Mole Ratio


A balanced chemical equation gives the mole ratios of reactants and products for a chemical reaction. If the formulas of all reactants and products are known, it is relatively easy to balance an equation to find out what these mole ratios are. When the formulas of the products are not known, the mole ratios for a chemical reaction may be determined experimentally. The method of continuous variation is a general procedure that may be used to find the mole ratio between reactants and the identity of the products.


  • Stoichiometry
  • Oxidation–reduction reaction
  • Mole ratio
  • Heat of reaction


Sodium hypochlorite, NaClO, 0.3 M, 175 mL (Solution A)*
Sodium thiosulfate, Na2S2O3, 0.3 M in NaOH, 0.30 M, 175 mL as (Solution B)*
Water, distilled or deionized
Beakers, 400-mL, 3
Covers for polystyrene cups
Cup, large plastic, for water
Graduated cylinder, 10-mL
Graduated cylinder, 50-mL
Polystyrene cups, 2*
Thermometer, digital, 0–100 °C
Wash bottle
*Materials included in kit.

Safety Precautions

Sodium hypochlorite solution is a corrosive liquid; it may cause skin burns and is moderately toxic by ingestion and inhalation. The solution will react with both acid and heat to evolve chlorine gas—keep away from acids and do not heat. Avoid contact of all chemicals with eyes, skin and clothing. Work in a fume hood or in a well-ventilated lab only. Wear chemical splash goggles, chemical-resistant gloves and a chemical-resistant apron. Wash hands thoroughly with soap and water before leaving the laboratory. Please review current Safety Data Sheets for additional safety, handling and disposal information.


Please consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding. Sodium thiosulfate solution may be disposed of according to Flinn Suggested Disposal Method #12b. Sodium hypochlorite solution may be disposed of according to Flinn Suggested Disposal Method #26b. The solutions remaining at the end of the demonstration contain sodium sulfate and sodium hydroxide may be neutralized, then disposed of according to Flinn Suggested Disposal Method #26b.


  1. Set up a calorimeter consisting of two nested polystyrene cups with a cover having a hole in it to accept a thermometer (see Figure 1). Place the calorimeter in a 400-mL beaker for stability.
  2. Obtain approximately 175 mL of the sodium hypochlorite solution in a clean 400-mL beaker and 175 mL of sodium thiosulfate solution as “Solution B” in another clean 400-mL beaker. Label the beakers.
  3. Using a digital thermometer, measure the temperature of the NaClO solution and of “Solution B.” Have students record the data in the Data Table. The solutions should be the same temperature. If they are not, determine the weight average to use as the initial temperature.
  4. Using a clean 10-mL graduated cylinder, measure 5.0 mL of NaClO solution and pour the solution into the nested polystyrene cup. Using a clean 50-mL graduated cylinder, measure 45.0 mL of “Solution B” and add this to the polystyrene cup.
  5. Stir with a digital thermometer, and have students record the maximum temperature (°C) of the final solution in the Data Table.
  6. Pour the solution out into a large plastic cup, rinse the cup and thermometer, and repeat steps 4 and 5 using a different volume ratio of the two substances, always keeping the total volume at 50.0 mL.
  7. Continue testing various ratios until you have at least three measurements on each side of the one that appears to give the greatest temperature difference ΔT.
  8. Have students plot the data on their worksheet graph as shown in the Answer Key.
  9. Students should draw two straight lines that best fit the data, and determine where they intersect. Be sure to have them include the points at the 0:50-mL and 50:0-mL ratios. From this graph, students can find the stoichiometric mole ratio of reactants from the point of intersection on their graph.

Student Worksheet PDF


Teacher Tips

  • This kit includes enough chemicals and consumables to perform the demonstration as written five times: 950 mL of 0.3 M sodium hypochlorite solution, 1000 mL of 0.3 M sodium thiosulfate, and 14 polystyrene cups.
  • There is a twofold purpose for including NaOH in the solutions. First, the bleach itself is basic. By mixing it with a second solution of approximately the same basicity, the heat evolved due to the dilution of a base does not contribute to the final temperature change due to the redox reaction. Secondly, keeping the solutions basic helps to prevent the evolution of sulfur dioxide (SO2) gas.
  • Students can use the data from the experiment to calculate the enthalpy change for the reaction.
  • The data may be plotted using a spreadsheet program or a graphing program such as Graphical Analysis for Windows.

Correlation to Next Generation Science Standards (NGSS)

Science & Engineering Practices

Analyzing and interpreting data
Using mathematics and computational thinking

Disciplinary Core Ideas

MS-PS1.B: Chemical Reactions
MS-PS3.A: Definitions of Energy
HS-PS1.B: Chemical Reactions

Crosscutting Concepts

Scale, proportion, and quantity
Energy and matter
Stability and change

Performance Expectations

HS-PS1-7. Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction.

Sample Data

Initial Temperature: 22.0 °C


Answer to Graph



  1. Balance the following redox equations.

4 NaClO(aq) + Na2S2O3(aq) + 2 NaOH (aq) → 2 Na2SO4(aq) + 4 NaCl(aq) + H2O(l)
3 NaClO(aq) + KI(aq) → 3 NaCl(aq) + KIO3(aq)
NaClO(aq) + Na2SO3(aq) → Na2SO4(aq) + NaCl(aq) (Balanced as written.)

Answers to Questions

  1. Explain how the method of continuous variation is used to determine the mole ratio of reactants in a chemical reaction.

    In the continuous variation method the ratio of moles of reactants is gradually changed while a constant solution volume is maintained. The reaction is exothermic. The maximum amount of heat will be given off when the correct mole ratio is combined. Because the solution volume is constant, the change in temperature at the optimum mole ratio will be the greatest.

  2. What is meant by the term limiting reagent?

    The limiting reagent is the reagent that is completely consumed in a chemical reaction.

  3. Which reactant is the limiting reagent along the upward sloping line of the graph? Which is the limiting reagent along the downward sloping line?

    On the upward sloping line of the graph (given in the sample data section) the limiting reagent is NaClO and Na2S2O3 is present in excess. At the point 40 mL NaClO : 10 mL Na2S2O3 both reactants were totally consumed. Beyond this point there is an excess of NaClO, and Na2S2O3 is the limiting reagent.

  4. What other physical properties, other than temperature change, could be used in the method of continuous variation?

    Some other properties which could be used are the intensity of the color of a reactant or product, the mass of a precipitate that forms, or the volume of a gas that is released.

  5. Why is it more accurate to use the point of intersection of the two lines to find the mole ratio rather than the ratio associated with the greatest temperature change?

    It may be that the exact mole ratio was not chosen as a data value. Also, the graph averages several values to find the optimum ratio rather than relying on only one value.


This demonstration uses the method of continuous variation to determine the mole ratio of two reactants in an oxidation–reduction reaction. Several steps are involved in the general method of continuous variation. First, solutions of the reactants are prepared in which the concentrations are known. Second, the solutions are mixed a number of times using different volume ratios of reactants. Third, some property of the reaction that depends on the amount of product formed or on the amount of reactant that remains is measured. This property may be the color intensity due to a reactant or product, the mass of a precipitate that forms, the volume of a gas evolved, or the temperature change due to the heat of reaction.

In the method of continuous variation, the total number of moles of reactants is kept constant for the series of measurements. Each measurement is made with a different mole ratio of reactants. The optimum ratio, which is the stoichiometric ratio for the reactants in the balanced chemical equation, should consume the greatest amount of reactants, form the greatest amount of product, or generate the most heat and produce the maximum temperature change.

In this demonstration, sodium hypochlorite is used an oxidizing agent—it will be reduced by an unknown reducing agent, Solution B. The change in temperature will be measured as the reactants are mixed in different volume (and mole) ratios. The reaction is exothermic, so the heat produced will be directly proportional to the amount of reaction that occurs. The maximum temperature change will occur at the optimum mole ratio.

Give students the demonstration worksheet. Listed at the top of the worksheet are the unbalanced chemical equations of sodium hypochlorite with the three possible choices for the identity of Solution B in the demonstration. Students should balance the equations, record and graph the data obtained in this demonstration, and then identify Solution B—potassium iodide, sodium thiosulfate or sodium sulfite—based on the results for the optimum mole ratio.


Vonderbrink, S. A. Laboratory Experiments for Advanced Placement Chemistry: Flinn Scientific: Batavia, IL; 2006; p 45.

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