The Arrhenius equation models the temperature dependence of a chemical reaction rate: The formula is most commonly written as

$k=A{e}^{\frac{-E_a}{RT}}$

where $k$ is the rate constant in units of inverse seconds, $T$ is the temperature in units of Kelvin, $A$ is the pre$-$exponential factor that is a constant for a specific chemical reaction, $E_a$ is the activation energy $($also a constant$)$ for the reaction with units of Joules$/$mole$,$ and $R$ is the ideal gas constant and has a value of $8\mathrm{.}3144$ Joules$/($mole$-$Kelvin$).$ Note the $e$ in the formula is the exponential function.

Consider a reaction in which $E_a=1\mathrm{.}21{10}^5$ Joules$/$mole and $A=2\mathrm{.}127{10}^9$ inverse seconds. Write a script to compute values of $k$ for temperatures ranging from $250$ Kelvin to $400$ Kelvin in increments of $2$ Kelvin. Assign the temperature values as a column vector to the variable temp$\_$kelvin. Assign the $k$ values as column vector to a variable named reaction$\_$rate.

Solve this problem using vectorized code $($i$.$e$.$ do not use a loop in$.$ your solution.$)$