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(B) According to the Arrhenius equation,$k = A \cdot e^{-E_a / RT}$.Taking the natural logarithm on both sides: $\ln k = \ln A - \frac{E_a}{RT}$.Takin

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$2$

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(B) According to the Arrhenius equation,$k = A \cdot e^{-E_a / RT}$.Taking the natural logarithm on both sides: $\ln k = \ln A - \frac{E_a}{RT}$.Taking the base-$10$ logarithm: $\log k = \log A - \frac{E_a}{2.303 R} \cdot \frac{1}{T}$.Evaluating the statements:$(A)$ Correct: $A$ higher $E_a$ leads to a steeper slope $(-\frac{E_a}{2.303 R})$ in the $\log k$ vs $\frac{1}{T}$ plot,meaning the rate constant $k$ changes more rapidly with temperature.$(B)$ Correct: If $E_a = 0$,then $k = A \cdot e^0 = A$,which is constant and independent of temperature.$(C)$ Incorrect: This is the opposite of statement $(A)$.$(D)$ Incorrect: If there is no correlation between temperature and rate constant,it implies $E_a = 0$,not a negative activation energy.Thus,there are $2$ correct statements ($A$ and $B$).

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