To find the final pressure in the flasks after they are connected, we can use the principle of Dalton's law of partial pressures. According to this law, the total pressure in a mixture of non-reacting gases is equal to the sum of the partial pressures of each gas.
Let's calculate the partial pressure of each gas in the final state:
In Flask A:
- Volume (V_A) = 4.0 L
- Pressure (P_A) = 2.0 ATM
In Flask B:
- Volume (V_B) = 10.0 L
- Pressure (P_B) = 1.4 ATM
Since the flasks are connected and assuming that there is no change in temperature or any reaction between the gases, the total number of moles (n) of gas in the system remains constant.
Now, we can use the formula for the partial pressure of a gas:
Partial Pressure = (moles of gas / total moles) * total pressure
To find the moles of gas, we can use the ideal gas law:
PV = nRT
Where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant
- T is the temperature (which we assume remains constant)
Let's assume that the temperature remains constant and cancel out the constant values. We can set up the following equations for the moles of gas in each flask:
n_A = (P_A * V_A) n_B = (P_B * V_B)
Now, let's calculate the total moles of gas:
Total moles = n_A + n_B
Next, we can calculate the mole fractions of each gas:
Mole fraction of A = n_A / Total moles Mole fraction of B = n_B / Total moles
Finally, we can find the final pressure (P_final) using Dalton's law of partial pressures:
P_final = (Mole fraction of A * P_A) + (Mole fraction of B * P_B)
Substituting the values:
n_A = (2.0 ATM * 4.0 L) = 8.0 mol n_B = (1.4 ATM * 10.0 L) = 14.0 mol
Total moles = n_A + n_B = 8.0 mol + 14.0 mol = 22.0 mol
Mole fraction of A = n_A / Total moles = 8.0 mol / 22.0 mol ≈ 0.364 Mole fraction of B = n_B / Total moles = 14.0 mol / 22.0 mol ≈ 0.636
P_final = (0.364 * 2.0 ATM) + (0.636 * 1.4 ATM) P_final = 0.728 ATM + 0.8904 ATM P_final ≈ 1.6184 ATM
Therefore, the final pressure in the flasks after they are connected is approximately 1.6184 ATM.