With reference to Arrhenius equation $k = Ae^{-E_a/RT}$

The rate constant increases exponentially with decreasing activation energy and increasing temperature.

The correct answer is Option (2) → The rate constant increases exponentially with decreasing activation energy and increasing temperature.

Reasoning:
According to the Arrhenius equation

k = A e^(−Eₐ / RT)

• Eₐ (Activation Energy) is in the numerator with a negative sign.
  If Eₐ decreases, the negative exponent becomes smaller in magnitude, so k increases.

• T (Temperature) is in the denominator.
  If T increases, the value of (−Eₐ / RT) becomes less negative, so the exponential term increases and k increases rapidly.

Thus:

• Lower activation energy → faster reaction → larger k

• Higher temperature → faster reaction → larger k

Therefore, the correct statement is that k increases exponentially with decreasing activation energy and increasing temperature.