What happens to the pressures in two connected flasks filled with different gases when the valve is opened?

When the valve between the two flasks is opened, the gases will mix and the total pressure in the combined volume will change. To understand this, we can use the ideal gas law and the principle of partial pressures.

Initially, we have:

• Flask 1 (He): Volume = 650 L, Pressure = 402 torr
• Flask 2 (Ar): Volume = 185 L, Pressure = 115 torr

First, we can find the number of moles of each gas using the ideal gas law, which states: PV = nRT. However, for our purposes, we can also work directly with pressure and volume in terms of partial pressures after the gases mix.

When the valve is opened, the total volume becomes the sum of both flasks:

Total Volume = 650 L + 185 L = 835 L

Next, we need to calculate the individual contributions of the gases after mixing. The partial pressure of each gas can be calculated using the relation:

P_He = (P_initial * V_He) / V_total

Substituting for Helium:

P_He = (402 torr * 650 L) / 835 L ≈ 313.24 torr

Similarly, for Argon:

P_Ar = (P_initial * V_Ar) / V_total

P_Ar = (115 torr * 185 L) / 835 L ≈ 25.71 torr

Now, the total pressure after the gases mix is the sum of the partial pressures:

P_total = P_He + P_Ar ≈ 313.24 torr + 25.71 torr ≈ 338.95 torr

In conclusion, upon opening the valve, the gases will mix, and the resulting pressure in the combined volume of 835 L will stabilize around 338.95 torr. This process exemplifies gas behavior and the principles of mixing under the ideal gas approximation.