Question

1.5 kmol of carbon dioxide is mixed with 2.5 kmol of air in a vessel at 1 bar (abs) and 15 °C. If the volumetric composition of air is 79% nitrogen and 21% oxygen, determine the density and molecular weight of the mixture. Given: molecular weights

Answer 1

To determine the density and molecular weight of the mixture, we need to calculate the total mass of the mixture and then divide it by the total volume.

First, let's calculate the total mass of the mixture:

Mass of CO2 = Number of kmol of CO2 * Molecular weight of CO2

Mass of CO2 = 1.5 kmol * 44.01 g/mol

Mass of air = Number of kmol of air * Molecular weight of air

Mass of air = 2.5 kmol * (0.79 * Molecular weight of nitrogen + 0.21 * Molecular weight of oxygen)

Next, we calculate the total volume of the mixture using the ideal gas law:

PV = nRT

Where:

P = Pressure (1 bar)

V = Volume

n = Number of kmol of gas

R = Gas constant (8.314 J/(mol·K))

T = Temperature (15 °C converted to Kelvin)

Rearranging the equation to solve for V, we get:

V = nRT / P

Finally, we can calculate the density of the mixture by dividing the total mass by the total volume:

Density = Total mass / Total volume

To find the molecular weight of the mixture, we sum up the mass of CO2 and the mass of air, and then divide it by the total number of kmol.

Given the molecular weights for CO2 (44.01 g/mol), nitrogen (28.0134 g/mol), and oxygen (31.9988 g/mol), you can substitute these values into the equations to find the desired results.