For the reaction , `A+BhArr 3C`, if 'a' mol/litre of each 'A' and 'B' are taken initially then at equilibrium the incorrect relation is :

Options

A. (A) `[A]-[B]=0`
B. (B) `3[B]+[C]=3a`
C. (C) `3[A]+[C]=3a`
D. (D) `[A]+[B]=3[C]`

Explanation

To solve the problem step by step, we will analyze the reaction and the equilibrium conditions given.

### Step 1: Write the balanced chemical equation
The reaction given is:
\[ A + B \rightleftharpoons 3C \]

### Step 2: Set up initial concentrations
Initially, we have:
- Concentration of \( A = a \) mol/L
- Concentration of \( B = a \) mol/L
- Concentration of \( C = 0 \) mol/L

### Step 3: Define change in concentration at equilibrium
Let \( x \) be the amount of \( A \) and \( B \) that reacts to reach equilibrium. Therefore, at equilibrium:
- Concentration of \( A = a - x \)
- Concentration of \( B = a - x \)
- Concentration of \( C = 3x \)

### Step 4: Write the expressions for the equilibrium concentrations
From the above, we can summarize the equilibrium concentrations as:
- \( [A] = a - x \)
- \( [B] = a - x \)
- \( [C] = 3x \)

### Step 5: Analyze each option given in the question
Now we will evaluate each of the provided relations to identify the incorrect one.

1. **Option A: \( a - b = 0 \)**
- This means \( a = b \).
- Since both \( A \) and \( B \) start with the same concentration \( a \), this is true. (Correct)

2. **Option B: \( 3b + c = 3a \)**
- Substitute \( b \) and \( c \):
\[ 3(a - x) + 3x = 3a \]
- This simplifies to \( 3a - 3x + 3x = 3a \), which is true. (Correct)

3. **Option C: \( 3a + c = 3a \)**
- Substitute \( c \):
\[ 3(a - x) + 3x = 3a \]
- This simplifies to \( 3a - 3x + 3x = 3a \), which is true. (Correct)

4. **Option D: \( a + b = 3c \)**
- Substitute \( a \) and \( b \):
\[ (a - x) + (a - x) = 3(3x) \]
- This simplifies to \( 2(a - x) = 9x \).
- Rearranging gives \( 2a - 2x = 9x \) or \( 2a = 11x \), which is not generally true. (Incorrect)

### Conclusion
The incorrect relation is:
\[ a + b \neq 3c \]
Thus, the answer is **Option D**.