For the reaction:
`2A(g)+B(g) hArr 3C(g)+D(g)`
Two moles each of `A` and `B` were taken into a flask. The following must always be true when the system attained equilibrium

Options

A. `[A] = [B]`
B. `[A] lt [B]`
C. `[B]=[C]`
D. `[A] gt [B]`

Explanation

To solve the problem systematically, we will analyze the given chemical reaction and the changes in the concentrations of the reactants and products as the system reaches equilibrium.

### Step-by-Step Solution:

1. **Write the Balanced Chemical Equation:**
The reaction is given as:
\[ 2A(g) + B(g) \rightleftharpoons 3C(g) + D(g) \]

2. **Initial Moles:**
We start with 2 moles of \(A\) and 2 moles of \(B\). At the beginning (time \(t = 0\)):
- Moles of \(A\) = 2
- Moles of \(B\) = 2
- Moles of \(C\) = 0
- Moles of \(D\) = 0

3. **Change in Moles:**
Let \(x\) be the amount of \(D\) produced at equilibrium. According to the stoichiometry of the reaction:
- For every 1 mole of \(D\) produced, 3 moles of \(C\) are produced.
- For every 1 mole of \(D\) produced, 1 mole of \(B\) is consumed.
- For every 1 mole of \(D\) produced, 2 moles of \(A\) are consumed.

Therefore, at equilibrium:
- Moles of \(A\) = \(2 - 2x\)
- Moles of \(B\) = \(2 - x\)
- Moles of \(C\) = \(3x\)
- Moles of \(D\) = \(x\)

4. **Equilibrium Concentrations:**
The concentrations at equilibrium can be expressed in terms of \(x\):
- Concentration of \(A\) = \(\frac{2 - 2x}{V}\)
- Concentration of \(B\) = \(\frac{2 - x}{V}\)
- Concentration of \(C\) = \(\frac{3x}{V}\)
- Concentration of \(D\) = \(\frac{x}{V}\)

Here, \(V\) is the volume of the flask, which is constant.

5. **Comparison of Concentrations:**
We need to compare the concentrations of \(A\) and \(B\):
- Concentration of \(A\) = \(2 - 2x\)
- Concentration of \(B\) = \(2 - x\)

Since \(x\) is a positive value (as products are formed), we can analyze:
- \(2 - 2x < 2 - x\)
- This implies that the concentration of \(B\) is always greater than the concentration of \(A\).

6. **Conclusion:**
Therefore, at equilibrium, the relationship that must always be true is:
\[ [B] > [A] \]