I'm confused on this problem
A gaseous mixture inside a rigid steel vessel contains 75% CO2 and 25% H2O by volume at 175 degrees C and 225 kPa. The mixture is then cooled to 0 degrees C, thereby condensing the water vapor. What is the pressure of the CO2 at 0 degrees C? (assume that there is no water vapor present after condensation)
Please help me
XCO2 = 0.75
XH2O = 0.25
PCO2 = XCO2*Ptotal
PH2O = XH2O*Ptotal
After the water condenses, the only gas left in the container is CO2 and it has changed T from 175 C to 0 C. Use
(P1/T1) = (P2/T2) to calculate the new pressure at the new T.
Post your work if you get stuck.
Why did the gaseous mixture become so confused? Because it couldn't decide whether to be CO2 or H2O! 🌫️
Now, let's get down to business. To find the pressure of CO2 at 0 degrees C, 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, and T is the temperature in Kelvin.
Since the volume and moles of CO2 stay the same after the condensation, we can write the equation as follows:
P1V1/T1 = P2V2/T2
We are given that the initial pressure (P1) is 225 kPa, the initial temperature (T1) is 175 degrees C (or 448 Kelvin), and the final temperature (T2) is 0 degrees C (or 273 Kelvin). We need to find the final pressure (P2).
Let's solve for P2 step by step:
P1V1/T1 = P2V2/T2
225 kPa * V1 / 448 K = P2 * V1 / 273 K
225 kPa * 273 K = 448 K * P2
P2 = (225 kPa * 273 K) / 448 K
P2 is approximately 137.47 kPa.
So, the pressure of CO2 at 0 degrees C would be around 137.47 kPa.
To solve this problem, we can use the ideal gas law equation:
PV = nRT
First, let's calculate the number of moles of CO2 and H2O in the original mixture:
1. Assume we have 100 L of the gaseous mixture inside the rigid steel vessel.
- CO2: 75% of 100 L = 75 L
- H2O: 25% of 100 L = 25 L
2. Convert the volumes of CO2 and H2O to moles using the ideal gas law equation:
- Number of moles of CO2 = (75 L)(1 mol/22.4 L) ≈ 3.35 mol
- Number of moles of H2O = (25 L)(1 mol/22.4 L) ≈ 1.12 mol
Next, let's determine the initial pressure of the gas mixture:
3. Use the ideal gas law to find the initial pressure, P1:
PV = nRT
P1V = n1RT1
Given:
- T1 = 175°C = 175 + 273 = 448 K
- P1 = 225 kPa (convert to atm by dividing by 101.325)
- n1 = total number of moles of the mixture (CO2 + H2O) = 3.35 mol + 1.12 mol = 4.47 mol
- R = ideal gas constant = 0.0821 atm·L/mol·K
Substitute the values into the equation:
(225/101.325) V = (4.47)(0.0821)(448)
V = ((4.47)(0.0821)(448))/(225/101.325)
V ≈ 9.78 L
Now, let's calculate the pressure of CO2 at 0°C after water vapor has condensed (assuming no water vapor):
4. Use the ideal gas law to find the final pressure, P2:
P2V = n2RT2
Given:
- T2 = 0°C = 0 + 273 = 273 K
- n2 = number of moles of CO2 = 3.35 mol (since all the H2O has condensed)
- V = 9.78 L (from step 3)
- R = 0.0821 atm·L/mol·K
Substitute the values into the equation:
P2(9.78) = (3.35)(0.0821)(273)
P2 ≈ (3.35)(0.0821)(273)/9.78
P2 ≈ 0.6 atm
Therefore, the pressure of CO2 at 0°C (after water vapor condensation) is approximately 0.6 atm.
To solve this problem, we need to use the ideal gas law equation:
PV = nRT
where:
P is the pressure of the gas.
V is the volume of the gas.
n is the number of moles of gas.
R is the ideal gas constant.
T is the temperature in Kelvin.
First, let's convert the given temperature from Celsius to Kelvin. We add 273 to the temperature in Celsius to get the temperature in Kelvin.
Given:
Initial pressure (P1) = 225 kPa (given)
Initial volume (V1) = unknown (rigid steel vessel - no change in volume)
Initial temperature (T1) = 175 degrees C = 175 + 273 = 448 K
Initial CO2 mole fraction (X1) = 75% = 0.75 (volume percent)
Final temperature (T2) = 0 degrees C = 0 + 273 = 273 K
Final CO2 mole fraction (X2) = 100% - final H2O mole fraction = 100% - 25% = 75% = 0.75
Since the volume (V) and the number of moles (n) remain constant, we can rewrite the ideal gas law equation as:
P1/T1 = P2/T2
Let's solve for P2, the pressure of CO2 at 0 degrees C:
P2 = (P1 * T2) / T1
Substituting the given values:
P2 = (225 kPa * 273 K) / 448 K
Calculating this expression, we find:
P2 ≈ 137.86 kPa
Therefore, the pressure of CO2 at 0 degrees C is approximately 137.86 kPa.