JEE Mains · Chemistry · STD 12 - 3. Chemical kinetics

For an elementary chemical reaction, \({A_2} \underset{{{k_{ - 1}}}}{\overset{{{k_1}}}{\longleftrightarrow}} 2A\) the expression for \(\frac{{d\left[ A \right]}}{{dt}}\) is

A \({k_1}\left[ {{A_2}} \right] - {k_{ - 1}}{\left[ A \right]^2}\)
B \(2{k_1}\left[ {{A_2}} \right] - {k_{ - 1}}{\left[ A \right]^2}\)
C \({k_1}\left[ {{A_2}} \right] + {k_{ - 1}}{\left[ A \right]^2}\)
D \(2{k_1}\left[ {{A_2}} \right] - {2k_{ - 1}}{\left[ A \right]^2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(2{k_1}\left[ {{A_2}} \right] - {2k_{ - 1}}{\left[ A \right]^2}\)

Step-by-step Solution

Detailed explanation

\(\frac{1}{2}\frac{{d[A]}}{{dt}}\, = \, - \,{K_1}\,{[A]_2}\, + \,{K_{ - 1}}\,{[A]^2}\) \(\frac{{d[A]}}{{dt}}\, = \,2{K_1}\,{[A]_2}\, - \,2{K_{ - 1}}\,{[A]^2}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From JEE Mains

Match List \(I\) with List \(II\)

List \(I\) (Anion)	List \(II\) \((\)Gas evolved on reaction with dil \(H _{2} SO _{4})\)
\(A.\) \(CO _{3}^{2-}\)	\(I.\) Colourless gas which turns lead acetate paper black
\(B.\) \(S^{2-}\)	\(II.\) Colourless gas which turns acidified potassium dichromate solution green.
\(C.\) \(SO_{3}{ }^{2-}\)	\(III.\) Brown fumes which turns acidified KI solution containing starch blue.
\(D.\) \(NO _{2}^{-}\)	\(IV.\) Colourless gas evolved with brisk effervescence, which turns lime water milky.

Choose the correct answer from the options given below

JEE Mains 2022 Medium

Explore more questions on app

	\(n\)	\(l\)	\(m_l\)
\(A\)	\(3\)	\(3\)	\(-3\)
\(B\)	\(3\)	\(2\)	\(-2\)
\(C\)	\(2\)	\(1\)	\(+1\)
\(D\)	\(2\)	\(2\)	\(+2\)