ext{For the reaction } N_2(g) + 3H_2(g) ightleftharpoons 2NH_3(g) \Delta H = ext{-ve :}

Q: \text{For the reaction } N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \Delta H = \text{-ve :}

For the reaction $ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) $, the relationship between the equilibrium constants $ K_p $ and $ K_c $ can be determined using the equation: \[ K_p = K_c(RT)^{\Delta n} \] where: - $ R $ is the universal gas constant, - $ T $ is the temperature in Kelvin, - $ \Delta n $ is the change in the number of moles of gas between products and reactants. For this reaction: - The number of moles of gaseous reactants is $ 1 + 3 = 4 $. - The number of moles of gaseous products is $ 2 $. Thus, the change in moles of gas, $ \Delta n $, is: \[ \Delta n = \text{moles of products} - \text{moles of reactants} = 2 - 4 = -2 \] Substituting $ \Delta n = -2 $ into the equation for $ K_p $, we get: \[ K_p = K_c(RT)^{-2} \] This matches Option 1, which states $ K_p = K_c(RT)^{-2} $. Therefore, Option 1 is correct. **Explanation for why other options are incorrect:** - **Option 2: $ K_p = K_c $** This option would be correct if $ \Delta n = 0 $, meaning there is no change in the number of moles of gas between reactants and products. However, in this reaction, $ \Delta n = -2 $, so $ K_p \neq K_c $. - **Option 3: $ K_p = K_cRT $** This option implies that $ \Delta n = 1 $. Since $ \Delta n = -2 $ for this reaction, this relationship does not hold. - **Option 4: $ K_p = K_c(RT)^{-1} $** This option would be correct if $ \Delta n = -1 $. However, since $ \Delta n = -2 $ for this reaction, this relationship is incorrect. In conclusion, the correct relationship between $ K_p $ and $ K_c $ for the given reaction is $ K_p = K_c(RT)^{-2} $, which is why Option 1 is the correct answer.

Question

ext{For the reaction }  N_2(g) + 3H_2(g) ightleftharpoons 2NH_3(g) \Delta H = 	ext{-ve :}

Accepted Answer

For the reaction $ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) $, the relationship between the equilibrium constants $ K_p $ and $ K_c $ can be determined using the equation:

$$ K_p = K_c(RT)^{\Delta n} $$

where:
- $ R $ is the universal gas constant,
- $ T $ is the temperature in Kelvin,
- $ \Delta n $ is the change in the number of moles of gas between products and reactants.

For this reaction:
- The number of moles of gaseous reactants is $ 1 + 3 = 4 $.
- The number of moles of gaseous products is $ 2 $.

Thus, the change in moles of gas, $ \Delta n $, is:

$$ \Delta n = \text{moles of products} - \text{moles of reactants} = 2 - 4 = -2 $$

Substituting $ \Delta n = -2 $ into the equation for $ K_p $, we get:

$$ K_p = K_c(RT)^{-2} $$

This matches Option 1, which states $ K_p = K_c(RT)^{-2} $. Therefore, Option 1 is correct.

**Explanation for why other options are incorrect:**

- **Option 2: $ K_p = K_c $**

This option would be correct if $ \Delta n = 0 $, meaning there is no change in the number of moles of gas between reactants and products. However, in this reaction, $ \Delta n = -2 $, so $ K_p \neq K_c $.

- **Option 3: $ K_p = K_cRT $**

This option implies that $ \Delta n = 1 $. Since $ \Delta n = -2 $ for this reaction, this relationship does not hold.

- **Option 4: $ K_p = K_c(RT)^{-1} $**

This option would be correct if $ \Delta n = -1 $. However, since $ \Delta n = -2 $ for this reaction, this relationship is incorrect.

In conclusion, the correct relationship between $ K_p $ and $ K_c $ for the given reaction is $ K_p = K_c(RT)^{-2} $, which is why Option 1 is the correct answer.