Question

A vessel contains a mixture of 7g of nitrogen and 11g carbon dioxide at temperature T=290K. If pressure of the mixure is 1atm (=1.01×105N/m²), calculate its dencity (R=8.31J/mol−K).

Answer 1

To calculate the density of the gas mixture, first find the total moles of gases, then use the ideal gas law PV = nRT to find the volume, and apply the formula for density which is mass divided by volume.

Step-by-step explanation:

To calculate the density of a mixture of gases, we can apply the ideal gas law, which is PV = nRT. We will first calculate the total moles of gas in the mixture and then use the density formula Density = mass/volume. Assume standard molar volume at STP conditions which is 22.4 L/mol.

The molar mass of nitrogen (N₂) is 28.01 g/mol. For nitrogen, we have 7g, so we have 7g / 28.01g/mol = 0.250 moles of nitrogen. The molar mass of carbon dioxide (CO₂) is 44.01 g/mol. For carbon dioxide, we have 11g, so we have 11g / 44.01 g/mol = 0.250 moles of carbon dioxide. Thus, we have a total of 0.250 + 0.250 = 0.500 moles of gas.

Using the ideal gas law: PV = nRT, and the provided values (T=290K, P=1atm, R=8.31J/(mol⋅K)), we can solve for the volume V. Substituting the known values, we get 1 atm × V = 0.500 mol × 8.31J/(mol⋅K) × 290K. After calculating V, the density (ρ) will be ρ = mass / V where mass is the total mass of the gases (7g + 11g).