑃=2P=2 atm
• Gas constant, 𝑅=0.0821R=0.0821 L.atm/mol.K

First, we need to find the volume of CO2 using the ideal gas law: 𝑃𝑉=𝑛𝑅𝑇PV=nRT 𝑉=𝑛𝑅𝑇𝑃V=PnRT​ We can rearrange this equation to find the number of moles (𝑛n) of CO2: 𝑛=𝑃𝑉𝑅𝑇n=RTPV​ Once we have the number of moles, we can use the molar mass of CO2 to find the mass of CO2 and then calculate the density. The molar mass of CO2 is 12.01 g/mol12.01g/mol (for carbon) + 2×16.00 g/mol2×16.00g/mol (for oxygen) = 44.01 g/mol44.01g/mol. Now, let's plug in the values and calculate: 𝑛=(2 atm)×𝑉(0.0821 L.atm/mol.K)×(536.15 K)n=(0.0821L.atm/mol.K)×(536.15K)(2atm)×V​ 𝑛=2×𝑉44.01n=44.012×V​ 𝑛=0.04545×𝑉1n=10.04545×V​ Now, we need to convert moles to mass: mass=𝑛×molar massmass=n×molar mass mass=0.04545×44.01mass=0.04545×44.01 mass=1.998 gmass=1.998g Now, we need to convert grams to kilograms: mass=1.998×10−3 kgmass=1.998×10−3kg Now, we use the density formula: 𝜌=𝑚𝑉ρ=Vm​ 𝜌=1.998×10−3𝑉ρ=V1.998×10−3​ We need to calculate 𝑉V first. 𝑉=𝑛𝑅𝑇𝑃V=PnRT​ 𝑉=(0.04545×0.0821×536.15)2V=2(0.04545×0.0821×536.15)​ 𝑉=1.998𝜌V=ρ1.998​ 𝑉=0.0198865 m3V=0.0198865m3 Now, plug in 𝑉V to find 𝜌ρ: 𝜌=1.998×10−30.0198865ρ=0.01988651.998×10−3​ 𝜌≈100.57 kg/m3ρ≈100.57kg/m3 So, the density of CO2 at 263°𝐶263°C and 2 atm2atm is approximately 100.57 kg/m3100.57kg/m3. Among the provided options, none exactly matches this value. Therefore, the density of CO2 at 263°𝐶263°C and 2 atm2atm is not exactly 1, 2, 3, or 4 kg/m^3.