Please help! I don’t know where to start and I need step by step on how to solve:
A gaseous mixture inside a rigid steel vessel contains 75% CO2(g) and 25% H2O (g) by volume at 175 degrees Celcius and 225 kPa. The mixture is then cooled to 0 degrees celcius thereby converting the gaseous water to a liquid. What is the pressure of the CO2 (g) at 0 degrees celcius? Assume that there is no water vapor present after condensation.
Note, too, that celsius is the correct spelling.
75% of the pressure is CO2 ... 225 kPa * .75
reducing the temperature (absolute) lowers the pressure proportionately
pressure = (225 kPa * .75) * [(0 + 273) / (175 + 273)]
To solve this problem, you will need to use the ideal gas law and the concept of partial pressure.
Step 1: Convert the percentages to decimal form.
The mixture is composed of 75% CO2 and 25% H2O, so we convert these percentages to decimals: 75% = 0.75 and 25% = 0.25.
Step 2: Convert the temperature to Kelvin.
To use the ideal gas law, you need to convert the temperature from Celsius to Kelvin. The formula for converting Celsius to Kelvin is K = °C + 273.15. Therefore, 175°C + 273.15 = 448.15 K.
Step 3: Calculate the moles of CO2 and H2O.
To find the partial pressure of CO2, we need to calculate the number of moles of CO2 and H2O in the mixture. We can use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin.
The equation can be rearranged as follows: n = PV / RT.
For CO2:
Using the given information, the volume of the mixture is not provided, but since it is a rigid vessel, we can assume that the volume remains constant throughout the process. Therefore, the volume can be canceled out in the equation.
For H2O:
Since the gaseous water is condensed into a liquid, there is no water vapor present after condensation. This means that the pressure of H2O is no longer relevant, and we do not need to calculate the number of moles of H2O.
Step 4: Calculate the partial pressure of CO2 at 175°C.
Now we can calculate the partial pressure of CO2 using the ideal gas law equation. The partial pressure of CO2 is given by P_CO2 = n_CO2 * RT / V. We need to calculate the number of moles of CO2 (n_CO2) using the equation from Step 3.
Step 5: Convert the temperature to Kelvin.
Since the mixture is cooled to 0°C, we need to convert this temperature to Kelvin using the equation K = °C + 273.15. Therefore, 0°C + 273.15 = 273.15 K.
Step 6: Calculate the pressure of CO2 at 0°C.
Now we can use the ideal gas law equation to calculate the pressure of CO2 at 0°C. The partial pressure of CO2 at 0°C is given by P_CO2 = n_CO2 * RT / V. We need to calculate the number of moles of CO2 (n_CO2) using the equation from Step 3 and use the final temperature of 273.15 K.
Following these steps will allow you to solve the given problem systematically.