Two closed vessel A and B of equal volume of 8.21 L are connected by a narrow tube of negligible volume with open valve. The left hand side container is found to contain 3 mole `CO_(2)` and 2 mole of He at 400 K. What is the partial pressure of He in vessel B at 400 K?
(a)2.4 atm
(b)8atm
(c)12atm
(d)None of these

Options

A. 2.4 atm
B. 8 atm
C. 12atm
D. None of these

Explanation

To find the partial pressure of helium (He) in vessel B at 400 K, we can follow these steps:

### Step 1: Understand the System
We have two vessels, A and B, both with a volume of 8.21 L. Vessel A contains 3 moles of CO₂ and 2 moles of He at 400 K. Vessel B is initially empty.

### Step 2: Calculate Total Moles in Vessel A
Total moles in vessel A:
- Moles of CO₂ = 3 moles
- Moles of He = 2 moles

Total moles in vessel A (n_total) = 3 + 2 = 5 moles.

### Step 3: Use the Ideal Gas Law to Find Total Pressure in Vessel A
The ideal gas law is given by the equation:
\[ PV = nRT \]
Where:
- P = pressure (atm)
- V = volume (L)
- n = number of moles
- R = ideal gas constant (0.0821 L·atm/(K·mol))
- T = temperature (K)

Rearranging for pressure (P):
\[ P = \frac{nRT}{V} \]

Substituting the values:
- n = 5 moles
- R = 0.0821 L·atm/(K·mol)
- T = 400 K
- V = 8.21 L

Calculating P:
\[ P = \frac{5 \times 0.0821 \times 400}{8.21} \]

### Step 4: Calculate the Pressure
Calculating the numerator:
\[ 5 \times 0.0821 \times 400 = 164.2 \]

Now dividing by the volume:
\[ P = \frac{164.2}{8.21} \approx 20.0 \, \text{atm} \]

### Step 5: Calculate the Partial Pressure of Helium
The partial pressure of a gas in a mixture can be found using the formula:
\[ P_{He} = \left( \frac{n_{He}}{n_{total}} \right) \times P_{total} \]

Where:
- \( n_{He} = 2 \) moles (moles of He)
- \( n_{total} = 5 \) moles (total moles)
- \( P_{total} = 20.0 \, \text{atm} \)

Substituting the values:
\[ P_{He} = \left( \frac{2}{5} \right) \times 20.0 \]

### Step 6: Calculate the Partial Pressure of Helium
Calculating \( P_{He} \):
\[ P_{He} = 0.4 \times 20.0 = 8.0 \, \text{atm} \]

### Conclusion
The partial pressure of helium in vessel B at 400 K is **8 atm**.

### Final Answer
(b) 8 atm

---