Understanding $K_p$ and $K_c$ Relationship
The equilibrium constants $K_p$ and $K_c$ relate to reactions involving gases. $K_p$ is expressed in terms of partial pressures, while $K_c$ is expressed in terms of molar concentrations.
The relationship between $K_p$ and $K_c$ is given by the equation:
$K_p = K_c (RT)^{\Delta n}$
where:
- $R$ is the ideal gas constant.
- $T$ is the absolute temperature in Kelvin.
- $\Delta n$ is the change in the number of moles of gaseous products and reactants: $\Delta n = (\text{Sum of moles of gaseous products}) - (\text{Sum of moles of gaseous reactants})$.
For $K_p$ to be equal to $K_c$, the value of $\Delta n$ must be zero ($K_p = K_c (RT)^0 = K_c$). Therefore, the reaction for which $K_p \neq K_c$ is the one where $\Delta n \neq 0$.
Analyzing Gaseous Moles in Reactions
Let's calculate $\Delta n$ for each given reaction:
-
Option 1: $N_2 (g) + O_2 (g) \rightleftharpoons 2NO (g)$
Reactants: 1 mole $N_2$ + 1 mole $O_2$ = 2 moles of gas
Products: 2 moles $NO$ = 2 moles of gas
$\Delta n = 2 - 2 = 0$. Thus, $K_p = K_c$.
-
Option 2: $H_2O (g) + CO (g) \rightleftharpoons H_2 (g) + CO_2 (g)$
Reactants: 1 mole $H_2O$ + 1 mole $CO$ = 2 moles of gas
Products: 1 mole $H_2$ + 1 mole $CO_2$ = 2 moles of gas
$\Delta n = 2 - 2 = 0$. Thus, $K_p = K_c$.
-
Option 3: $H_2 (g) + I_2 (g) \rightleftharpoons 2HI (g)$
Reactants: 1 mole $H_2$ + 1 mole $I_2$ = 2 moles of gas
Products: 2 moles $HI$ = 2 moles of gas
$\Delta n = 2 - 2 = 0$. Thus, $K_p = K_c$.
-
Option 4: $N_2 (g) + 3H_2 (g) \rightleftharpoons 2NH_3 (g)$
Reactants: 1 mole $N_2$ + 3 moles $H_2$ = 4 moles of gas
Products: 2 moles $NH_3$ = 2 moles of gas
$\Delta n = 2 - 4 = -2$. Since $\Delta n \neq 0$, $K_p \neq K_c$.
Conclusion
The reaction $N_2 (g) + 3H_2 (g) \rightleftharpoons 2NH_3 (g)$ is the one for which $K_p \neq K_c$ because the change in the number of moles of gas ($\Delta n$) is not zero.
Similar Questions
- A solution of copper sulphate is electrolysed for $10 \text{ minutes}$ with a current of $1.5 \text{ amperes}$. The mass of copper deposited at cathode is :
(Given : Molar mass of Cu = $63 \text{ g mol}^{-1}$, $1 \text{ F} = 96487 \text{ C mol}^{-1}$) - The number of hydrogen atoms present in $5.4 \text{ g}$ of urea is :
(Given : Molar mass of urea : $60 \text{ g mol}^{-1}$, $N_A : 6.022 \times 10^{23} \text{ particles mol}^{-1}$) - Match List I with List II :
List I (Order of reaction) List II (Unit of rate constant) A. Zero order I. $mol^{-1} L s^{-1}$ B. First order II. $mol^{-2} L^2 s^{-1}$ C. Second order III. $s^{-1}$ D. Third order IV. $mol L^{-1} s^{-1}$
Choose the correct answer from the options given below : Consider the following reaction :
$2A (g) + B (g) \rightarrow 2D (g)$
$\Delta U^\ominus = -10 \text{ kJ mol}^{-1}$ and $\Delta S^\ominus = -44 \text{ J K}^{-1}$ at 298 K.
Identify the correct option with $\Delta G^\ominus$ for the reaction and spontaneity of the reaction at 298 K. (Given : $R = 8.31 \text{ J mol}^{-1} \text{K}^{-1}$)- A bulb is rated at 150 watt, converting 8% energy into light. If energy of one photon is $4.42 \times 10^{-19} \text{ J}$, how many photons are emitted by the bulb per second ?
Match List I with List II :
List I (Quantum Numbers )
$n$, $l$
List II (Orbital) A. 2, 1 I. 3d B. 4, 0 II. 2p C. 5, 3 III. 4s D. 3, 2 IV. 5f Choose the correct answer from the options given below :
For a certain reaction R $\rightarrow$ Product, the plot of [R] vs time has a negative slope as shown. The order of reaction is :
At 298 K, a certain buffer solution contains equal concentrations of $X^{-}$ and $HX$. $K_b$ for $X^-$ is $10^{-10}$. What is the pH of this buffer solution ?
- At a certain temperature T (K), during a process, 500 J is absorbed by the system and work of 200 J is done by the system. Then change in internal energy of the system is :
- In a qualitative analysis, $Bi^{3+}$ is detected by appearance of precipitate of $BiO(OH)(s)$. Calculate pH when the following equilibrium exists at 298 K :
$$BiO(OH) (s) \rightleftharpoons BiO^+ (aq) + OH^- (aq)$$
$K = 4 \times 10^{-10}$
(Given : $\log 2 = 0.3010$)
Important Questions from Physical Chemistry
- X and Y are the number of electrons involved, respectively during the oxidation of $\text{I}^-$ to $\text{I}_2$ and $\text{S}^{2-}$ to S by acidified $\text{K}_2\text{Cr}_2\text{O}_7$. The value of X + Y is ______.
- Consider two Group IV metal ions $\text{X}^{2+}$ and $\text{Y}^{2+}$.
A solution containing 0.01 M $\text{X}^{2+}$ and 0.01 M $\text{Y}^{2+}$ is saturated with $\text{H}_2\text{S}$. The pH at which the metal sulphide YS will form as a precipitate is ______. (Nearest integer)
(Given: $\text{K}_{sp}(\text{XS}) = 1 \times 10^{-22}$ at $25^\circ\text{C}$, $\text{K}_{sp}(\text{YS}) = 4 \times 10^{-16}$ at $25^\circ\text{C}$, $[\text{H}_2\text{S}] = 0.1\text{M}$ in solution, $\text{K}_{a1} \times \text{K}_{a2}(\text{H}_2\text{S}) = 1.0 \times 10^{-21}$, $\log 2 = 0.30$, $\log 3 = 0.48$, $\log 5 = 0.70$) - Electricity is passed through an acidic solution of $\text{Cu}^{2+}$ till all the $\text{Cu}^{2+}$ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solution for another 28 minutes by keeping the total volume of the solution fixed at 200 mL. The total volume of oxygen evolved at STP during the entire process is ______ mL. (Nearest integer)
[Given:
$\text{Cu}^{2+}\text{(aq)} + 2\text{e}^- \rightarrow \text{Cu(s)} \quad \text{E}^\circ_{\text{red}} = +0.34 \text{ V}$
$\text{O}_2\text{(g)} + 4\text{H}^+ + 4\text{e}^- \rightarrow 2\text{H}_2\text{O} \quad \text{E}^\circ_{\text{red}} = +1.23 \text{ V}$
Molar mass of Cu = $63.54 \text{ g mol}^{-1}$
Molar mass of $\text{O}_2$ = $32 \text{ g mol}^{-1}$
Faraday Constant = $96500 \text{ C mol}^{-1}$
Molar volume at STP = 22.4 L] - The half-life of ${}^{65}\text{Zn}$ is 245 days. After x days, 75% of original activity remained. The value of $x$ in days is _______. (Nearest integer)
(Given: $\log 3 = 0.4771$ and $\log 2 = 0.3010$) - Molar conductivity of a weak acid HQ of concentration $0.18 \text{ M}$ was found to be $1/30$ of the molar conductivity of another weak acid HZ with concentration of $0.02 \text{ M}$. If $\lambda^\circ_{Q^-}$ happened to be equal with $\lambda^\circ_{Z^-}$, then the difference of the $\text{pK}_a$ values of the two weak acids ($\text{pK}_a\text{(HQ)} - \text{pK}_a\text{(HZ)}$) is _______ (Nearest integer).
[Given: degree of dissociation ($\alpha$) < < 1 for both weak acids, $\lambda^\circ$ : limiting molar conductivity of ions]
