For the given hypothetical reactions, the equilibrium constants are as follows:
\[ X \rightleftharpoons Y; \, K_1 = 1.0 \]
\[ Y \rightleftharpoons Z; \, K_2 = 2.0 \]
\[ Z \rightleftharpoons W; \, K_3 = 4.0 \]
The equilibrium constant for the reaction
\[ X \rightleftharpoons W\]
is:
\[ X \rightleftharpoons Y; \, K_1 = 1.0 \]
\[ Y \rightleftharpoons Z; \, K_2 = 2.0 \]
\[ Z \rightleftharpoons W; \, K_3 = 4.0 \]
The equilibrium constant for the reaction
\[ X \rightleftharpoons W\]
is:
- 6.0
- 12.0
- 8.0
- 7.0
The Correct Option is C
Approach Solution - 1
To determine the equilibrium constant for the overall reaction \( X \rightleftharpoons W \), we need to combine the given reactions and their respective equilibrium constants (\( K_1, K_2, \) and \( K_3 \)) in the following sequence:
- The reactions are:
- \( X \rightleftharpoons Y \) with \( K_1 = 1.0 \)
- \( Y \rightleftharpoons Z \) with \( K_2 = 2.0 \)
- \( Z \rightleftharpoons W \) with \( K_3 = 4.0 \)
- The overall reaction \( X \rightleftharpoons W \) is the sum of the three individual reactions:
- \( X \rightleftharpoons Y \), \( Y \rightleftharpoons Z \), and \( Z \rightleftharpoons W \)
- To find the equilibrium constant \( K \) for the overall reaction, we multiply the equilibrium constants of the individual reactions:
- \( K = K_1 \times K_2 \times K_3 \)
- Substituting the given values:
- \( K = 1.0 \times 2.0 \times 4.0 \)
- Simplifying the multiplication:
- \( K = 8.0 \)
Thus, the equilibrium constant for the reaction \( X \rightleftharpoons W \) is \(8.0\).
Let's evaluate the options given:
- 6.0: This value comes from incorrect multiplication.
- 12.0: This option is irrelevant to the multiplication results.
- 8.0: Correct, as derived from \( 1.0 \times 2.0 \times 4.0 \).
- 7.0: This option is incorrect and irrelevant.
The correct answer is 8.0.
Approach Solution -2
The equilibrium constant for the net reaction $X \rightleftharpoons W$ is the product of the individual constants:
\[K = K_1 \cdot K_2 \cdot K_3.\]
Substitute values:
\[K = 1 \cdot 2 \cdot 4 = 8.\]
Final Answer:
8.0
Top JEE Main Chemistry Questions
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- At equilibrium the concentrations of and in a sealed vessel at . What will be for the reaction
- Find out the major products from the following reactions
Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
- The correct order of atomic radii is:
Top JEE Main Law Of Chemical Equilibrium And Equilibrium Constant Questions
- $\text{The following concentrations were observed at 500 K for the formation of NH}_3 \text{ from N}_2 \text{ and H}_2\text{. At equilibrium: [N}_2] = 2 \times 10^{-2} \, \text{M, [H}_2] = 3 \times 10^{-2} \, \text{M, and [NH}_3] = 1.5 \times 10^{-2} \, \text{M. Equilibrium constant for the reaction is \_\_\_\_\_\_.}$
- The following reaction occurs in the Blast furnace where iron ore is reduced to iron metal:
\(\text{Fe}_2\text{O}_3(s) + 3\text{CO}(g) \rightleftharpoons 2\text{Fe}(l) + 3\text{CO}_2(g)\)
Using Le Chatelier's principle, predict which one of the following will not disturb the equilibrium. - The equilibrium $\mathrm{Cr_2O_7^{2-}} \rightleftharpoons 2\mathrm{CrO_4^{2-}}$ is shifted to the right in:
At \(-20^\circ \text{C}\) and 1 atm pressure, a cylinder is filled with an equal number of \(H_2\), \(I_2\), and \(HI\) molecules for the reaction:
\[H_2(g) + I_2(g) \rightleftharpoons 2HI(g)\] The \(K_P\) for the process is \(x \times 10^{-1}\).
(x = ___________)
Given: \(R = 0.082 \, \text{L atm K}^{-1} \text{mol}^{-1}\)- Consider the equilibrium: \[ \text{CO(g)} + \text{3H}_2\text{(g)} \rightleftharpoons \text{CH}_4\text{(g)} + \text{H}_2\text{O(g)} \] If the pressure applied over the system increases by two fold at constant temperature then:
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.