Question:
At \(450\,K\), for the reaction
\[
2SO_2(g)+O_2(g)\rightleftharpoons 2SO_3(g),
\]
the value of
\[
K_p=2.0\times10^{10}.
\]
What is the value of \(K_c\) for the decomposition of sulphur trioxide at the same temperature?
\[
R=0.083\ \text{L bar mol}^{-1}\text{K}^{-1}
\]
At \(450\,K\), for the reaction
\[
2SO_2(g)+O_2(g)\rightleftharpoons 2SO_3(g),
\]
the value of
\[
K_p=2.0\times10^{10}.
\]
What is the value of \(K_c\) for the decomposition of sulphur trioxide at the same temperature?
\[
R=0.083\ \text{L bar mol}^{-1}\text{K}^{-1}
\]
Show Hint
Remember:
\[
K_p=K_c(RT)^{\Delta n}
\]
and for a reverse reaction,
\[
K_{\text{reverse}}
=
\frac{1}{K_{\text{forward}}}.
\]
Always calculate \(\Delta n\) using gaseous species only.
Updated On: Jul 29, 2026
- \[ 7.47\times10^{11} \]
- \[ 1.34\times10^{-12} \]
- \[ 7.47\times10^{-12} \]
- \[ 1.34\times10^{12} \]
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
For gaseous equilibria,
\[
K_p=K_c(RT)^{\Delta n},
\]
where
\[
\Delta n
=
\text{(moles of gaseous products)}
-
\text{(moles of gaseous reactants)}.
\]
Step 1: Find \(K_c\) for the given reaction. Given reaction: \[ 2SO_2(g)+O_2(g) \rightleftharpoons 2SO_3(g) \] Hence, \[ \Delta n=2-(2+1)=-1. \] Therefore, \[ K_p = K_c(RT)^{-1}. \] \[ K_c = K_p(RT). \] Substituting, \[ K_c = (2.0\times10^{10}) (0.083\times450). \] \[ = (2.0\times10^{10})(37.35). \] \[ = 7.47\times10^{11}. \]
Step 2: Find \(K_c\) for the decomposition reaction. Decomposition of sulphur trioxide is the reverse reaction: \[ 2SO_3(g) \rightleftharpoons 2SO_2(g)+O_2(g). \] For the reverse reaction, \[ K_c' = \frac{1}{K_c}. \] Thus, \[ K_c' = \frac{1}{7.47\times10^{11}}. \] \[ K_c' = 1.34\times10^{-12}. \]
Final Answer: \[ \boxed{K_c=1.34\times10^{-12}} \] \[ \boxed{\text{Answer = (B)}} \]
Step 1: Find \(K_c\) for the given reaction. Given reaction: \[ 2SO_2(g)+O_2(g) \rightleftharpoons 2SO_3(g) \] Hence, \[ \Delta n=2-(2+1)=-1. \] Therefore, \[ K_p = K_c(RT)^{-1}. \] \[ K_c = K_p(RT). \] Substituting, \[ K_c = (2.0\times10^{10}) (0.083\times450). \] \[ = (2.0\times10^{10})(37.35). \] \[ = 7.47\times10^{11}. \]
Step 2: Find \(K_c\) for the decomposition reaction. Decomposition of sulphur trioxide is the reverse reaction: \[ 2SO_3(g) \rightleftharpoons 2SO_2(g)+O_2(g). \] For the reverse reaction, \[ K_c' = \frac{1}{K_c}. \] Thus, \[ K_c' = \frac{1}{7.47\times10^{11}}. \] \[ K_c' = 1.34\times10^{-12}. \]
Final Answer: \[ \boxed{K_c=1.34\times10^{-12}} \] \[ \boxed{\text{Answer = (B)}} \]
Was this answer helpful?
0
0
Top AP EAPCET Chemistry Questions
- The four quantum numbers of the valence electron of potassium are :
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
- In which of the following the election gain enthalpy of elements is correctly arranged?
- The radii of $ \text{F,}{{\text{F}}^{-}}\text{O} $ and $ {{\text{O}}^{2-}} $ are in the order
- Which of the following has the highest first ionization potential?
View More Questions
Top AP EAPCET Equilibrium Constant Questions
- At $1000\, K$, the equilibrium constant. $K_{C}$ for the reaction $2 NOCl (g) \rightleftharpoons 2 NO (g)+ Cl _{2}(g)$ is $4.0 \times 10^{-6} mol\, L ^{-1}$. The $K_{P}$ (in bar) at the same temperature is $\left(R=0.083 \,L\right.$ bar $\left. K ^{-1}\, mol ^{-1}\right)$
- For the reaction X(g) $\rightarrow$ Y(g) at equilibrium, the partial pressure of Y is one-third that of X. What is the standard Gibbs energy change ($\Delta G^\circ$) for this reaction?
- At T(K) the $K_c$ for the reactions (I) and (II) are $2.4 \times 10^{30}$ and 1.4 respectively. What is the $K_c$ value for: $\frac{1}{2}N_2(g) + \frac{1}{2}O_2(g) + \frac{1}{2}Br_2(g) \rightleftharpoons NOBr(g)$?
- At a given temperature T in a 10.0 L flask, 2.0 moles of N$_2$O$_4$(g) is heated. At equilibrium, 20% of N$_2$O$_4$(g) dissociates into NO$_2$(g). The value of K$_C$ for the reaction N$_2$O$_4$(g) $\rightleftharpoons$ 2NO$_2$(g) is:
- At \(500\,\text{K}\), for the reaction, \[ N_2(g)+3H_2(g)\rightleftharpoons 2NH_3(g), \] the \(K_p\) is \(0.036\,\text{atm}^{-2}\). What is its \(K_c\) in \(L^2\text{mol}^{-2}\)? \((R=0.082\,L\,\text{atm mol}^{-1}\text{K}^{-1})\)
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions