The Magnesium-HCl Rate Study with a Confounded Trial
Students study the reaction of magnesium ribbon with hydrochloric acid by timing how long a 5.0 cm strip takes to disappear. They run four trials at room temperature unless noted: 0.50 M HCl, 95 s; 1.0 M HCl, 48 s; 1.5 M HCl, 18 s, but the water bath for that trial was 35 degrees Celsius because another class had used the room-temperature bath; 2.0 M HCl, 30 s, but the magnesium strip was only 3.0 cm because the supply ran low. The students calculate rates as 1/time and conclude that rate doubles when concentration doubles and that temperature has no effect. The teacher asks the class to decide which trials can support a rate-law claim and how to redesign the experiment. The lab clock is available, and the teacher has fresh 5.0 cm strips and a water bath that can be set to 25 degrees Celsius.
1. Identify which trials are valid for determining the effect of HCl concentration and which must be excluded. Justify each exclusion in terms of controlled variables.
Read the worked answer
Only the 0.50 M and 1.0 M trials with 5.0 cm strips at room temperature are directly comparable for the concentration effect. They hold strip length, surface area, and temperature approximately constant while changing HCl concentration.
The 1.5 M trial must be excluded because its temperature was 35 degrees Celsius rather than room temperature. Temperature changes the fraction of collisions with enough energy to react, so a faster time cannot be attributed to concentration alone. The 2.0 M trial must also be excluded because the strip was 3.0 cm instead of 5.0 cm. A shorter strip has less magnesium and less surface area; the time to disappear changes for reasons unrelated to HCl concentration. The students' conclusion that 'temperature has no effect' is especially unsupported because they never made a controlled temperature comparison. At most, they have one valid pair of concentration points and no valid temperature comparison.
2. Using only the valid trials, what can the class conclude about the reaction order with respect to HCl? Show a calculation using relative rates. What additional trial would you run next, and why?
Read the worked answer
Using rate proportional to 1/time, the rate at 1.0 M relative to 0.50 M is:
rate2/rate1 = (1/48)/(1/95) = 95/48 = 1.98.
The concentration ratio is 1.0/0.50 = 2.0. If rate = k[HCl]^n, then 1.98 = 2.0^n, so n is approximately 1. The data are consistent with first order in HCl. However, two points are weak evidence; a single pair cannot firmly establish a rate law, and the time-to-disappear method averages over changing surface area as the ribbon shrinks.
A good next trial is 1.5 M HCl at 25 degrees Celsius with a 5.0 cm strip. That adds a third concentration point under controlled conditions and tests whether the first-order pattern holds. The class could also run 2.0 M with a full 5.0 cm strip. For stronger evidence, they should measure initial rate, for example by collecting hydrogen gas volume over time, rather than only the total time to disappear.
3. Explain how the invalid trials illustrate collision theory and how the teacher should revise the procedure to test temperature independently.
Read the worked answer
The 1.5 M trial at 35 degrees Celsius was faster than a room-temperature trial at the same concentration would be because higher temperature increases the average kinetic energy of particles. More collisions have energy at or above the activation energy, so the reaction rate increases. The 2.0 M trial with a 3.0 cm strip was slower than expected because the smaller strip has less surface area and fewer exposed magnesium atoms; surface area affects how frequently acid particles can collide with the metal.
To test temperature independently, the teacher should fix HCl concentration, strip length, and surface preparation, then run the same reaction at several bath temperatures, such as 15, 25, 35, and 45 degrees Celsius. To test concentration, temperature and strip size must be fixed. Students should also control stirring and ribbon cleaning, because oxide layers and agitation affect the rate. Replicating each condition and graphing rate versus concentration or temperature would let the class separate the variables instead of drawing a conclusion from confounded trials.