Answer
Verified
452.7k+ views
Hint: Activation energy is defined as the amount of energy required to bring out the reaction. Both the terms (activation energy and temperature) are related by the expression, $\text{k=A}{{\text{e}}^{-\frac{{{\text{E}}_{\text{a}}}}{\text{RT}}}}$. Put the values given in the question to obtain the required relation. Rate of reaction depends on activation energy and temperature.
Complete step by step answer:
Let us first discuss the equation, there is an equation named as Arrhenius equation which shows the dependence of rate of reaction on temperatures. Mathematically, it is represented as $\text{k=A}{{\text{e}}^{-\frac{{{\text{E}}_{\text{a}}}}{\text{RT}}}}$ , k is the rate of reaction, A is Arrhenius constant or collision frequency or collision factor, ${{\text{E}}_{\text{a}}}$ is the activation energy, T is the temperature and R is universal gas constant with a constant value of $8.314\text{ J}\text{.mo}{{\text{l}}^{-1}}.{{\text{K}}^{-1}}$.
Now, coming back to the question, we are given that the activation energy of a reaction is zero, it means that ${{\text{E}}_{\text{a}}}$ is zero. Now, put ${{\text{E}}_{\text{a}}}=0$, in the formula.
Then, the expression will be $\text{k=A}{{\text{e}}^{-\frac{0}{\text{RT}}}}$. It is clear that ${{\text{e}}^{-\frac{0}{\text{RT}}}}={{\text{e}}^{-0}}$. Any value having zero as its power gives 1 as its answer. Finally, the expression is $\text{k=A}\times \left( 1 \right)$ or $\text{k=A}$. It means that the rate of reaction, when activation energy is zero will have the value equal to the value of the collision frequency not temperature.
The activation energy of a reaction is zero. The rate constant of the reaction is nearly independent of temperature. The correct option is (D).
Additional Information: The important relation between two different rate of reactions $\left( {{\text{k}}_{1}}\text{ and }{{\text{k}}_{2}} \right)$ at two different temperatures $\left( {{\text{T}}_{1}}\text{ and }{{\text{T}}_{2}} \right)$. In this equation, there is no need for a collision constant to find the rates, temperatures and activation energy. The relation is $\text{ln}\left( \frac{{{\text{k}}_{2}}}{{{\text{k}}_{1}}} \right)=-\frac{{{\text{E}}_{\text{a}}}}{\text{R}}\left( \frac{1}{{{\text{T}}_{2}}}-\frac{1}{{{\text{T}}_{1}}} \right)$.
Note: In the real world, there is no reaction which has zero activation energy. This is because when activation energy is zero, then, the rate of reaction equals collision frequency. That means there will be effective collisions between the particles or molecules which is not possible, as the occurrence of a reaction also depends on successful collisions not all collisions. The activation energy is always positive. As it is defined as the amount of energy required to bring out the reaction.
Complete step by step answer:
Let us first discuss the equation, there is an equation named as Arrhenius equation which shows the dependence of rate of reaction on temperatures. Mathematically, it is represented as $\text{k=A}{{\text{e}}^{-\frac{{{\text{E}}_{\text{a}}}}{\text{RT}}}}$ , k is the rate of reaction, A is Arrhenius constant or collision frequency or collision factor, ${{\text{E}}_{\text{a}}}$ is the activation energy, T is the temperature and R is universal gas constant with a constant value of $8.314\text{ J}\text{.mo}{{\text{l}}^{-1}}.{{\text{K}}^{-1}}$.
Now, coming back to the question, we are given that the activation energy of a reaction is zero, it means that ${{\text{E}}_{\text{a}}}$ is zero. Now, put ${{\text{E}}_{\text{a}}}=0$, in the formula.
Then, the expression will be $\text{k=A}{{\text{e}}^{-\frac{0}{\text{RT}}}}$. It is clear that ${{\text{e}}^{-\frac{0}{\text{RT}}}}={{\text{e}}^{-0}}$. Any value having zero as its power gives 1 as its answer. Finally, the expression is $\text{k=A}\times \left( 1 \right)$ or $\text{k=A}$. It means that the rate of reaction, when activation energy is zero will have the value equal to the value of the collision frequency not temperature.
The activation energy of a reaction is zero. The rate constant of the reaction is nearly independent of temperature. The correct option is (D).
Additional Information: The important relation between two different rate of reactions $\left( {{\text{k}}_{1}}\text{ and }{{\text{k}}_{2}} \right)$ at two different temperatures $\left( {{\text{T}}_{1}}\text{ and }{{\text{T}}_{2}} \right)$. In this equation, there is no need for a collision constant to find the rates, temperatures and activation energy. The relation is $\text{ln}\left( \frac{{{\text{k}}_{2}}}{{{\text{k}}_{1}}} \right)=-\frac{{{\text{E}}_{\text{a}}}}{\text{R}}\left( \frac{1}{{{\text{T}}_{2}}}-\frac{1}{{{\text{T}}_{1}}} \right)$.
Note: In the real world, there is no reaction which has zero activation energy. This is because when activation energy is zero, then, the rate of reaction equals collision frequency. That means there will be effective collisions between the particles or molecules which is not possible, as the occurrence of a reaction also depends on successful collisions not all collisions. The activation energy is always positive. As it is defined as the amount of energy required to bring out the reaction.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
What percentage of the solar systems mass is found class 8 physics CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Why is there a time difference of about 5 hours between class 10 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE