JEE Advanced · Chemistry · 18. Chemical Kinetics

According to the Arrhenius equation,

A A high activation energy usually implies a fast reaction
B Rate constant increase with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy
C Higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant
D The pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy.

Verified Solution

Answer & Solution

Correct Answer

(B) Rate constant increase with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy

Step-by-step Solution

Detailed explanation

k = A e^{- E_{a} / R T}

High

E_{a}

means less k, hence slower rate.
B]

e^{- E_{a} / R T}

= fraction of molecules having kinetic energy greater than activation energy which increase as temperature increases.
C] ln

\frac{k_{2}}{k_{1}} = \frac{E_{a}}{R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}]

i.e., ln

\frac{K_{2}}{k_{1}} \propto E_{a}

D] Rate of reaction

\propto

Total number of collisions × Fraction of collisions which can form product
Rate of reaction

\propto Z_{A B} \times (P \times e^{- E_{a} / R T})

\propto A e^{- E_{a} / R T}

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

The wave function,

ψ_{n, l, m_{l}}

is a mathematical function whose value depends upon spherical polar coordinates

(r, θ, ϕ)

of the electron and characterized by the quantum numbers

n, l

and

m_{l}

. Here

r

is the distance from the nucleus,

θ

is colatitude and

ϕ

is azimuth. In the mathematical functions given in the Table,

Z

is the atomic number and

a_{o}

is Bohr radius

Column 1	Column 2	Column 3
(I) 1s orbital	\(\text {(i) } \psi_{ n , 1, m_1}\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{3}{2}} e ^{-\left(\frac{ Zr }{ e _{ o }}\right)}\)	(P)
(II) 2s orbital	(ii) One radial node	(Q) Probability density at the nucleus \(\propto \frac{1}{ a _{ o }^3}\).
(III) \(2 p _{ z }\) orbital	\(\text {(iii) } \psi_{ n }, 1, m_{ l }\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{5}{2}} re ^{-\left(\frac{ Zr }{2 a _{ o }}\right)} \cos \theta\)	(R) Probability density is maximum at the nucleus.
(IV) \(3 d_{ z }^2\) orbital	(iv) \(x y\)-plane is a nodal plane	(S) Energy needed to excite an electron from \(n =2\) state to \(n =4\) state is \(\frac{27}{32}\) times the energy needed to excite are electron from \(n =2\) state to \(n =6\) state.

For hydrogen atom, what is the only CORRECT combination?

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