Question

A \(250-\mathrm{g}\) sample of hard water contains \(0.20 \mathrm{~g}\) of \(\mathrm{Ca}\left(\mathrm{CO}_{3}\right)\). What is the hardness of the water in parts per million? How would the water be classified?

Short answer

The hardness of the water is 800 ppm (calculated by \(800 = (0.20 / 250) \times 10^6\)). Based on the hardness, the water would be classified as very hard.

Step-by-step solution

Understanding Water Hardness

Water hardness is typically measured in parts per million (ppm), which indicates the number of parts of a substance (in this case, \(\mathrm{CaCO}_3\)) in one million parts of water. Here, we want to determine how many parts per million of \(\mathrm{CaCO}_3\) are in the sample of hard water.

Calculating the Hardness

To calculate the ppm of \(\mathrm{CaCO}_3\) in the water, use the formula: \[\text{ppm} = \left(\frac{\text{mass of substance in grams}}{\text{mass of water in grams}}\right) \times 10^6\]. Substitute the given values into the formula to calculate the hardness.

Evaluating Water Classification

Classify the water based on its ppm hardness value. Water is generally considered soft if the hardness is less than 60 ppm, moderately hard if between 61 to 120 ppm, hard if between 121 to 180 ppm, and very hard if above 180 ppm.

Key concepts

Parts Per Million

When measuring the concentration of a substance in water, 'parts per million' (ppm) is a commonly used unit. It's a way of expressing very dilute concentrations of substances. One ppm indicates one part of a substance per one million parts of the total solution, which is equivalent to milligrams of the substance per liter of water (mg/L).

Suppose you dissolve a small amount of salt in a large tank of water. If you dissolve 1 milligram of salt in one liter of water, this is a concentration of 1 ppm. The same concept applies to pollutants in air and soil. To calculate ppm in a water sample, we use the formula \[\text{ppm} = \left(\frac{\text{mass of substance in grams}}{\text{mass of water in grams}}\right) \times 10^6\]. This is a useful measure because it allows us to understand and communicate very small quantities in a more comprehensible way, essential for water quality assessment.

Calcium Carbonate

Calcium carbonate, or \(\mathrm{CaCO}_3\), is a mineral found in various parts of the environment. It's the primary component of substances like limestone, marble, and chalk. In water, \(\mathrm{CaCO}_3\) contributes to hardness when it dissolves. It's important to know the concentration of calcium carbonate in water because it determines how 'hard' the water is, which can affect everything from household cleaning to the efficiency of boilers and hot water heaters.

Hard water might not be a health hazard, but it can cause scale buildup in pipes and on fixtures. This scaling, over time, can lead to reduced water flow and increased energy consumption as appliances work harder to heat water. In detergency, it can reduce the lathering capability of soaps and detergents, requiring more product to achieve the desired cleaning effect. Measuring the calcium carbonate concentration thus becomes critical for managing these practical aspects of water use.

Hard Water Classification

Water hardness is classified based on the concentration of calcium carbonate it contains. The hardness levels help policymakers, service engineers, and homeowners make informed decisions about water treatment needs. Here are the general classifications for water hardness:

• Soft Water: Less than 60 ppm of \(\mathrm{CaCO}_3\). Soft water is preferred for soap and detergent use, as it doesn't hinder the effectiveness of these cleaning agents.
• Moderately Hard Water: 61 to 120 ppm of \(\mathrm{CaCO}_3\). While not ideal, moderately hard water is generally acceptable for most domestic uses without significant scaling issues.
• Hard Water: 121 to 180 ppm of \(\mathrm{CaCO}_3\). Hard water begins to cause scaling in pipes and appliances, affecting performance and efficiency.
• Very Hard Water: Over 180 ppm of \(\mathrm{CaCO}_3\). Such levels of hardness can lead to severe scaling and necessitate the use of water softeners or other treatment methods to protect infrastructure and appliances.

To give an example from the exercise we're looking at, a 250-gram water sample contains 0.20 grams of \(\mathrm{CaCO}_3\), which calculates to 800 ppm, a concentration considered very hard. This level would typically require treatment to reduce the hardness to prevent the negative consequences mentioned earlier.