The concentration of carbon dioxide exiting a car's tailpipe is approximately 12% on a volume basis. assuming the exhaust-gas temperature is 500°C, determine the concentration of CO2 in the fas stream in the units and temperature specified.
a) ppmv at 500°C and 25°C respectively
b) μg/m³ at 500°C and 25°C respectively
12% of what is coming out of the tail pipe.
How will questions a and b be solved?
To determine the concentration of CO2 in the exhaust gas stream at different units and temperatures, we need to apply the ideal gas law and conversion factors. Here's how you can calculate it:
a) ppmv at 500°C and 25°C:
To calculate the concentration in parts per million by volume (ppmv), we need to know the molar volume of carbon dioxide at different temperatures.
1. Convert the given concentration from a percentage to a decimal fraction:
12% = 0.12
2. Determine the molar volume of carbon dioxide at 500°C:
The ideal gas law provides a relationship between pressure, volume, temperature, and the number of moles of a gas:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
The molar volume (Vm) can be calculated using the ideal gas equation:
Vm = (V) / (n)
Since we are considering one mole of CO2:
Vm = V
To determine Vm at 500°C, we'll use the ideal gas law at this temperature:
Vm_500°C = R * T_500°C / P
Where:
R = Ideal gas constant (0.0821 L·atm / (mol·K))
T_500°C = 500°C + 273.15 (converted to Kelvin)
P = Pressure (not provided, but assuming it's constant)
3. Calculate Vm at 25°C:
We'll repeat the same process to determine Vm at 25°C using the ideal gas law:
Vm_25°C = R * T_25°C / P
Where:
T_25°C = 25°C + 273.15 (converted to Kelvin)
4. Convert the concentration to ppmv at 500°C:
ppmv_500°C = (0.12 * Vm_500°C) / 10000
Note: Dividing by 10,000 converts the percentage to parts per million.
5. Convert the concentration to ppmv at 25°C:
ppmv_25°C = (0.12 * Vm_25°C) / 10000
b) μg/m³ at 500°C and 25°C:
To convert ppmv to μg/m³, we need to know the density of carbon dioxide at different temperatures.
1. Convert ppmv at 500°C to mass concentration in μg/m³:
We'll start by calculating the molar mass of carbon dioxide (CO2), which is 44.01 g/mol.
2. Use the ideal gas law to relate concentration, molar mass, and density:
ppmv_500°C * (molar mass) * (density_500°C) = mass concentration (μg/m³)
3. Convert ppmv at 25°C to mass concentration in μg/m³:
ppmv_25°C * (molar mass) * (density_25°C) = mass concentration (μg/m³)
Note: The density of CO2 at different temperatures can be obtained from reference tables or thermodynamic properties.
Please note that specific values for the pressure and density are required to provide a numerical answer.