Ethylene dibromide `(C_(2)H_(4)Br_(2))` and 1, 2 - dibromo propane from a series of ideal solutions over the whole range of composition. At `85^(@)C`, the vapour pressure of these two liquids are 173 and 127 torr respectively. What would be the mole fraction of ethylene dibromide in a solution at `85^(@)C` equilibrated with `1:1` molar mixture in the vapour?

Explanation

To solve the problem, we need to find the mole fraction of ethylene dibromide `(C2H4Br2)` in a solution that is in equilibrium with a 1:1 molar mixture in the vapor phase at `85°C`. We are given the vapor pressures of ethylene dibromide and 1,2-dibromopropane.

### Step-by-Step Solution:

1. **Identify the Given Data**:
- Vapor pressure of ethylene dibromide, \( P_{A}^0 = 173 \, \text{torr} \)
- Vapor pressure of 1,2-dibromopropane, \( P_{B}^0 = 127 \, \text{torr} \)
- Molar ratio in vapor = 1:1
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