Quarryhill Soap Titration: Calibrating a Water Hardness Test

Step 1 (safety). Wear goggles for the whole lab. Epsom salt and diluted castile soap are low-hazard household products, but soap stings the eyes, so keep caps tight while shaking and rinse eyes at the eyewash if any splashes in. Do not taste or drink any sample, including the tap water. Wipe up spills right away, because soapy water on the floor is slippery. Handle test strips by the end and follow the kit directions for disposal.

Step 2 (teacher preparation, before session 1). Mix one batch of soap reagent for the whole class, 1 part liquid castile soap to 10 parts distilled water, and fill each group's dropper bottle from it. The reagent must be made with distilled water, because hardness in tap water would use up part of the soap before it reaches the bottle. Every group runs its standards and its unknowns with this same batch. If a new batch must be mixed between sessions, groups rerun the 0 and 250 mg/L standards; if either mean shifts by more than one drop, the whole calibration is repeated.

Step 3 (session 1, stock solution). Complete Data & Analysis item 1 before you weigh anything, and have your teacher check it. Then weigh 1.23 g of Epsom salt in a weighing boat on the balance. Transfer all of it into the 500 mL flask or cylinder, add about 300 mL of distilled water, and swirl until no crystals remain. Fill to the 500.0 mL mark with distilled water, cap or cover the top, and invert or stir ten times. Label it "Stock."

Step 4 (standards). Make six 100.0 mL standards. For each one, measure the listed volume of stock in the 25 mL graduated cylinder, pour it into the 100 mL graduated cylinder, and fill to the 100.0 mL mark with distilled water. Pour the standard into a labeled beaker and stir. Rinse both cylinders with distilled water between standards.

Step 5 (titration technique). Rinse a tube twice with distilled water. Measure 25.0 mL of the sample in the 25 mL graduated cylinder and pour it into the tube. One student adds all the drops for the whole lab, holding the dropper bottle straight up and squeezing gently, because drop size changes with the angle and the squeeze. Add one drop, cap the tube, shake it hard for 5 seconds, and stand it upright. If foam covers the whole surface in an unbroken layer, start the timer. The endpoint is reached when that layer stays unbroken for 30 seconds. If it breaks before 30 seconds, or never covers the surface, add another drop and repeat. Record the total number of drops, counting the endpoint drop.

Step 6 (calibration runs). Run S0 first, then S50 through S250 in order, three trials each, and record every count in Table A. To save time on trials 2 and 3, you may add drops without shaking until you are three drops short of the trial 1 count, then shake and continue one drop at a time. Rinse the tube twice with distilled water between trials, because leftover soap film or leftover sample changes the next count.

Step 7 (session 2, tap water). Finish any calibration runs left from session 1 first, using the same dropper bottle. Then run four trials on tap water and record them in Table A. If the tap-water mean is higher than your S250 mean, the sample is outside your calibration. In that case, mix 12.5 mL of tap water with 12.5 mL of distilled water, run four trials on the diluted sample, and note the dilution in the table.

Step 8 (test strip). Dip a total hardness test strip into tap water as the kit directs, compare it with the color chart at the stated time, and record the value of the closest color block. Repeat with a second strip and record both readings.

Step 9 (optional unknown). If time allows, test a bottled water or a labeled sample from home with the same method, and place it on your calibration line.

Step 10 (cleanup). The standards, soap solutions and tap samples contain only Epsom salt, soap and water, and may be poured down the drain with running water. Put used strips in the trash, rinse all glassware with distilled water, and wipe the bench dry.

Session 3 is for the analysis. Work items 1 through 8 with the Quarryhill reference data first, so you can check your method against the key. Then repeat items 3, 5 and 6 with your own group's data in Table A and record the results in Table D.

Constants. Molar mass of Epsom salt, MgSO4·7H2O: 246.47 g/mol. Molar mass of CaCO3: 100.09 g/mol. Hardness "as CaCO3" counts each mole of Ca2+ or Mg2+ as one mole of CaCO3. Treat castile soap as potassium oleate, C17H33COOK, which dissolves as K+ and the oleate anion C17H33COO-.

Table A. Your group's data (drops to a 30-second lather, 25.0 mL samples)

Record your two tap-water test-strip readings in Table D.

Table B. Quarryhill reference data: calibration standards (fictional class data, same procedure, one soap batch)

Table C. Quarryhill reference data: unknowns (same class, same soap batch)

The well sample came from a farm outside Quarryhill. The class's two test strips on the school tap water both matched the 120 block on a chart with blocks at 0, 25, 50, 120, 250 and 425 mg/L as CaCO3.

Report excerpt: Quarryhill Water Department (fictional), monthly distribution report for the school's service zone. Total hardness by EDTA titration: 131 mg/L as CaCO3. Calcium hardness by EDTA titration: 97 mg/L as CaCO3. Customer classification scale (mg/L as CaCO3): soft, 0 to 60; moderately hard, 61 to 120; hard, 121 to 180; very hard, above 180.

Table D. Your group's results

1. The stock solution is 1.23 g of Epsom salt dissolved to 500.0 mL. Calculate the stock's hardness in mg/L as CaCO3 to three significant figures, then calculate the hardness of the S150 standard (15.0 mL of stock diluted to 100.0 mL) to the nearest whole mg/L. Explain why the molar mass of the hydrate, not of anhydrous MgSO4, must be used.

2. Write the balanced molecular equation and the net ionic equation for the reaction of the Epsom-salt standards with potassium oleate, and the net ionic equation for the same reaction with the calcium in tap water. Name the spectator ions, and explain why a lasting lather cannot form until the precipitation is complete.

3. Find the mean drop count for each standard in Table B. Fit a least-squares line to the six points (hardness, mean drops), and report the slope to three significant figures, the intercept to two decimal places, and r to three decimal places. Explain what the slope and the intercept each mean for this test.

4. Using your line from item 3 with the rounded slope and intercept, calculate the residual (observed mean minus predicted) for each standard to two decimal places. Identify the largest residual, and decide whether the residuals support using a straight line from 0 to 250 mg/L as CaCO3.

5. Find the mean and sample standard deviation of the four school tap-water trials in Table C, with the standard deviation to three significant figures. Use your calibration line to estimate the tap water's hardness to the nearest whole mg/L as CaCO3.

6. Convert the tap-water standard deviation from drops into mg/L as CaCO3, to the nearest 0.1 mg/L. Then state the tap-water result at a precision this method supports, and decide whether the soap test alone can classify the tap water on the department's scale.

7. Explain why the undiluted well-water counts in Table C cannot be converted with the calibration line. Then use the diluted trials to calculate the hardness of the original well water to the nearest whole mg/L as CaCO3, and classify it. Explain why doubling the diluted drop count before using the line would give the wrong answer.

8. Calculate the percent difference between your tap-water estimate from item 5 and the department's EDTA total hardness, using the EDTA value as the reference, to the nearest 0.1 percent. Decide whether the difference is larger than the soap method's own spread from item 6, give two chemical or procedural reasons the soap method could be biased for this water, and explain why the department relies on EDTA titration rather than soap or test strips.