`A(s)hArr2B(g)+C(g)`
The above equilibrium was established by initially taking `A(s)` only. At equilibrium, `B` is removed so that its partial pressure at new equilibrium becomes `1//3^(rd)` of original total pressure. Ratio of total pressure at new equilibrium and at initial equilibrium will be :

Options

A. `2//3`
B. `14//13`
C. `5//3`
D. `17//19`

Explanation

To solve the problem step by step, we will analyze the equilibrium reaction and the changes that occur when the partial pressure of B is altered.

### Step 1: Understand the Initial Equilibrium
The reaction is given as:
\[ A(s) \rightleftharpoons 2B(g) + C(g) \]

Initially, only solid A is present. At equilibrium (let's call it Equilibrium 1), let the partial pressure of B be \( 2P \) and the partial pressure of C be \( P \). Therefore, the total pressure at this equilibrium can be calculated as:
\[ P_{T1} = P_B + P_C = 2P + P = 3P \]

**Hint:** Identify the pressures of the gases produced at equilibrium based on stoichiometry.

### Step 2: Analyze the New Equilibrium After Removing B
According to the problem, after reaching the first equilibrium, B is removed so that its new partial pressure becomes one-third of the original total pressure. Hence:
\[ P_B = \frac{P_{T1}}{3} = \frac{3P}{3} = P \]

Let the new partial pressure of C be \( P' \). The total pressure at the new equilibrium (Equilibrium 2) can be expressed as:
\[ P_{T2} = P_B + P' = P + P' \]

**Hint:** Remember to express the new total pressure in terms of the new partial pressures after the removal of B.

### Step 3: Establish the Equilibrium Constant
The equilibrium constant \( K_p \) for the first equilibrium can be expressed as:
\[ K_{p1} = \frac{(P_B)^2 \cdot (P_C)}{1} = (2P)^2 \cdot P = 4P^3 \]

For the new equilibrium, the equilibrium constant \( K_p \) is:
\[ K_{p2} = P_B^2 \cdot P' = P^2 \cdot P' \]

Since \( K_p \) is constant at a given temperature, we have:
\[ K_{p1} = K_{p2} \]
\[ 4P^3 = P^2 \cdot P' \]

**Hint:** Use the fact that the equilibrium constant remains unchanged when the temperature is constant.

### Step 4: Solve for \( P' \)
From the equation \( 4P^3 = P^2 \cdot P' \), we can solve for \( P' \):
\[ P' = \frac{4P^3}{P^2} = 4P \]

**Hint:** Rearranging the equation helps isolate the variable you need.

### Step 5: Calculate the Total Pressure at New Equilibrium
Now we can substitute \( P' \) back into the equation for \( P_{T2} \):
\[ P_{T2} = P + P' = P + 4P = 5P \]

**Hint:** Combine the pressures to find the new total pressure.

### Step 6: Find the Ratio of Total Pressures
Now we can find the ratio of the total pressure at the new equilibrium to that at the initial equilibrium:
\[ \text{Ratio} = \frac{P_{T2}}{P_{T1}} = \frac{5P}{3P} = \frac{5}{3} \]

**Hint:** Simplifying the ratio gives you the final answer.

### Final Answer
The ratio of the total pressure at the new equilibrium to that at the initial equilibrium is:
\[ \frac{5}{3} \]