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# Determine the rate equation for the reaction of hydrochloric acid with magnesium metal, and find the activation energy for the reaction: 2HCl(aq) + Mg(s) &amp;agrave; MgCl2(aq) + H2(g).

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Introduction

Order of reaction - Concentration Problem The problem is to determine the rate equation for the reaction of hydrochloric acid with magnesium metal, and find the activation energy for the reaction: 2HCl(aq) + Mg(s) --> MgCl2(aq) + H2(g) Background Information Rate of reaction is the change in concentration of a reactant or product with respect to time as the reaction progresses. Particles react when they come into contact with each other with sufficient kinetic energy. This amount of energy is called the activation energy of the reaction. For my experiment I define rate as the change in concentration of hydrochloric acid per second. The rate of a reaction is affected by four factors.1 1. Concentration is the number of particles of a substance per unit volume. The higher the concentration, the greater the chance of a collision between reactants. 2. For a heterogeneous reaction, where reactants are in different physical states, the reaction takes place on the interface between the reactants. Therefore the surface area of the interface is a factor. The greater the surface area, the higher the chance of there being collisions between reactant particles. 3. Rates of reaction are dependent on temperature. Reactant particles are constantly moving randomly and colliding in ways that may break or form bonds. Increasing temperature increases the kinetic energy these particles have, so at higher temperature they move faster, which increases the force with which they collide, making a reaction more likely. 4. For a certain reaction, there may be a catalyst that works by providing an alternative reaction route with a lower activation energy. This means that under the same conditions more particles will have the necessary activation energy to react, and the rate of reaction will be higher. Method The initial rate of the reaction between magnesium and hydrochloric acid was measured for a range of concentrations of hydrochloric acid. The first method I used was to measure the volume of hydrogen gas produced in the first 10 seconds of the reaction. ...read more.

Middle

If consecutive half-lives are constant, then the reaction is of 1st order. If the consecutive half-lives are increasing, then the reaction is 2nd order or greater. As shown on the graph of time against concentration, the consecutive half-lives (t1=15s, t2=29s, t3=54s) for my experiment are increasing. Therefore I must use a different method for determining the order of reaction. Logarithms involving concentration and reaction rate can be used to produce a graph from which we can work out the order and rate constant of reaction. Rate = k[HCl]n , where k is the rate constant, and n is the order of the reaction. If we take the logarithm of both sides of this equation then we get: log rate = n log[HCl] + log k . In the graph below of log[HCl] vs. log(rate), the gradient of the line produced will be the order of the reaction, and the y-intercept will be the logarithm of the rate constant. From this graph the order of the reaction is 1.98 and the rate constant is 100.426 = 2.67 mol-1 dm3 s. 1.98 is sufficiently close to 2 for me to draw the conclusion that the reaction is of 2nd order with respect to concentration of HCl, since there are significant sources of error in my experiment. Sources of error The reaction between HCl and magnesium is exothermic. This means that as the reaction proceeds, heat is produced. Temperature is a factor affecting the rate of reaction: the rate is faster as temperature increases. This means that despite my efforts to make the experiment a fair test, concentration was not the only factor influencing my results, there was also the increasing temperature of the reaction mixture. I repeated the experiment twice more to measure the temperature increase. The mixture went from 23�C to 30�C and 31�C on each test. From the results of the second part of this investigation, we can estimate the error as a factor of the rate. Using the Arrhenius equation, k = Ae-Ea/RT. ...read more.

Conclusion

The main source of error however is judging when the reaction is complete. As the reaction progresses, there is less and less visual activity, until suddenly there is no magnesium left. It is difficult to judge exactly when that point is. Therefore I estimate that on any of my tests there could be an error of up to �2 seconds. As well as being heated up by the exothermic nature of the reaction, the reaction mixture will cool down as the reaction proceeds if it is at a temperature higher than that of its surroundings. This would have affected my results much more than the heat produced by the reaction, as the volume of HCl was very large. Therefore my results must be inaccurate due to the reduction in rate of reaction due to the falling temperature of the reactants at starting temperatures. Limitations More accurate readings would have been obtained if I was able to control the change in temperature over the course of the reaction. This would be possible if I could place the beaker in which the reaction takes place inside a water bath which is maintained at the desired temperature for the reaction. The water bath would receive some of the heat produced by the exothermic reaction, and also it would warm up the reaction mixture as if its temperature falls. Ideally the water bath should be large, for maximum heat capacity, and the reaction mixture small, to allow maximum heat exchange. Visually judging when the reaction is complete is a method that always has a margin of error due to human error. This was estimated at about �2 seconds. I could have instead timed how long it took the reaction to produce a certain amount of hydrogen gas, say 50cm3, and taken the inverse of this time to find a rate. This would eliminate the problem of being uncertain when to stop the stopwatch. 1 Nuffield Advanced Chemistry, Students Book p242. 2 Nuffield Advancing Chemistry website: www.chemistry-react.org/go/Tutorial/Tutorial_4425.html 3 Nuffield Advanced Chemistry Student Book, p257 Hubert Rogers - 1 - Candidate No: 4484 ...read more.

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