In the reactions
` H_2(g) +Cl_2 ( g) hArr 2HCl (g)` .

Options

A. `Kp = K_c`
B. ` K_p ne K_c`
C. ` K_p gt K_c`
D. ` K_p lt K_c`

Answer

To solve the problem regarding the relationship between Kp and Kc for the reaction:

\[ H_2(g) + Cl_2(g) \rightleftharpoons 2HCl(g) \]

we will follow these steps:

### Step 1: Understand Kp and Kc
Kp is the equilibrium constant for gaseous reactions expressed in terms of partial pressures, while Kc is the equilibrium constant expressed in terms of molar concentrations. The relationship between Kp and Kc is given by the formula:

\[ K_p = K_c (RT)^{\Delta N_g} \]

where:
- \( R \) is the ideal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta N_g \) is the change in the number of moles of gas, calculated as the number of moles of gaseous products minus the number of moles of gaseous reactants.

### Step 2: Calculate \(\Delta N_g\)
For the given reaction:

- Products: \( 2HCl(g) \) → 2 moles of gas
- Reactants: \( H_2(g) + Cl_2(g) \) → 1 + 1 = 2 moles of gas

Now, calculate \(\Delta N_g\):

\[ \Delta N_g = \text{(moles of products)} - \text{(moles of reactants)} = 2 - 2 = 0 \]

### Step 3: Determine the relationship between Kp and Kc
Since we found that \(\Delta N_g = 0\), we can use the relationship between Kp and Kc:

\[ K_p = K_c (RT)^{\Delta N_g} \]

Substituting \(\Delta N_g = 0\):

\[ K_p = K_c (RT)^0 = K_c \cdot 1 = K_c \]

### Conclusion
Thus, the relationship between Kp and Kc for the given reaction is:

\[ K_p = K_c \]