Question

explain how the method of continuous variation might be used to determine the stoichiometries of a reaction between two strong electrlytes in solution to form a soluble, nonionized product

Answer 1

A balanced chemical equation gives the mole ratios of reactants and products in a chemical reaction. How can the stoichiometry of a chemical reaction be determined experimentally? This experiment uses the method of continuous variations to determine the mole ratio of the two reactants.

In the method of continuous variations, the total number of moles of reactants is kept constant for a series of measurements. Each measurement is made with a different mole ratio or mole fraction of reactants. The maximum change will occur when the mole ratio of the reactants is closest to the optimum ratio which is the stoichiometric ratio in the chemical equation.

An extensive property of the reaction that depends on the amount of product formed is measured. This property may be the color intensity of a reactant or product, the mass of a precipitate, the amount of heat produced, or the volume of a gas evolved. A typical set of results for this investigation is shown below.

Experiment	Volume AgNO3	Volume K2CrO4	Mass Of Precipitate
Number	(mL)	(mL)	(g)
1	0.0	50.0	0.0
2	5.0	45.0	1.7
3	15.0	35.0	5.0
4	25.0	25.0	8.3
5	30.0	20.0	10.0
6	35.0	15.0	9.9
7	40.0	10.0	6.6
8	45.0	5.0	3.3
9	50.0	0.0	0.0

The graph shows that the amount of product increases in a continuous manner and then decreases. To find the optimum mole ratio, two best-fit straight lines are drawn with their intersection being the maximum change. The maximum change occurs when when each reactant is a limiting reactant. As shown above, the region where the volume of AgNO₃ (mole ratio) increases from 0 to ≈ 33 mL shows the AgNO₃ to be the limiting reactant. The intersection shows the maximum mole ratio and now K₂CrO₄becomes the limiting reactant.

The optimum mole (volume) ratio is 33 mL AgNO₃/17 mL K₂CrO₄ or 2:1 which is the stoichiometric mole ratio as well as the ratio of moles in the empirical formula for Ag₂CrO₄.

2AgNO₃(aq) + K₂CrO₄(aq) → 2KNO₃(aq) + Ag₂CrO₄(s)

2Ag⁺(aq) + CrO₄^2-(aq) → Ag₂CrO₄(s)

Hope this helps