# The number of molecules with energy greater than the threshold energy

Question:

The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a rise of temperature from $27{ }^{\circ} \mathrm{C}$ to $42{ }^{\circ} \mathrm{C}$. Its energy of activation in

$\mathrm{J} / \mathrm{mol}$ is $($ Take $\ln 5=1.6094$ $\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

Solution:

$\mathrm{T}_{1}=300 \mathrm{~K} \quad \mathrm{~T}_{2}=315 \mathrm{~K}$

As per question $\mathrm{K}_{\mathrm{T}_{2}}=5 \mathrm{~K}_{\mathrm{T}_{1}}$ as molecules activated are increased five times so $\mathrm{k}$ will increases 5 times

Now

$\ln \left(\frac{\mathrm{K}_{\mathrm{T}_{2}}}{\mathrm{~K}_{\mathrm{T}_{1}}}\right)=\frac{\mathrm{Ea}}{\mathrm{R}}\left(\frac{1}{\mathrm{~T}_{1}}-\frac{1}{\mathrm{~T}_{2}}\right)$

$\ln 5=\frac{E a}{R}\left(\frac{15}{300 \times 315}\right)$

So $\mathrm{Ea}=\frac{1.6094 \times 8.314 \times 300 \times 315}{15}$

$\mathrm{Ea}=84297.47$ Joules/mole