Temperature Dependence of Reaction Rates

The activation energy for the reaction $2\mathrm{HI}\left(\mathrm{g}\right)\to {\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{I}}_2\left(\mathrm{g}\right)$  is $209.5{\mathrm{kJmol}}^{-1}$ at $581\mathrm{K}$. The fraction of molecules having energy equal to or greater than activation energy is: $[\mathrm{R}=8.31{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}]$

Given below are two statements: one labelled as Assertion A and other is labelled as Reason R:

Assertion A: A reaction can have zero activation energy

Reason R: The minimum extra amount of energy absorbed by reactant molecules so that their energy becomes equal to threshold value, is called activation energy.

For the adsorption of hydrogen on platinum, the activation energy is $30 \mathrm{kJ} {\mathrm{mol}}^{–1}$ and for the adsorption of hydrogen on nickel, the activation energy is $41.4 \mathrm{kJ} {\mathrm{mol}}^{–1}.$ The logarithm of the ratio of the rates of chemisorption on equal areas of the metals at $300 \mathrm{K}$ is $\_\_\_\_\_\_\_$ (Nearest integer)

Given: $\mathrm{In}10=2.3$

$\mathrm{R}=8.3 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$

Draw the graphical representation of arrenhious equation.

The rate constant of a reaction is increased $4$ times after addition of catalyst to the reaction mixture at the same temperature of $27 °\mathrm{C}$. The change in the activation energy of this reaction is
(Take $\ln \left(\frac{1}{4}\right)=-1.386,\mathrm{R}=8.314$)

For the reaction ${\mathrm{CO}}_{\left(\mathrm{g}\right)}+{\mathrm{Cl}}_{2\left(\mathrm{g}\right)}\to {\mathrm{COCl}}_{2\left(\mathrm{g}\right)}$ under the same concentration conditions of the reactants, the rate of reaction at ${250}^{\mathrm{o}}\mathrm{C}$ IS 1500 times as fast as the same reaction at ${150}^{\mathrm{o}}\mathrm{C}$. Calculate the activation energy of the reaction.If the frequency factor is $2 \times {10}^{-10}$${\mathrm{M}}^{-1}{\sec }^{-1}$ Calculate the rate constant of the reaction at ${150}^{\mathrm{o}}\mathrm{C}$.

A certain first order reaction is $20\%$ complete in $15$ minutes at $20°\mathrm{C}$. How long will it take to complete $40\%$ reaction at $40°\mathrm{C}$? Energy of activation of this reaction is $23.03 \mathrm{K} \mathrm{cal} {\mathrm{mol}}^{-1}$.

Calculate the factor by which the rate of first order reaction is increased for a temperature rise from ${25}^{\circ }\mathrm{C}$ to ${35}^{\circ }\mathrm{C}$. The energy of activation is $35 \mathrm{K} \mathrm{cal} {\mathrm{mol}}^{-1}$.

Write Arrhenius equation showing the effect of temperature on the reaction rate. What do different symbols signify? How does it help in the calculation of activation energy of a reaction? 

The reaction $2{\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\stackrel{ }{\to }2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$  is feasible. How is that hydrogen and oxygen mixture allowed to stand at room temperature shows no formation of water at all?
 

The activation energy of a reaction is zero. Will the rate constant of the reaction depend upon temperature? Give reason.

The values of the rate constant for the decomposition of $\mathrm{HI}$ into ${\mathrm{H}}_2$ and ${\mathrm{I}}_2$ at different temperatures are given below:

$$\begin{gathered} \mathrm{T}/\mathrm{K} 633 667 710 738 \\ {10}^4\mathrm{k}/{\mathrm{M}}^{-1}{\mathrm{s}}^{-1} 0.19 1.00 8.31 25.1 \end{gathered}$$

Draw a graph between $\ln \mathrm{k}$ against $1/\mathrm{T}$ and calculate the values of Arrhenius parameters.

A hydrogenation reaction is carried out at $500 \mathrm{K}$. If the same reaction is carried out in the presence of a catalyst at the same rate, the temperature required is $400 \mathrm{K}$. Calculate the activation energy of the reaction if the catalyst lowers the activation energy by $20 \mathrm{kJ}{ \mathrm{mol}}^{-1}$.

A given sample of milk turns sour at room temperature $\left(27°\mathrm{C}\right)$ in $5$ hours. In a refrigerator at $-3°\mathrm{C}$, it can be stored $10$ times longer. Calculate the energy of activation of souring of milk.

The time required for $10\%$ completion of a first order reaction at $298 \mathrm{K}$ is equal to that required for its $25\%$ completion at $308 \mathrm{K}$. If the pre-exponential factor for the reaction is $3.56\times {10}^9{ \mathrm{s}}^{-1}$, calculate its rate constant at $318 \mathrm{K}$ and also the energy of activation.

Rate constant 'k' of a reaction varies with temperature 'T' according to the equation:

$\mathrm{logk}=\mathrm{logA}-\frac{{\mathrm{E}}_{\mathrm{a}}}{2·303\mathrm{R}}\left(\frac{1}{ \mathrm{T}}\right)$

where ${\mathrm{E}}_{\mathrm{a}}$ is the activation energy. When a graph is plotted for $\mathrm{logk} \mathrm{vs} 1/\mathrm{T}$, a straight line with a slope of $-4250 \mathrm{K}$ is obtained. Calculate ${\mathrm{E}}_{\mathrm{a}}$ for the reaction $\left(\mathrm{R}=8.314{\mathrm{JK}}^{-1}{ \mathrm{mol}}^{-1}\right)$.

The decomposition of $\mathrm{A}$ into product has value of $\mathrm{k}$ as $4·5\times {10}^3{ \mathrm{s}}^{-1}$  at $10°\mathrm{C}$ and activation energy is $60 \mathrm{k} \mathrm{J} {\mathrm{mol}}^{-1}$. Calculate the temperature at which the value of $\mathrm{k}$ will be $1·5\times {10}^4{ \mathrm{s}}^{-1}$?

Write short note on Arrhenius equation.