Question

Consider the Arrhenius equation given below and mark the correct option. $k=Ae-\frac{Ea}{RT}$

• A. Rate constant increases exponentially with decreasing activation energy and decreasing temperature.
• B. Rate constant decreases exponentially with increasing activation energy and decreasing temperature.
• C. Rate constant increases exponentially with increasing activation energy and decreasing temperature.
• D. Rate constant increases exponentially with decreasing activation energy and increasing temperature.

Answer 1

The correct option is A Rate constant increases exponentially with decreasing activation energy and decreasing temperature.

According to Arrhenius equation
$k=Ae-\frac{Ea}{RT}$

Where,
𝑘 = 𝑅𝑎𝑡𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝐴 = 𝑃𝑟𝑒−𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡𝑖𝑎𝑙 𝑓𝑎𝑐𝑡𝑜𝑟
$E_a$ = 𝐴𝑐𝑡𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦
𝑅 = 𝐺𝑎𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑇 = 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒

In the Arrhenius equation it is observed that as activation energy decreases, value of exponential term $e-\frac{Ea}{RT}$ will increase and thus rate constant will also increase (since pre-exponential factor is a constant).

And Arrhenius equation can be written as: $k=\frac{A}{Ea}$


Now, if temperature increases, the value of 1/T will decrease and thus the value of the exponential term in the denominator will