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To teach stoichiometry, I have students heat various masses of sodium bicarbonate in evaporating dishes on hot plates and compare molar ratios of the sodium bicarbonate to the sodium carbonate. The 2:1 ratio works for class data very nicely with relatively no error.

2NaHCO3(s) ↔Na2CO3(s) + CO2(g) + H2O (g)

Next, students complete a single displacement reaction

Cu(s) + 2 AgNO3 (aq) ↔ Cu(NO3)2 (aq) + 2Ag(s)

using a large excess of copper and again they compare molar ratios. This data rarely comes out as perfect as in the decomposition lab, but the students find the experiment very exciting because of the blue colored copper(II) nitrate solution and the fact that they “make” silver metal. We talk about possible sources of error, including copper wire that is included in the silver mass, some silver adhering to the copper wire, or a possible side reaction of the copper wire such as forming red Cu2O.

One student suggested an alternative procedure. He proposed that if stoichiometric amounts of both reactants were used, that might eliminate some error. I allowed him the opportunity to test out his theory. He did two trials, and below are pictures of the original experiment with excess copper solid (Figure 1) and his modified experiment with 2:1 molar ratios (Figure 2), and also a summary of his lab.  (Left photo: Figure 1. Reaction after 24 hours using excess copper. Right photo: Figure 2. Reaction after 24 hours using exact stoichiometric amounts)

#### Lab Summary: Reducing error

"After learning how to balance a chemical equation, our class conducted a lab on mole ratios in displacement reactions. In the lab, I observed the reaction between a copper coil and aqueous silver nitrate. Using class data, I calculated the ratios between the moles of silver nitrate used to moles of copper reacted, and the moles of silver formed to moles of silver nitrate used. The balanced equation is Cu (s) + 2AgNO3 (aq) → 2Ag (s) + Cu(NO3)2 (aq). From the balanced equation it is clear that the mole ratio between silver and copper reacted is 2 mol:1 mol, and the ratio of silver to silver nitrate is 1 mol:1 mol. Theoretically, the data from the lab should have supported these ratios. Based on class data, the ratio between silver formed and copper reacted was 1.65 ±.09 mol:1 mol, and the ratio between silver and silver nitrate was 1.11±.03 mol:1 mol. These ratios do not represent the balanced equation even within reported error. I redid the experiment, but this time after measuring out the silver nitrate, I calculated exactly how much copper would be needed to react and that is what I used. After the reaction, I again calculated the mole relationships. This time, based on two trials, the ratio between silver and copper was 2.1±.1 mol:1 mol, and the mole ratio between silver and silver nitrate was 0.96±.05 mol: 1 mol. Both ratios represented the balanced equation within the margin of error. Understanding what the mole ratios in the lab represented allowed me to revise the experiment and obtain improved results."

— Felix Rosen

With the current emphasis on inquiry, when a student suggests an alternative method for an experiment, I offer them the chance to try their idea. This student came during his lunch on three separate days and conducted the experiment with the exact stoichiometric amounts rather than having any excess copper. He mentioned that by doing this, he solidified his understanding of how to do the calculations. He effectively eliminated any chance of excess copper wire being included in the mass of the silver as well as having some silver metal adhere to excess copper wire. In addition, there did not appear to be any side reactions with the copper since, there was no excess that could react. I encouraged him to then read scientific journals to get an idea of how to present his findings.

I think it’s very worthwhile, if time allows, to not only ask students for possible sources of error, but to let them test their ideas of how to minimize them.