Two vessels of volumes 1.22 L and 3.18 L contain krypton gas and are connected by a thin tube. Initially, the vessels are at the same temperature, 16.0ºC. Calculate the final pressure. (Hint: There are no leaks.)

To find the final pressure of the krypton gas in the two connected vessels, we can apply the principles of gas laws, specifically the ideal gas law and the concept of pressure equilibrium. Since the vessels are connected and there are no leaks, the total amount of gas remains constant, and the pressure will equalize between the two vessels.

Understanding the Initial Conditions

We have two vessels with different volumes:

• Volume of Vessel 1 (V1) = 1.22 L
• Volume of Vessel 2 (V2) = 3.18 L

Both vessels contain krypton gas at the same initial temperature of 16.0ºC. We need to calculate the final pressure after the gases in both vessels have equilibrated.

Applying the Ideal Gas Law

The ideal gas law is given by the formula:

PV = nRT

Where:

• P = pressure
• V = volume
• n = number of moles of gas
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature in Kelvin

Converting Temperature to Kelvin

First, we need to convert the temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15

So, T = 16.0 + 273.15 = 289.15 K.

Calculating Initial Pressures

Let’s denote the initial pressure in Vessel 1 as P1 and in Vessel 2 as P2. Since we don’t have the initial pressures, we can express them in terms of the number of moles of krypton gas (n1 and n2) in each vessel:

P1 = (n1RT) / V1

P2 = (n2RT) / V2

Combining the Vessels

When the vessels are connected, the total volume (V_total) is:

V_total = V1 + V2 = 1.22 L + 3.18 L = 4.40 L

The total number of moles of gas (n_total) is the sum of the moles in both vessels:

n_total = n1 + n2

Final Pressure Calculation

After the gases have equilibrated, the final pressure (P_final) can be expressed as:

P_final = (n_total * R * T) / V_total

Since we don’t have the values for n1 and n2, we can assume that the initial pressures are equal (P1 = P2) for simplicity, leading to:

P_final = (P1 * V1 + P2 * V2) / V_total

Assuming Equal Initial Pressures

If we assume that both vessels initially had the same pressure (P_initial), we can simplify our calculations:

P_final = P_initial * (V1 + V2) / V_total

Since V_total is equal to the sum of the volumes, we can conclude that:

P_final = P_initial

Final Thoughts

In this scenario, the final pressure will equal the initial pressure of the gas in both vessels, provided that the temperature remains constant and there are no leaks. To find the numerical value of the final pressure, you would need the initial pressure of the gas in either vessel. If you have that value, you can directly state that the final pressure will be the same.