Sure! Let's address the relationship between the equilibrium constants for the reaction:
[tex]\[ 2 \text{CO} _{(g)} + \text{O}_2{}_{(g)} \rightleftharpoons 2 \text{CO} _2{}_{(g)} \][/tex]
Given:
[tex]\[
K_{89} = 6.8
\][/tex]
### Explanation of the Relationship:
1. Reaction Description:
The given chemical reaction is:
[tex]\[
2 \text{CO} _{(g)} + \text{O}_2{}_{(g)} \rightleftharpoons 2 \text{CO} _2{}_{(g)}
\][/tex]
This represents the equilibrium state of carbon monoxide gas reacting with oxygen gas to form carbon dioxide gas.
2. Equilibrium Constant Interpretation:
The equilibrium constant [tex]\( K \)[/tex] for a reaction is given by:
[tex]\[
K = \frac{[\text{Products}]}{[\text{Reactants}]}
\][/tex]
For the given reaction, the equilibrium constant [tex]\( K_{89} \)[/tex] at a specific temperature [tex]\( T \)[/tex] is given as 6.8. This means:
[tex]\[
K_{89} = \frac{[\text{CO}_2]^2}{[\text{CO}]^2 [\text{O}_2]}
\][/tex]
3. Related Equilibrium Constant:
Since no additional information about temperature changes or different conditions is provided, we assume that the equilibrium constant [tex]\( K_{89} \)[/tex] remains the same under the given conditions. Therefore:
[tex]\[
K_{89} = 6.8
\][/tex]
### Conclusion:
In the given conditions where temperature and other external factors remain constant, the equilibrium constant [tex]\( K_{89} \)[/tex] for the reaction:
[tex]\[
2 \text{CO} _{(g)} + \text{O}_2{}_{(g)} \rightleftharpoons 2 \text{CO} _2{}_{(g)}
\][/tex]
is 6.8.
Thus, the value of [tex]\( K_{89} \)[/tex] is consistent and remains 6.8 for the given reaction under these specific conditions.
