To determine the relationship between the concentrations of the products and reactants at equilibrium for the reaction given:
[tex]$
N_2(g) + 3 H_2(g) \longleftrightarrow 2 NH_3(g)
$[/tex]
we need to consider the value of the equilibrium constant [tex]\( K \)[/tex].
The equilibrium constant [tex]\( K \)[/tex] for a reaction is defined as:
[tex]\[
K = \frac{[\text{products}]}{[\text{reactants}]}
\][/tex]
For the given reaction, the expression for the equilibrium constant [tex]\( K \)[/tex] is:
[tex]\[
K = \frac{[NH_3]^2}{[N_2][H_2]^3}
\][/tex]
Given that [tex]\( K = 1.0 \times 10^5 \)[/tex], let’s analyze what this large value means.
### Analyzing the Value of [tex]\( K \)[/tex]
- Value of [tex]\( K \)[/tex]: The value [tex]\( 1.0 \times 10^5 \)[/tex] is very large (100,000).
- Implication: A large equilibrium constant means that the numerator (the concentration of products) is much greater than the denominator (the concentration of reactants). This implies that at equilibrium, there is a much higher concentration of products compared to reactants.
### Conclusion
Given the very large value of the equilibrium constant:
1. Reactants are favored: No. A large [tex]\( K \)[/tex] suggests products are favored.
2. The reaction is incomplete and reaches equilibrium at a later stage: No. A large [tex]\( K \)[/tex] indicates the reaction strongly favors the formation of products rather than being incomplete.
3. Concentrations of products and reactants are approximately equal: No. If [tex]\( K \)[/tex] were close to 1, then this could be true. However, [tex]\( 1.0 \times 10^5 \)[/tex] is far from 1.
4. Products are favored: Yes. As [tex]\( K = 1.0 \times 10^5 \)[/tex] is much greater than 1, this means the reaction heavily favors the products at equilibrium.
Therefore, the relationship between the concentrations at equilibrium is that products are favored.
