2. A gas mixture under normal conditions has the following mass composition: CO_(2)=25.0% O_(2)=4.0% ;N_(2)=71.0% To what pressure must this mixture be compressed so that its density is rho =1.9kg/m^3

To solve this problem, we need to use the ideal gas law equation:<br /><br />PV = nRT<br /><br />Where:<br />P = pressure<br />V = volume<br />n = number of moles<br />R = universal gas constant<br />T = temperature<br /><br />Given information:<br />- Mass composition of the gas mixture:<br /> - CO2: 25.0%<br /> - O2: 4.0%<br /> - N2: 71.0%<br />- Density of the gas mixture: ρ = 1.9 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 = (0.25 × 44.01) + (0.04 × 32.00) + (0.71 × 28.02) = 36.86 g/mol<br /><br />Step 3: Calculate the number of moles of the gas mixture per unit volume.<br />n/V = ρ / (Molar mass of the gas mixture)<br />n/V = 1.9 kg/m³ / 36.86 g/mol = 0.0516 mol/m³<br /><br />Step 4: Calculate the pressure of the gas mixture.<br />P = (n/V)RT<br />P = (0.0516 mol/m³) × (8.314 J/(mol·K)) × (298.15 K)<br />P = 123.6 kPa<br /><br />Therefore, the pressure to which the gas mixture must be compressed so that its density is 1.9 kg/m³ is 123.6 kPa.