The activation energy of a chemical reaction can be determined by:

For the following reactions:
$A \xrightarrow{700 \ K}$ Product
$A \xrightarrow[\text{catalyst}]{500 \ K}$ Product
it was found that $E_{a}$ is decreased by $30 \ kJ/mol$ in the presence of a catalyst. If the rate remains unchanged,the activation energy for the catalysed reaction is (Assume pre-exponential factor is same):

The rate of a chemical reaction doubles for every $10\,^{\circ}C$ rise in temperature. If the temperature is increased to $50\,^{\circ}C$ from $0\,^{\circ}C$,by how many times will the rate of reaction increase?

The variation of the rate constant with temperature is given by the Arrhenius equation $k = A e^{-E_a / (RT)}$. If $T \to \infty$,the rate constant $k$ will be equal to:

In respect of the equation $k = A e^{-E_a/RT}$ in chemical kinetics,which one of the following statements is correct?

Which one of the following does not represent the Arrhenius equation?