A certain chemical reaction has an activation energy of 0.500 × 10⁻¹⁹ J. What temperature is required for the reaction rate to be double what it is at 20°C? A) 290 K B) 310 K C) 330 K D) 350 K E) 360 K

Question

Quizplus · Accepted Answer

The Arrhenius equation relates the rate of a chemical reaction to the temperature, with the equation in the form $k = A \exp\left(-\frac{E_a}{RT}\right)$, where $k$ is the rate constant, $A$ is the pre-exponential factor, $E_a$ is the activation energy, $R$ is the gas constant (8.314 J/mol·K), and $T$ is the temperature in Kelvin. To double the reaction rate, the equation can be set up as $\frac{k_2}{k_1} = 2 = \frac{\exp\left(-\frac{E_a}{RT_2}\right)}{\exp\left(-\frac{E_a}{RT_1}\right)}$, where $T_1$ is the initial temperature (20°C or 293 K) and $T_2$ is the final temperature. Solving this equation for $T_2$ with the given activation energy and converting the temperatures to Kelvin gives a temperature close to 310 K.

A Certain Chemical Reaction Has an Activation Energy of 0