The temperature dependence of a reaction rate can be represented by the Arrhenius equation

\[K =Ae^{-E_a/RT}\]

The pre-exponential factor \(A\) is called the frequency factor and \(E_a\) is the energy of activation. The unit of \(E_a\) is J/mol or Kcal/mol.

The rate constants at two different temperatures are related as

\[log\frac{K_2}{K_1} = \frac{E_a}{2.303R}\left[\frac{T_2 – T_3}{T_1T_2}\right]\]

Log K versus 1/T gives a linear graph with negative slope. The reactant molecules collide with each other to cross over an energy barrier existing between the reactants and products. If the value of the difference in the internal energies of reactants and product is positive, the reaction is exothermic and if it is negative, the reaction is endothermic. If the temperature is raised the kinetic energy of the molecules increases which causes increase in (i) number of collisions (ii) number of molecules halving higher energy than threshold energy. For every 10°C rise in temperature, the increase in kinetic energy is about 3.3%. So the increase in number of collisions is about \(\sqrt{3.3}\) . , i.e., 1.8%. Hence the rate of reaction must increase only by about 1.8%. For every 10°C rise in temperature, the rate of reaction increases by 100%, i.e., two times If the rate of reaction is doubled for every rise of 10 K temperature, the rate of reaction increased for rise of temperature from 30°C to 80°C is 32 times. The activation energy does not depend on the concentration. The ratio of the rate constants at two different temperatures (preferably 35°C and 25°C) is known as temperature coefficient. If the activation energy is zero, then all the collisions will be fruitful and the reaction is 100% complete.

Rate of which reaction increase with temperature? 

of any

The correct answer is option 1. of any.

The rate of any chemical reaction generally increases with temperature. This is explained by the Arrhenius equation, which shows that the rate constant \(k\) increases exponentially with an increase in temperature:

\(k = A e^{-E_a/(RT)}\)

where:

\(k\) is the rate constant,

\(A\) is the pre-exponential factor (frequency of collisions),

\(E_a\) is the activation energy,

\(R\) is the gas constant,

\(T\) is the temperature in Kelvin.

As temperature \(T\) increases, the exponential term \(e^{-E_a/(RT)}\) increases, leading to an increase in the rate constant \(k\), and consequently, the reaction rate.

Analyzing the Options:

1. of any: Correct. The rate of any reaction typically increases with temperature due to the reasons outlined above.

2. of exothermic reaction: These reactions release heat. Despite the release of heat, the rate of exothermic reactions generally increases with temperature due to the increased kinetic energy of the reacting molecules, which helps them overcome the activation energy barrier.

3. of endothermic reactions: These reactions absorb heat. Similarly, the rate of endothermic reactions increases with temperature because the increased thermal energy helps more reactant molecules to have enough energy to reach the transition state.

4. none: Incorrect. This contradicts the general principle that reaction rates increase with temperature.

Therefore, the correct answer is 1. of any.