# Find the rate constant, given temperature and activation energy.

• Agent M27
In summary, the conversation discusses finding the rate constant for a reaction at a specific temperature given the activation energy and rate constant at a different temperature. The solution involves using the equation ln(K2/K1) = (Ea/R)((1/T1)-(1/T2)) and correctly converting units.
Agent M27

## Homework Statement

A reaction is found to have an activation energy of 38.0 kJ/mol. If the rate constant for this reaction is 1.60 × 102 M-1s-1 at 249 K, what is the rate constant at 436 K?

## Homework Equations

$$ln\frac{K_{2}}{K_{1}}=\frac{E_{a}}{R}\left(\frac{1}{T_{1}}-\frac{1}{T_{2}}\right)$$

## The Attempt at a Solution

Given:

R=8.314
T1=249K
T2=436K
Ea=160

$$ln(K_{2})=\frac{38}{8.314}\left(\frac{1}{249}-\frac{1}{436}\right)+ln(160)$$

Which equals 161.257 which is incorrect. Any clues where I went wrong would be greatly appreciated. Thanks in advance.

Joe

38000

Ah ha! I should have noticed that being that R has units of J not Kj. Thank you very much Borek.

Joe

kJ, not Kj...

I would like to point out that your attempt at a solution is close, but there are a few errors in your calculations.

Firstly, the activation energy (Ea) should be in units of J/mol, not kJ/mol. So it should be 38,000 J/mol.

Secondly, the natural logarithm function (ln) should be applied to the ratio of the rate constants, not just the second rate constant. So your equation should be:

ln\frac{K_{2}}{K_{1}}=\frac{38,000}{8.314}\left(\frac{1}{249}-\frac{1}{436}\right)

This will give you a value of 3.009 for the natural logarithm of the ratio of rate constants.

To find the actual ratio of rate constants, you will need to take the inverse natural logarithm (e^x) of this value. So your final equation should be:

\frac{K_{2}}{K_{1}}=e^{3.009}

This will give you a value of approximately 20.26 for the ratio of rate constants.

To find the rate constant at 436 K, you can then multiply the rate constant at 249 K (1.60 x 10^2 M^-1s^-1) by this ratio. This will give you a value of approximately 3.24 x 10^3 M^-1s^-1 for the rate constant at 436 K.

I hope this helps and good luck with your calculations!

## What is the rate constant?

The rate constant, also known as the rate coefficient, is a proportionality constant that relates the rate of a chemical reaction to the concentrations of reactants and the temperature.

## How is the rate constant calculated?

The rate constant can be calculated using the Arrhenius equation, which includes the temperature and activation energy as factors. The equation is k = A * e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

## What is the effect of temperature on the rate constant?

An increase in temperature typically leads to an increase in the rate constant. This is because higher temperatures provide more energy for molecules to collide and react, resulting in a faster reaction rate.

## How does activation energy affect the rate constant?

Activation energy is the minimum amount of energy required for a reaction to occur. It determines the rate at which reactants are converted into products. A higher activation energy leads to a slower reaction rate, while a lower activation energy leads to a faster reaction rate.

## Can the rate constant change over time?

The rate constant is generally considered to be a constant value for a particular reaction at a specific temperature. However, it may change over time if the conditions of the reaction change, such as the concentration of reactants or the temperature.

Replies
2
Views
1K
Replies
1
Views
2K
Replies
2
Views
1K
Replies
4
Views
2K
Replies
1
Views
2K
Replies
3
Views
4K
Replies
2
Views
2K
Replies
1
Views
3K
Replies
4
Views
5K
Replies
131
Views
6K