Question

What will be the effect of temperature on the rate constant?

Answer 1

Hint: The proportionality constant which explains the relationships between the molar constant concentration of the reactants and the rate of a chemical reaction is known as the rate constant.


Complete Step by step answer:

-The change in the concentration of a reactant or a product with respect to time is known as the reaction rate. Suppose let A be the reactants converting into product B.
\[A\to B\]

-The reaction rate is given by the change in concentration of A as a function of time. The rate of disappearance of A is proportional to the concentration of A, that is
\[-\dfrac{\Delta [A]}{\Delta t}\propto [A]\]

The proportionality is removed by inserting the constant k, which is known as the rate constant.
$rate=-\dfrac{\Delta [A]}{\Delta t}=k[A]$

The specific rate constant (k) is the proportionality constant which gives the relationship between the rate of the reaction to the concentrations of reactants.

\[\text{Average rate}=\dfrac{\text{change in number of moles of B}}{\text{change in time}}=\dfrac{\Delta \text{(moles of B)}}{\Delta t}=\dfrac{\Delta [B]}{\Delta t}\]

-Since reactants go away with time, hence they are expressed as a negative sign and products with a positive sign.
\[Rate=-\dfrac{\Delta [A]}{\Delta t}=\dfrac{\Delta [B]}{\Delta t}\]

-The temperature dependence of the rate constant is given by the Arrhenius equation. Most of the chemical reactions speed up with the increase in temperature, for example, the food spoils rate is increased when the temperature increases. Therefore,

k = f(T), where ‘f’ is some function. Here rate constant is the function of time.

-The rate constant may be expressed using the Arrhenius equation which is a mathematical expression for describing the effect of temperature on the velocity of a chemical reaction which is the basis of all predictive expressions used for calculating reaction-rate constants.

-The Arrhenius equation is given as-
$k=A{{e}^{-\dfrac{{{E}_{a}}}{RT}}}$

Where ‘k’ is the reaction-rate constant,
 ‘A’ is the constant for the frequency of particles,
 ‘${{E}_{a}}$ ’ is the activation energy of the reaction,
 ‘R’ is the universal gas constant, and
 ‘T’ is the absolute temperature.

-From the Arrhenius equation, we can clearly say that the temperature is the main factor that affects the rate of a chemical reaction.


Note: The units of rate constant depends on the order of reaction and also shows that the rate constant depends on temperature. For a zero-order reaction, the rate constant has units M/s or $mol.{{L}^{-1}}.{{s}^{-1}}$. For a first-order reaction, the rate constant has units as ${{s}^{-1}}$. For a second-order reaction, the rate constant has units as $L.mo{{l}^{-1}}.{{s}^{-1}}$. For a third-order reaction, the rate constant has units as ${{L}^{2}}.mo{{l}^{-2}}.{{s}^{-1}}\text{ or }{{M}^{-2}}.{{s}^{-1}}$ .