2. A gas mixture under normal conditions has the following mass composition: CO_(2)=32.0% O_(2)=8.0% ;N_(2)=60.0% To what pressure must this mixture be compressed so that its density is rho =1.8kg/m^3

To solve this problem, we need to use the ideal gas law and the given mass composition of the gas mixture.<br /><br />Given information:<br />- Mass composition of the gas mixture: CO2 = 32.0%, O2 = 8.0%, N2 = 60.0%<br />- Density of the gas mixture: ρ = 1.8 kg/m³<br /><br />Step 1: Calculate the molar masses of the individual gases.<br />- Molar mass of CO2 = 44.01 g/mol<br />- Molar mass of O2 = 32.00 g/mol<br />- Molar mass of N2 = 28.02 g/mol<br /><br />Step 2: Calculate the average molar mass of the gas mixture.<br />Average molar mass = (0.32 × 44.01) + (0.08 × 32.00) + (0.60 × 28.02) = 35.21 g/mol<br /><br />Step 3: Use the ideal gas law to find the pressure.<br />PV = nRT<br />P = (nRT) / V<br /><br />Where:<br />P = Pressure<br />V = Volume<br />n = Number of moles<br />R = Universal gas constant (8.314 J/(mol·K))<br />T = Temperature (assumed to be 298 K, standard temperature)<br /><br />Step 4: Calculate the number of moles of the gas mixture.<br />n = m / M<br />n = (1.8 kg/m³) / (35.21 g/mol) = 0.0511 mol/m³<br /><br />Step 5: Calculate the pressure using the ideal gas law.<br />P = (nRT) / V<br />P = (0.0511 mol/m³ × 8.314 J/(mol·K) × 298 K) / 1 m³<br />P = 123.6 Pa<br /><br />Therefore, the pressure to which the gas mixture must be compressed so that its density is 1.8 kg/m³ is 123.6 Pa.