A vessel at 1000 K contains `CO_2` with a pressure of 0.5 atm. Some of the `CO_2` is converted to CO on addition of graphite. Calculate the value of K, if the total pressure at equilibrium is 0.8 atm.

Explanation

To solve the problem, we need to analyze the reaction and the changes in pressure that occur when some of the \( \text{CO}_2 \) is converted to \( \text{CO} \) upon the addition of graphite.

### Step-by-Step Solution:

1. **Write the Reaction:**
The reaction for the conversion of carbon dioxide to carbon monoxide is:
\[
\text{CO}_2 (g) + \text{C} (s) \rightleftharpoons 2 \text{CO} (g)
...