The initial concentration of X and Y were 2 and 4 mole / L respectively . For the following equilibrium `X+2YhArrZ` which of the following relationship among equilibrium concentrations of x , y and z is not feasible ?

Options

A. `[X]lt[Z]`
B. `[X]lt[Y]`
C. `[X]gt[Y]`
D. `[Y]gt[Z]`

Answer

To solve the problem, we need to analyze the equilibrium reaction and the initial concentrations of the reactants. The reaction is:

\[ X + 2Y \rightleftharpoons Z \]

**Step 1: Identify Initial Concentrations**
- Initial concentration of \( X \) = 2 M
- Initial concentration of \( Y \) = 4 M

**Step 2: Set Up Change in Concentration**
Let \( a \) be the amount of \( X \) that reacts at equilibrium. According to the stoichiometry of the reaction:
- Change in concentration of \( X \) = \( -a \)
- Change in concentration of \( Y \) = \( -2a \) (since 2 moles of \( Y \) react for every mole of \( X \))
- Change in concentration of \( Z \) = \( +a \)

**Step 3: Write Equilibrium Concentrations**
At equilibrium, the concentrations will be:
- Concentration of \( X \) = \( 2 - a \)
- Concentration of \( Y \) = \( 4 - 2a \)
- Concentration of \( Z \) = \( a \)

**Step 4: Analyze Each Relationship**
Now, we will analyze the given relationships among the equilibrium concentrations of \( X \), \( Y \), and \( Z \).

1. **Relationship 1: \( [X] < [Z] \)**
- \( 2 - a < a \)
- Rearranging gives \( 2 < 2a \) or \( a > 1 \)

2. **Relationship 2: \( [X] < [Y] \)**
- \( 2 - a < 4 - 2a \)
- Rearranging gives \( 2a < 2 \) or \( a < 1 \)

3. **Relationship 3: \( [X] > [Y] \)**
- \( 2 - a > 4 - 2a \)
- Rearranging gives \( a > 2 \)

4. **Relationship 4: \( [Y] > [Z] \)**
- \( 4 - 2a > a \)
- Rearranging gives \( 4 > 3a \) or \( a < \frac{4}{3} \)

**Step 5: Determine Feasibility**
Now we need to check which of these relationships can coexist:
- From Relationship 1, we have \( a > 1 \).
- From Relationship 2, we have \( a < 1 \) (not feasible with Relationship 1).
- From Relationship 3, we have \( a > 2 \) (not feasible with Relationship 1).
- From Relationship 4, we have \( a < \frac{4}{3} \) (not feasible with Relationship 3).

**Conclusion:**
The relationship that is not feasible is **Relationship 3: \( [X] > [Y] \)** because it requires \( a > 2 \), which contradicts the limits established by the initial concentrations of \( X \) and \( Y \).

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