For the reaction N 2(g) + 3H 2(g) \(\rightleftharpoons\) 2NH 3(g) ΔH = -ve :
K p= K c(RT) -2
Understanding the Kp and Kc Relationship in Equilibrium
The equilibrium constant for a reversible reaction can be expressed in terms of partial pressures ($K_p$) or molar concentrations ($K_c$). There is a standard relationship between these two constants, which depends on the change in the number of moles of gas during the reaction.
General Formula for Kp and Kc Relation
The relationship between $K_p$ and $K_c$ is given by the following equation:
\[K_p = K_c(RT)^{\Delta n_{\text{g}}}\]
Where:
- \(K_p\) is the equilibrium constant in terms of partial pressures.
- \(K_c\) is the equilibrium constant in terms of molar concentrations.
- \(R\) is the ideal gas constant.
- \(T\) is the absolute temperature in Kelvin.
- \(\Delta n_{\text{g}}\) is the change in the number of moles of gas in the balanced chemical equation. It is calculated as the total moles of gaseous products minus the total moles of gaseous reactants.
Calculating \(\Delta n_{\text{g}}\) for the Given Reaction
The given reaction is the synthesis of ammonia:
\[\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightleftharpoons 2\text{NH}_3\text{(g)}\]
To find \(\Delta n_{\text{g}}\), we look at the stoichiometric coefficients of the gaseous species:
- Moles of gaseous reactants = moles of \(\text{N}_2\text{(g)}\) + moles of \(\text{H}_2\text{(g)}\) = $1 + 3 = 4$ moles.
- Moles of gaseous products = moles of \(\text{NH}_3\text{(g)}\) = $2$ moles.
Now, calculate \(\Delta n_{\text{g}}\):
\[\Delta n_{\text{g}} = (\text{Moles of gaseous products}) - (\text{Moles of gaseous reactants})\]
\[\Delta n_{\text{g}} = 2 - 4 = -2\]
Note: The information about \(\Delta H = -\text{ve}\) indicates that the reaction is exothermic, but this fact is not required to determine the relationship between \(K_p\) and \(K_c\).
Determining the Relationship between Kp and Kc
Substitute the calculated value of \(\Delta n_{\text{g}}\) into the general formula:
\[K_p = K_c(RT)^{\Delta n_{\text{g}}}\]
\[K_p = K_c(RT)^{-2}\]
This equation shows the relationship between \(K_p\) and \(K_c\) for the given reaction at temperature T.
Comparing with Options
Let's compare our derived relationship with the provided options:
| Option | Relationship |
|---|---|
| 1 | \(K_p = K_c(RT)^{-2}\) |
| 2 | \(K_p = K_c\) |
| 3 | \(K_p = K_cRT\) |
| 4 | \(K_p = K_c(RT)^{-1}\) |
Our calculated relationship \(K_p = K_c(RT)^{-2}\) matches Option 1.
Important Questions from Equilibrium
What is the pH of a solution prepared by dissolving $0.0025$ moles of $HNO_3$ in $250\,mL$ of water?
Which species acts as acid like behaviour in the following reaction?
\(HPO_4^{2-}+NH_4^{1+}\rightarrow H_2PO_4^{1-}+NH_3\)
Aqueous solution of CH 3COONa is:
pH of a neutral solution is ___________.
A stain of curry on a white cloth become reddish brown when soap is used because the soap is:
