Which one of the following given graphs represents the variation of rate constant (k) with temperature (T) for an endothermic reaction?

Solution

Chemistry ma’am · 3 steps

Endothermic means a large positive Eₐ, so k rises with T, and rises faster and faster.

1. Sign of Ea. For an endothermic reaction the products lie above the reactants. The barrier must be at least as high as that energy gap, so Eₐ ≥ Δ H > 0, and Eₐ is large.

   k = A e^(-Eₐ/RT) ⇒ dk/dT = k Eₐ/RT² > 0

2. Shape of curve. Since Eₐ > 0, k increases with T. In the usual range Eₐ is many times RT (about 20 times for Eₐ = 50 kJ mol⁻¹ at 300 K), so the curve bends upward. Each 10 K rise multiplies k by about 2 to 3 instead of adding a fixed amount.

   Graph	What it shows	Fits Arrhenius?
   (a)	Rises, bending upward (exponential)	Yes
   (b)	Straight line, k ∝ T	No, k is exponential in -1/T
   (c)	Rises, bending downward	No, growth slows instead of speeding up
   (d)	Falls as T rises	No, that would need Eₐ < 0

3. So. The exponentially rising curve in (a) shows how k varies with T for an endothermic reaction.

The idea to keep. Plot k against T and you get an upward-bending exponential. Plot ln k against 1/T and you get a straight line with slope -Eₐ/R. Do not mix up the two plots.

Answer from the NTA final answer key. Solution by PrepWiser.