At 800 K a reaction mixture contained 0.5 mole of `SO_(2)`, 0.12 mole of `O_2` and 5 moles of `SO_3` at equilibrium. `K_c` for the equilibrium `2SO_(2) +O_2 Leftrightarrow 2SO_3,` is 833 lit/mol. If the volume of the container is 1 litre, calculate how much `O_2` is to be added at this equilibrium in order to get 5.2 moles of `SO_3` at the same temperature.

Explanation

To solve the problem, we need to determine how much \( O_2 \) should be added to the equilibrium mixture to increase the amount of \( SO_3 \) from 5 moles to 5.2 moles at 800 K.

### Step-by-step Solution:

1. **Write the balanced chemical equation:**
\[ 2SO_2 + O_2 \leftrightarrow 2SO_3 \]
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