In a chemical equilibrium, `K_(c)=K_(p)` when

Options

A. The number of molecules entering into a reaction is more than the number of molecules produced.
B. The number of molecules entering into the reaction is equal to the number of molecules produced.
C. the number of molecules entering into the reaction is less to the number of moleculed produced.
D. None of the above

Answer

To determine when \( K_c = K_p \) in a chemical equilibrium, we can follow these steps:

### Step 1: Understand the relationship between \( K_c \) and \( K_p \)
The relationship between the equilibrium constants \( K_c \) (concentration-based) and \( K_p \) (pressure-based) is given by the equation:
\[ K_p = K_c (RT)^{\Delta n_g} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta n_g \) is the change in the number of moles of gas, calculated as:
\[ \Delta n_g = n_{\text{products}} - n_{\text{reactants}} \]

### Step 2: Analyze the condition for \( K_c = K_p \)
For \( K_c \) to equal \( K_p \), the equation can be simplified:
\[ K_p = K_c (RT)^{\Delta n_g} \implies K_c = K_c (RT)^{\Delta n_g} \]
This implies that:
\[ (RT)^{\Delta n_g} = 1 \]
The only way for this to be true is if \( \Delta n_g = 0 \) because any non-zero exponent would not yield 1.

### Step 3: Determine what \( \Delta n_g = 0 \) means
The condition \( \Delta n_g = 0 \) means that the number of moles of gaseous products is equal to the number of moles of gaseous reactants:
\[ n_{\text{products}} = n_{\text{reactants}} \]

### Step 4: Conclusion
Thus, \( K_c = K_p \) when the number of molecules entering into the reaction is equal to the number of molecules produced.

### Final Answer
The correct option is: **the number of molecules entering into the reaction is equal to the number of molecules produced.**

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