Comparing the Hardness of Water Samples

Introduction

Is the water in one town harder than in another? Is bottled mineral water harder than tap water? A simple investigation answers these questions using nothing more than soap solution and some careful measuring. Because hard water wastes soap by forming scum, the volume of soap solution needed to form a lasting lather is a direct measure of how hard the water is. This page explains how the comparison works and how to make it a fair test.

Core explanation

The principle. When soap solution is added to hard water, it first reacts with the dissolved Ca²⁺ and Mg²⁺ ions to form scum. Only when these ions have been used up does extra soap produce a lasting lather . So:

- more soap needed → more calcium and magnesium ions → harder water ; - less soap needed → softer water .

The method in outline. A fixed volume of each water sample — say 25 cm³ — is placed in a conical flask. Soap solution is added from a burette in small portions, 1 cm³ at a time. After each addition the flask is stoppered and shaken, then left to stand. The end point is reached when a lather forms that lasts for a chosen time, such as 30 seconds. The total volume of soap solution added is recorded.

Controlling variables. For a fair test, only the water sample should change. The following must be kept the same:

- the volume of water tested; - the concentration and batch of soap solution; - the way the flask is shaken (number of shakes and vigour); - the definition of a "lasting lather" (the same time); - the temperature of the water.

Using a control. Distilled water is tested in the same way. It contains no hardness, so the small volume of soap it needs shows how much soap is required just to make a lather in pure water. Subtracting this from each sample's result gives the soap used up by hardness.

Finding the type of hardness. Each sample is tested twice: once as it is, and once after being boiled, cooled and filtered. Boiling removes temporary hardness only. So:

- soap used by unboiled water (minus control) = total hardness ; - soap used by boiled water (minus control) = permanent hardness ; - the difference = temporary hardness .

Improving reliability. Repeating each test and calculating a mean reduces the effect of random errors, such as judging the lather.

Step-by-step reasoning

Interpreting a results table:

1. Subtract the distilled-water result from every reading. 2. Rank the unboiled samples: largest volume = hardest. 3. Compare each sample's unboiled and boiled results. 4. A large drop after boiling means mostly temporary hardness. 5. Little or no drop means mostly permanent hardness.

Visual explanation

Picture a row of stoppered flasks. In the flask of distilled water, a thick foam appears after the first millilitre of soap. In the tap-water flask, the liquid turns cloudy grey with scum and only foams after many additions. A bar chart of the volumes, with a pale bar for unboiled and a darker bar for boiled water, shows the hardness of each sample at a glance.

Real-world analogy

It is like finding out how hungry a crowd is by counting how many sandwiches are eaten before some are left over on the plate. The "hungrier" the water — the more calcium ions it has — the more soap it eats before any lather is left over.

Real-world example

Water companies measure hardness more precisely by chemical analysis and publish it by postcode. Their figures are often given in milligrams of calcium carbonate per litre. Water above about 200 mg/L is described as hard or very hard, while water below about 50 mg/L is soft.

Why?

Why test boiled water that has been filtered? Boiling precipitates calcium carbonate. If the solid were left in the flask it would not react with soap, but filtering makes sure the result reflects only the hardness that is still dissolved, which is the permanent hardness.

Common misconception

"The sample that makes the most foam is the hardest." The opposite is true. Hard water makes the least foam for a given amount of soap because soap is being used up as scum.

Worked example

Question: Results (cm³ of soap solution for 25 cm³ of water): distilled water 1; sample X unboiled 13, boiled 5; sample Y unboiled 9, boiled 8. Find the total, temporary and permanent hardness of each sample in cm³ of soap.

Reasoning: Subtract the control of 1 cm³. X: total 12, permanent 4, temporary 12 − 4 = 8. Y: total 8, permanent 7, temporary 1.

Answer: X is harder overall (12 cm³ against 8 cm³) and mainly temporarily hard; Y is mainly permanently hard.

Quick check

1. Why is distilled water tested alongside the samples? Answer: As a control, to show how much soap is needed to form a lather when no hardness is present.

Exam focus

Be able to describe the soap-solution method, list the control variables and explain the purpose of the distilled-water control. Practise interpreting tables of results before and after boiling to identify temporary and permanent hardness.

Advanced insight

A more accurate method is a titration with EDTA , a compound that binds Ca²⁺ and Mg²⁺ ions tightly. An indicator changes colour once all these ions have been bound, giving a sharp end point. This avoids the subjective judgement of when a lather is "lasting" and allows hardness to be calculated in mg/L.

Summary

Hardness can be compared by measuring the volume of soap solution needed to produce a lasting lather in a fixed volume of water: the more soap needed, the harder the water. Fair testing requires the same volumes, soap solution, shaking and lather time. Distilled water acts as a control. Testing before and after boiling separates total hardness into its temporary and permanent parts.

Practice questions

1. State the dependent variable in the soap-solution hardness test. Answer: The volume of soap solution needed to form a lasting lather. 2. Give two variables that must be controlled. Answer: The volume of water tested and the concentration of soap solution (also shaking method, lather time, temperature). 3. A sample needs the same volume of soap before and after boiling. What does this show? Answer: Its hardness is all permanent; it contains no temporary hardness. 4. Suggest why repeating each test improves the results. Answer: Taking a mean of repeats reduces the effect of random errors, such as misjudging when the lather is lasting.