The Determination of rate equation

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The determination of rate equation

Aim:

The aim of this investigation is to determine the rate equation of the reaction between sodium thiosulphate Na2S2O3 (aq) and hydrochloric acid HCl (aq), using a graphical method.

Background information

The experiment is based on the effect of varying the concentration of the respective solutions and finding out the effect it has on the rate of the reaction; in this investigation i will change both sodium thiosulphate and hydrochloric acid. When hydrochloric acid is in excess to the sodium thiosulphate, the reaction may be different to when sodium thiosulphate is in excess. This will show the effect of change in concentration on the rate of reaction.

 Even though the reaction equation is known, it is not possible to work out the rate equation from the reaction equation and therefore the experiment has to be conducted.

Theory:

The rate of a reaction can be explained in terms of the rate of decrease in concentration of a reactant or the rate of increase in concentration of a product.

The most general method used to determine the rate of reaction is to measure the change in concentration of the reactant(s) per second. The rate of a reaction may be represented by a mathematical equation related to the chemical equation for a reaction.

Rate equation has the form rate = k [A]x [B]y which shows how the rate of a chemical reaction depends on the concentration of the reactants (A&B) and the rate constant k. A rate equation is used to describe how the concentration of a product increases or the concentration of the reactants decreases with time, the equation also indicates how the concentration of one or more reactants directly affects the rate. Occasionally it can even be the concentration of a product that affects the rate. In general the rate equation for the reaction:

                                        A + B               C + D

Is found by experiment to follow simple kinetics with the rate equation being written as:

                                        Rate = k [A]x[B]y       

k = rate constant, x = order with respect to [A], y = order with respect with [B].

To determine the rate equation I will first need to find the order of the reaction with respect to A (which is concentration HCl) and order of the reaction with respect to B (which is concentration of Na2S2O3).

As order of reaction cannot be deducted simply by looking at the equation for the reaction I will have to find the order experimentally.

Finding order of reaction:

There are 2 graphical methods from which the order of reaction can be obtained.

  1. From the shape of rate-concentration graph:

By plotting a graph of rate-concentration and looking at the shape of the graph to determine the order of reaction with respect to the reactant 

There are three orders of reactions, zero order, first order and second order.

Zero order = the rate does not depend upon the concentration of the reactant. The rate of reaction is fixed. Doubling or tripling the concentration of the reactant makes no difference to the rate. Thus:

Rate of reaction = k or rate of reaction = k[A]0.

First order = the rate of reaction depends directly upon the concentration of the reactant. If the concentration of the reactant is doubled, the rate doubles, thus:

Rate of reaction = k[A] or rate of reaction = k[A]1

Second order = the rate of reaction depends directly upon the square of the concentration of the reactants. If its concentration is doubled, its rate of reaction quadruples. Thus:

Rate of reaction = k [A] 2    

The graph below shows zero, first and second order reactions and how changes in the concentration of a reactant affect the reaction rate.

(Graph adapted from Cambridge Chemistry 2- A2)

  1. from the shape of concentration-time graph:

By plotting a graph of concentration-time and looking at the shape of the graph to determine the order of reaction with respect to the reagent.

Zero order = If the graph obtained is a straight line as in the figure below, the gradient of the graph which represents the rate, is the same everywhere whatever the concentration of R. The order with respect to R is therefore zero.

First order = If the graph obtained is a curve with a constant half life the, as shown in the figure below, the order of reaction with respect to R is first order.

Second order = If the graph obtained is a curve with but half life is not constant and the curve is deeper than the first order one, as shown in the figure  below, then the order of reaction with respect to R is second order.

How to calculate the order of reaction

There are different ways of calculating the order of reaction, the one I will be using in my experiment is the flow chart shown bellow and the first graphical method shown above - By plotting a graph of rate-concentration and looking at the shape of the graph to determine the order of reaction with respect to the reactant;

Variables

In general, a factor that increases the number of collisions between particles will increase the reaction rate and a factor that decreases the number of collisions between particles will decrease the chemical reaction rate. According to the collision theory there are five factors that can influence the rate of a chemical reaction; Temperature, surface area, concentration, pressure and catalysis. In this experiment I am going to investigate the effect of concentration on the rate of reaction, and therefore the only variable in this experiment will be concentration and the other factors will be the constant.

Controlled variable

Concentration of Reactants – this is the amount of the molecules in a certain volume. If there is a low concentration of reactants than there will be fewer molecules in a certain volume, and therefore there will be few of them to collide so the rate of reaction will differ due to its concentration. A higher concentration of reactants leads to more effective collisions per unit time, which leads to an increasing reaction rate (except for zero order reactions).

These will all be varied and compared to each other so that their individual orders can be determined. By keeping them all constant and varying only one at a time this can be achieved. The concentration of water will not be measured and will be assumed to be constant.

The concentration of sodium thiosulphate and hydrochloric acid will be varied and compared to each other o that their individual orders can be determined. During the experiment only one concentration will be changed and the rest will be kept constant. The total volume of each concentration will be the same through out the whole experiment to increase the reliability of the results obtained. To measure the concentration of different solution burettes will be used, the use of burettes as a piece of apparatus will increase the accuracy of the measure solution.

Confounding variables

Temperature

Temperature is a confounding variable in this experiment as it will contribute to the increase or decrease in the rate of reaction and would affect the results that would be collected. To prevent the temperature affecting the rate of reaction I will carry out the experiment under room temperature, I will carry out the whole experiment in the same room in an hour slot, which will allow the temperature to be kept constant. By doing this I will ensure the experiment is controlled and minimise the effect of temperature on the rate of reaction.

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Usually, an increase in temperature is accompanied by an increase in the reaction rate. If the molecules are moving faster then they will collide more which will increase the chances of them making a successful collision and reaction.
In a mixture of molecules, there may be some which do not have the required energy to react and some which do. The proportion of these molecules can be shown by the Maxwell-Boltzmann distribution curve. As shown on the graph, all the molecules in the shaded area have the required energy (activation energy) for the reaction and will react if it makes ...

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