The equilibrium constant for the reaction `Br_2(l)+Cl_(2)(g)hArr2Br Cl(g)` at `27^@C` is `k_P=1` atm in a closed container of volume 164 L initially 10 moles of `Cl_2` are present at `27^@C`.
What minimum mole of `Br_2(l)` must be introduced into this container so that above equilibrium is maintained at total pressure of 2.25 atm.Vapour pressure of `Br_2(l)` at `27^@C` is 0.25 atm.Assume that volume occupied by liquid is negligible . [R=0.082 L atm `"mole"^(-1) K^(-1)`, Atomic mass of bromine =80]

Explanation

To solve the problem, we need to determine the minimum moles of \( Br_2(l) \) that must be introduced into the container to maintain the equilibrium at a total pressure of 2.25 atm.

### Step-by-Step Solution:

1. **Identify Initial Conditions:**
- Initial moles of \( Cl_2 \) = 10 moles
- Volume of the container = 164 L
- Temperature = 27°C = 300 K
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