A 265- mL flask contains pure helium at a pressure of 747 torr. A second flask with a volume of 485 mL contains pure argon at a pressure of 721 torr .If the two flasks are connected through a stopcock and the stopcock is opened, what is the partial pressure of helium?
Use PV = nRT for the He flask to determine the number of moles He. Then use PV = nRT for the two flasks connected (add volumes to obtain total volume) and solve for P. Remember pressure must be in atmospheres. There is no T given; therefore, make up a convenient number. I suggest 273 K.
To find the partial pressure of helium when the two flasks are connected, we need to consider the ideal gas law and Dalton's law of partial pressures.
Dalton's law of partial pressures states that in a mixture of non-reacting gases, the total pressure is equal to the sum of the partial pressures of the individual gases. Mathematically, this can be represented as:
P_total = P_1 + P_2 + ...
In this case, we have two flasks connected, one containing pure helium and the other containing pure argon. When the stopcock is opened, the gases will mix, but they will not react with each other.
First, let's find the partial pressure of argon in the mixture. Since the flask containing argon is not connected to any other source of gas, the partial pressure of argon will remain the same. Therefore, the partial pressure of argon is 721 torr.
Now, let's find the partial pressure of helium. To do this, we need to know the total pressure of the mixture. When the stopcock is opened, the gases will mix and equilibrate to the same pressure. The final pressure is determined by the combined volumes of the flasks.
To calculate the total pressure of the mixture, we use Dalton's law: P_total = P_helium + P_argon.
We have the pressure of argon (721 torr) and we need to find the pressure of helium. We know that the total pressure of the mixture is determined by the combined volumes of the flasks, so we can set up a proportion:
(P_helium) / (P_total) = (V_helium) / (V_total)
The volume of the helium flask is 265 mL, and the volume of the argon flask is 485 mL. The total volume is therefore 265 mL + 485 mL = 750 mL.
Substituting the known values into the equation:
(P_helium) / (P_total) = (265 mL) / (750 mL)
Now, we solve for P_helium:
P_helium = (P_total) * (265 mL) / (750 mL)
Substituting the total pressure of the mixture, which we'll call P_mix, gives:
P_helium = (P_mix) * (265 mL) / (750 mL)
To find P_mix, we need to know the pressure after the gases have equilibrated. Since the two flasks have connected, the pressure will be the same in both flasks. Therefore, the pressure after equilibration is 747 torr.
Substituting the values:
P_helium = (747 torr) * (265 mL) / (750 mL)
Now, we can find the partial pressure of helium:
P_helium = (747 torr) * (265 mL) / (750 mL)
P_helium ≈ 263.98 torr
Therefore, the partial pressure of helium in the mixture is approximately 264 torr.