Is the answer for part c 0.91?
A 1.0 L ball containing Ar at 5 atm is connected to a 10.0 L ball containing N2 at 2atm.
A)Calculate the partial pressures and mole fractions of Ar and N2 after the valve is opened and the gases are allowed to mix (they fill the balls on both sides).
My answers:
P argon = 0.455 atm
P nitrogen = 1.82 atm
X argon = 0.2
X nitrogen= 0.8
B) Total pressure?
My answer: 2.275 atm
C) If we added enough argon to raise its mole fraction to 0.5 in the mixture, what would the new total pressure be?
My answer: 4.55 atm
Chemistry - DrBob222, Saturday, March 12, 2016 at 4:07pm
A and B look ok to me but I don't agree with C.
To find the answer to part C, you need to consider the ideal gas law and the concept of mole fraction. The ideal gas law is given by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. As both balls are connected and allowed to mix, the total number of moles of gas remains constant.
In part C, you are asked what the new total pressure would be if enough argon is added to raise its mole fraction to 0.5 in the mixture. Let's break down the steps to find the answer:
1. Calculate the initial moles of Ar and N2 in the mixture:
- The initial pressure of the Ar ball is 5 atm and the volume is 1 L. Using the ideal gas law, we can calculate the initial moles of Ar:
n_Ar_initial = (P_Ar_initial * V_Ar_initial) / (R * T)
- Similarly, for N2, the initial pressure is 2 atm and the volume is 10 L:
n_N2_initial = (P_N2_initial * V_N2_initial) / (R * T)
2. Calculate the initial mole fractions of Ar and N2:
- The initial total moles of gas can be found by summing the individual moles:
n_total_initial = n_Ar_initial + n_N2_initial
- The initial mole fraction of Ar is then given by:
X_Ar_initial = n_Ar_initial / n_total_initial
3. Determine the moles of Ar needed to raise its mole fraction to 0.5:
- Let's assume x is the additional moles of Ar needed to raise its mole fraction to 0.5.
- Since the total moles remain constant, the new moles of Ar can be expressed as:
n_Ar_new = n_Ar_initial + x
4. Calculate the new total moles:
- Since the total moles remain constant, the new total moles can be expressed as:
n_total_new = n_total_initial + x
5. Calculate the new mole fraction of Ar:
- The new mole fraction of Ar is given by:
X_Ar_new = n_Ar_new / n_total_new
6. Calculate the new total pressure using the mole fraction and the ideal gas law:
- The new total pressure is given by:
P_total_new = X_Ar_new * P_Ar_initial + (1 - X_Ar_new) * P_N2_initial
By following these steps, you should be able to correctly calculate the new total pressure in part C.