Rate Lab #2  Determination of the Order of a Simple Reaction         Return
Paul St. Louis, Fellowes High School, Pembroke, ON
Introduction
In this experiment you will measure the time required for magnesium metal to react with hydrochloric acid solutions of various concentrations.  From these data, you can calculate the rate of reaction for each experiment and graphically determine the order of reaction with respect to the hydrogen ion concentration.

You will clean a 28-cm length of magnesium ribbon (to remove any oxide) and then cut it into seven equal pieces, each 4 cm long.  Since the ribbon is fairly uniform, the surface area is proportional to the length, and hence the area for reaction will be the same for each piece. i.e., the concentration of the Mg is constant for each trial.  The variations in rate then will be solely attributable to the variations in acid concentration.

You will make seven aliquots of HCl, 50 mL each, of 0.5 M, 1.0 M, 1.5 M, 2.0 M, 2.5 M, 3.0 M and 3.5 M, using 6.0 M stock HCl solution.

The reaction is:      Mg(s)  + 2 H+(aq)  --->  H2(g)  +  Mg2+(aq)
The general rate law expression for this reaction is:  rate = k[H+]n
where n is the order of the reaction.  The rate can be expressed in terms of reciprocal time since the concentration (or surface area) of the magnesium is a constant.  So,  rate is  directly proportional  to 1/t  and 1/t = k'[H+]n

Then take the natural logarithm of both sides, giving  ln(1/t) = n ln [H+] + ln k'  which now has the form of a linear equation, y = mx + b, where the slope (m) is equivalent to the order of the reaction, n, and the y-intercept is the natural logarithm of the rate law constant, k'.

Procedure
1.  Prepare the 7 aliquots of HCl as described in  the introduction using the dilution equation.  Use graduated cylinders and pipets for accuracy.
2. Prepare the seven pieces of magnesium metal.
3. Drop the piece of Mg into the acid solution and time how long it takes for the magnesium to disappear, while stirring gently.  Be sure the metal does not stick to the sides of the beaker.  Repeat with the other six solutions.  Record your data in the table below.
4. Plot a full page scatter graph with ln(1/t) (on the vertical axis) vs ln [H+] (on the horizontal axis), and use a curve of best fit to draw your line.  Using the equation given for your graph, note the slope of the line and the y-intercept.
5. State the order of this reaction relative to the [H+] and the value of the rate law constant.  Then write the completed rate law expression with k' and n values included.
6.   Now complete the last column in your data sheet.  Show each calculation.
Trial # [HCl] ln[H+] Time, t 1/t ln(1/t) Rate
1 0.5 M               
2 1.0 M           
3 1.5 M          
4 2.0 M          
5 2.5 M          
6 3.0 M          
7 3.5 M          

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