# Meaning of the rate in the Rate Law

• Tim0
In summary, the rate in the rate law refers to the rate of disappearance of reactants or the rate of appearance of products. The instantaneous rate of reaction is the initial rate at which the reaction proceeds and can vary over time. The rate equation for a reaction can be used to calculate the initial rate, but the actual rate may change as the reaction progresses. The half-life of reactants in a first-order reaction is not constant and can depend on the initial concentrations of all reactants present.

#### Tim0

Hi all, I don't fully grasp definition of the rate as stated in the rate law. I do hope you guys could enlighten me! Here is what I don't understand:

What does the rate in the rate law refer to? So let's say 3A + 2B -> 4C + D. Does the instantaneous rate derived from the rate law, given that I already have the rate equation and the instantaneous [A] and , refer to the rate of disappearance of A or B, or the rate of appearance of C or D.

What I'm confused about is how the word rate as used in the rate law is simply referred to as the "instaneous rate of reaction". So if i get a figure from inputting all the data into the rate equation, what does this figure actually represent?

In addition to my above question, I was wondering if the rate equation was as such:

rate=k[A]

This means its a general second order reaction overall. How since its first order with respect to A and B, does it mean both A and B have constant half lifes each?

Thanks!

Tim0 said:
Hi all, I don't fully grasp definition of the rate as stated in the rate law. I do hope you guys could enlighten me! Here is what I don't understand:

What does the rate in the rate law refer to? So let's say 3A + 2B -> 4C + D. Does the instantaneous rate derived from the rate law, given that I already have the rate equation and the instantaneous [A] and , refer to the rate of disappearance of A or B, or the rate of appearance of C or D.

What I'm confused about is how the word rate as used in the rate law is simply referred to as the "instaneous rate of reaction". So if i get a figure from inputting all the data into the rate equation, what does this figure actually represent?

It is the rate of the reaction what your wrote. Therefore it is the rate of disappearance of A and B and of appearance of C and D.

Tim0 said:
What does the rate in the rate law refer to? So let's say 3A + 2B -> 4C + D. Does the instantaneous rate derived from the rate law, given that I already have the rate equation and the instantaneous [A] and , refer to the rate of disappearance of A or B, or the rate of appearance of C or D.

By convention the reaction rate is defined as the rate of disappearance of reactants or the rate of appearance of products divided by their stoichiometric coefficients. So, in your example, the rate would be given by:
$$\text{rate} = \frac{-1}{3} \frac{d[A]}{dt} = \frac{-1}{2} \frac{d}{dt} = \frac{1}{4} \frac{d[C]}{dt} = \frac{d[D]}{dt}$$
Note that all four expressions for the rate are equivalent. In other words, the rate of appearance of C is four times greater than the rate of appearance of D, the rate of disappearance of B is half the rate of appearance of C, etc. (Please let me know if you are not familiar with calculus and differential equations, otherwise this explanation might not make sense to you yet).

What I'm confused about is how the word rate as used in the rate law is simply referred to as the "instaneous rate of reaction". So if i get a figure from inputting all the data into the rate equation, what does this figure actually represent?

This represents the initial rate at which your reaction will proceed. The reaction, however, will not always go at the rate you calculate. As the reaction goes on, the concentration of reactants decreases, decreasing the rate of the reaction over time. This is why we refer to the rate as the "instantaneous rate."

Tim0 said:
In addition to my above question, I was wondering if the rate equation was as such:

rate=k[A]

This means its a general second order reaction overall. How since its first order with respect to A and B, does it mean both A and B have constant half lifes each?

No. Although the reaction is first-order with respect to A and first order with respect to B, A and B will not have constant half-lives. The half-life of A will depend on the initial concentrations of A and B, and the same goes for the half-life of B.

You can, however, have certain reaction conditions where this reaction acts like a first-order reaction. For example, if you have much more B present than A, even though B gets used up in the reaction, it's concentration hardly changes (for example, if you have 1 mole of A and 100 moles of B, the concentration of B decreases by only 1% when the reaction goes to completion). Under these conditions, we can treat the concentration of B as a constant, and the reaction acts like its a first-order reaction with the rate law: rate = k'[A]. Still, the half-life of A will depend on the initial amount of B that was present (although it will not depend on the concentration of A).

The rate in the rate law refers to the rate of the overall reaction, which can be measured by the change in concentration of any reactant or product over time. In the example given, the rate of the reaction is the change in concentration of A, B, C, or D over time.

The rate law is an equation that relates the rate of the reaction to the concentrations of the reactants. It is derived from experimental data and can be used to determine the rate of the reaction at any given time.

The instantaneous rate of reaction is the rate at a specific moment in time, and it can be calculated using the rate law and the concentrations of the reactants at that moment. This rate can be used to determine the rate of disappearance of A or B, or the rate of appearance of C or D, depending on which reactant or product is being measured.

The figure obtained from the rate equation represents the rate of the reaction at a specific time, and it can be used to compare the rates of different reactions or to determine the order of the reaction with respect to each reactant. It is an important factor in understanding the kinetics of a reaction and can provide valuable insights into the mechanism of the reaction. I hope this helps clarify the meaning of the rate in the rate law.

## 1. What is the rate law and why is it important?

The rate law is a mathematical expression that shows the relationship between the rate of a chemical reaction and the concentrations of the reactants. It is important because it helps us understand the factors that affect the rate of a reaction and allows us to predict and control the rate of a reaction.

## 2. What is the meaning of the rate in the rate law?

The rate in the rate law refers to the speed at which a reaction occurs. It is a measure of how quickly the reactants are being converted into products. The rate is typically expressed in terms of moles per liter per second.

## 3. How is the rate law determined experimentally?

The rate law is determined by conducting a series of experiments where the concentrations of the reactants are varied while keeping all other factors constant. The initial rates of the reaction are then measured and used to calculate the rate constant and the order of the reaction for each reactant. These values are then combined to form the rate law equation.

## 4. What is the difference between the rate constant and the rate in the rate law?

The rate constant (k) is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants. It is specific to a particular reaction and is determined experimentally. The rate in the rate law, on the other hand, is the actual rate of the reaction as expressed in the rate law equation.

## 5. How does temperature affect the rate in the rate law?

Increasing the temperature generally increases the rate of a reaction, as the particles have more kinetic energy and are able to collide more frequently and with greater energy. This is reflected in the rate law by the inclusion of the temperature-dependent rate constant, which typically increases with increasing temperature.