Question

Arrhenius plot for predicting drug stability at room temperature is drawn between _______

• A. \( \text{K vs. } 1/\text{T} \)
• B. \( \log \text{K vs. T} \)
• C. \( \log \text{K vs. } 1/\text{T} \)
• D. \( \log \text{C vs. } 1/\text{T} \)

Hint:

Remember the linear form of the Arrhenius equation involves the logarithm of the rate constant and the inverse of the temperature.

Answer 1

The Correct Option is C

The Arrhenius equation describes the relationship between the rate constant ($K$) of a chemical reaction and the absolute temperature ($T$): $$ K = A e^{-E_a/RT} $$ where $A$ is the pre-exponential factor, $E_a$ is the activation energy, and $R$ is the gas constant. To obtain a linear plot for determining activation energy and predicting stability at different temperatures, the Arrhenius equation is often rearranged into its logarithmic form: $$ \ln K = \ln A - \frac{E_a}{R} \left( \frac{1}{T} \right) $$ Converting to base-10 logarithm: $$ \log K = \log A - \frac{E_a}{2.303 R} \left( \frac{1}{T} \right) $$ This equation has the form of a straight line, $y = mx + c$, where $y = \log K$, $x = 1/T$, the slope $m = -E_a / (2.303 R)$, and the y-intercept $c = \log A$. Therefore, an Arrhenius plot for predicting drug stability is drawn between $\log K$ (or $\log$ of the rate constant of degradation) on the y-axis and $1/T$ (the reciprocal of the absolute temperature) on the x-axis.