Question at position 16 Which of the following decreases as temperature increases? Half life (t1/2) Activation energy (Ea) Rate constant (k) Reaction rate k onlyEa onlyt1/2 onlyk and Ea onlyreaction rate onlyreaction rate and t1/2 onlySingle choice
A
k only
B
Ea only
C
t1/2 only
D
k and Ea only
E
reaction rate only
F
reaction rate and t1/2 only

Question

Question at position 16 Which of the following decreases as temperature increases? Half life (t1/2) Activation energy (Ea) Rate constant (k) Reaction rate k onlyEa onlyt1/2 onlyk and Ea onlyreaction rate onlyreaction rate and t1/2 onlySingle choice

A

k only

B

Ea only

C

t1/2 only

D

k and Ea only

E

reaction rate only

F

reaction rate and t1/2 only

BlackTom AI · Accepted Answer

Arrhenius equation k = A·e^(−Ea/RT) shows that the rate constant k increases as temperature T increases (because the negative exponent becomes less negative). This is the central kinetic relation used below.

1) Relevant knowledge points and concepts
- Arrhenius equation: k = A e^(−Ea/RT). For typical chemical reactions, Ea (activation energy) is a fixed characteristic of the reaction and does not decrease with T.
- Reaction rate (for a reaction of order n): rate = k·[reactants]^n. If k increases, the rate increases (for fixed concentrations).
- Half‑life relationships: for first‑order t1/2 = ln2 / k. For zero‑ and second‑order reactions t1/2 is also inversely proportional to k (e.g., zero order t1/2 = [A]0/(2k); second order t1/2 = 1/(k[A]0)). Thus increasing k reduces t1/2 for common reaction orders.

2) Step‑by‑step reasoning
- From Arrhenius, as T increases, e^(−Ea/RT) increases → k increases (d k/dT > 0).
- Since rate = k·[ ]^n, increasing k → reaction rate increases.
- Because t1/2 is inversely proportional to k for standard kinetic orders, increasing k → t1/2 decreases.
- Ea is a property of the reaction and does not decrease when T increases (it appears in the exponential but is not temperature‑dependent in the simple Arrhenius model).

3) Intermediate steps / equations
- k = A e^(−Ea/RT). If T ↑, exponent −Ea/(RT) becomes less negative → e^(...) ↑ → k ↑.
- First‑order example: t1/2 = ln2 / k. If k doubles (due to higher T), t1/2 halves.

4) Why the correct answer is correct
Only t1/2 decreases with increasing temperature because k increases with T (making t1/2 = constant/k smaller) while reaction rate increases and Ea remains essentially unchanged.

5) Why other options are incorrect
- "k only": incorrect because k increases, not decreases.
- "Ea only": Ea does not decrease with T (it is a constant parameter).
- "k and Ea only": both are incorrect — k increases, Ea stays constant.
- "reaction rate only": reaction rate increases as k increases.
- "reaction rate and t1/2 only": reaction rate does not decrease, so this pair is wrong.

6) Conclusion
Therefore only the half‑life (t1/2) decreases as temperature increases. This matches the provided answer: t1/2 only.

Question at position 16 Which of the following decreases as temperature increases? Half life (t1/2) Activation energy (Ea) Rate constant (k) Reaction rate k onlyEa onlyt1/2 onlyk and Ea onlyreaction rate onlyreaction rate and t1/2 onlySingle choice

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