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 relationships between the concentrations of X, Y, and Z.

### Step 1: Write the equilibrium expression
The given reaction is:
\[ X + 2Y \rightleftharpoons Z \]

### Step 2: Identify initial concentrations
The initial concentrations are:
- \([X]_0 = 2 \, \text{mol/L}\)
- \([Y]_0 = 4 \, \text{mol/L}\)
- \([Z]_0 = 0 \, \text{mol/L}\)

### Step 3: Define changes in concentrations at equilibrium
Let \( x \) be the amount of X that reacts at equilibrium. Then, we can express the equilibrium concentrations as:
- \([X] = 2 - x\)
- \([Y] = 4 - 2x\)
- \([Z] = x\)

### Step 4: Analyze the relationships
We need to check the feasibility of the following relationships:
1. \([X] < [Z]\)
2. \([X] > [Y]\)
3. \([X] < [Y]\)
4. \([Y] > [Z]\)

#### Relationship 1: \([X] < [Z]\)
From our expressions:
\[ 2 - x < x \]
This simplifies to:
\[ 2 < 2x \]
\[ x > 1 \]
This is feasible since \( x \) can be greater than 1.

#### Relationship 2: \([X] > [Y]\)
From our expressions:
\[ 2 - x > 4 - 2x \]
This simplifies to:
\[ 2x > 2 \]
\[ x > 1 \]
This is also feasible.

#### Relationship 3: \([X] < [Y]\)
From our expressions:
\[ 2 - x < 4 - 2x \]
This simplifies to:
\[ x < 2 \]
This is feasible as \( x \) can be less than 2.

#### Relationship 4: \([Y] > [Z]\)
From our expressions:
\[ 4 - 2x > x \]
This simplifies to:
\[ 4 > 3x \]
\[ x < \frac{4}{3} \]
This is also feasible.

### Step 5: Identify the non-feasible relationship
Now we need to check which of these relationships cannot hold true simultaneously.

From the analysis:
- Relationship 1 requires \( x > 1 \)
- Relationship 2 requires \( x > 1 \)
- Relationship 3 requires \( x < 2 \)
- Relationship 4 requires \( x < \frac{4}{3} \)

However, if we consider Relationship 2 (\([X] > [Y]\)), it requires \( x > 1 \) and Relationship 3 (\([X] < [Y]\)) requires \( x < 2 \).

If we set \( x = 1.5 \), it satisfies Relationship 1 and 4, but fails Relationship 2. Therefore, the relationship \([X] > [Y]\) is not feasible.

### Conclusion
The relationship among equilibrium concentrations of X, Y, and Z that is not feasible is:
\[ [X] > [Y] \]