Question

The activation energy for the reaction $2HI\,(g)\, \to \,{H_2}{I_2}(g)\,\,is\,\,\,209.5\,mo{l^{ - 1}}$ at $581\,K$ . Calculate the fraction of molecules of reactants having energy equal to or greater than activation energy.

Answer 1

Hint: Apply Arrhenius equation for the above reaction and solve for ${e^{\dfrac{{ - {E_a}}}{{RT}}}}$ because it represents the fraction of molecules of reactants while ${E_a}$ is the activation energy. Here in the above reaction hydrogen iodide which is in gaseous form changes to ${H_2}{I_2}$ which is also in gaseous state. While solving the $anti\log $ which is also known to be ${e^{power}}$ .

Complete step-by-step answer:According to Arrhenius theory the reacting molecules are spherical in shapes and they have to cross an energy barrier. Some molecules have that minimum energy which they require for transition while for some extra energy is given. The energy for the transition is called activation energy, while the minimum energy is called threshold energy.
The amount of activation energy gets lower for reactants when a catalyst is used. So applying the Arrhenius equation for the above reaction.
Arrhenius equation is given as- $k = \,A\,{e^{\dfrac{{ - {E_a}}}{{RT}}}}$
Here we have ${E_a}$ is the activation energy and ${e^{\dfrac{{ - {E_a}}}{{RT}}}}$ is the fraction of molecules of reactants having equal to or greater than activation energy. Therefore, on putting the value for fraction of molecule ${e^{\dfrac{{ - {E_a}}}{{RT}}}} = \,{e^{\dfrac{{ - 209500}}{{8.314 \times 581}}}}$
On solving further we get, ${e^{ - 43.4}}$ or we can write it as $\dfrac{1}{{{e^{43.4}}}}$
Now this (e) is written as antilog so on solving antilog we get the answer as $1.47\, \times {10^{ - 19}}$

Note:Keep in mind that you don’t need a full equation for solving a fraction of a molecule. You just have the activation energy and the temperature at which the reaction is taking place. Thus we write the same above for calculating the fraction. Also when you are solving antilog use table which is generally used to give behind the chemistry books.