Question

The rate constant $\left(k\right)$ of a reaction is measured at different temperatures $\left(T\right)$, and the data are plotted in the given figure. The activation energy of the reaction in $kJmo{l}^{-1}$ is:
Here,
$R$ is gas constant :

• A. $0.5R$
• B. $R$
• C. $1.5R$
• D. $2R$

Answer 1

The correct option is B $R$

For a reaction, relationship between temperature and rate constant follows the equation,
$k=A{e}^{-\frac{E_a}{RT}}...eqn\left(i\right)$
where,
$k$ : Rate constant
$E_a$ : Activation energy (in J/mol)
$R$ : Gas constant
$T$ : Temperature of reaction (in Kelvin(K))
$A$ : Arrhenius factor or frequency factor or pre-exponential factor. It is constant, specific to a particular reaction

Taking $l{n}_e$ both sides in eqn(i)
$lnk=lnA-\frac{E_a}{RT}$
Comparing with the given graph,
Slope is $=-\frac{E_a}{R}$
$\frac{(10-0)}{(0-10)}=-\frac{E_a}{R}$
$-1=\frac{-E_a}{R}{E}_a=R$