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(D) $A.$ Correct. According to the Arrhenius equation,$k = Ae^{-\frac{E_a}{RT}}$. As $E_a$ increases,the exponential term $e^{-\frac{E_a}{RT}}$ decrea

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$4$

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(D) $A.$ Correct. According to the Arrhenius equation,$k = Ae^{-\frac{E_a}{RT}}$. As $E_a$ increases,the exponential term $e^{-\frac{E_a}{RT}}$ decreases,so $k$ decreases.$B.$ Correct. The temperature coefficient is defined as $\frac{k_{T+10}}{k_T} = e^{\frac{10E_a}{RT(T+10)}}$. As $E_a$ increases,the value of the temperature coefficient increases.$C.$ Correct. The rate constant $k$ increases exponentially with temperature. The derivative $\frac{dk}{dT} = k \cdot \frac{E_a}{RT^2}$ shows that the rate of change of $k$ with respect to $T$ is higher at lower temperatures for a given $E_a$.$D.$ Correct. From $\ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T}$,the plot of $\ln k$ vs $\frac{1}{T}$ is a straight line with slope $-\frac{E_a}{R}$.All four statements are correct. Therefore,the number of correct statements is $4$.

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