Question

Hardness of water sample is \(300 \mathrm{ppm} \mathrm{CaCO}_{3}\). Hence its molarity is a. \(0.30 \mathrm{M}\) b. \(0.003 \mathrm{M}\) c. \(0.030 \mathrm{M}\) d. \(0.0013 \mathrm{M}\)

Short answer

The molarity is \(0.003 \text{ M}\). Choice b is correct.

Step-by-step solution

Understand the Problem

We need to convert the hardness of water given in ppm (parts per million) of CaCO3 to molarity (M). Molarity is the number of moles of solute per liter of solution.

Calculate Mass of CaCO3

Since 1 ppm means 1 mg of solute per liter of solution, 300 ppm of CaCO3 means there are 300 mg of CaCO3 per liter of water.

Convert Mass to Grams

Convert 300 mg of CaCO3 to grams because molarity is expressed in moles per liter. We have \( 300 \text{ mg} = 0.300 \text{ g} \) of CaCO3.

Determine Moles of CaCO3

Calculate the number of moles of CaCO3. The molar mass of CaCO3 is 100 g/mol. Use the formula: moles = mass (g) / molar mass (g/mol). So, \( \frac{0.300 \text{ g}}{100 \text{ g/mol}} = 0.003 \text{ moles} \).

Calculate Molarity

Using the definition of molarity, which is moles of solute per liter of solution, and knowing you have 0.003 moles of CaCO3 in 1 liter of water, the molarity is \(0.003 \text{ M}\).

Key concepts

ppm (parts per million)

When discussing the hardness of water, ppm, or parts per million, is an essential measurement. It describes the concentration of a solute in a solution at one part of the solute per one million parts of the total solution. Consider it a way to express very diluted concentrations of a substance.
For example, if water has a hardness of 300 ppm CaCO3, it means there are 300 parts by weight of calcium carbonate dissolved in one million parts by weight of the water solution. Since the density of water is approximately 1 g/mL, and one liter of water weighs about 1000 grams, identifying ppm becomes straightforward:

• 1 ppm equals 1 mg of solute per liter of solution.
• 300 ppm signifies 300 mg of a substance in 1 liter of water.

Understanding ppm is crucial for water quality assessments and chemical calculations.

molarity

Molarity is a fundamental concept in chemistry, representing the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution.
Knowing molarity helps us to understand how much solute is present in a given volume of solvent, which is essential for preparing and using chemical solutions effectively. The formula for molarity is given by:
\[M = \frac{n}{V}\]
where \(M\) is molarity, \(n\) is the number of moles of solute, and \(V\) is the volume of the solution in liters.
To calculate molarity, we must first convert mass into moles, using the molar mass of the solute, and then divide by the solution volume in liters. For example, with 0.003 moles of CaCO3 in 1 liter of water, the molarity would be 0.003 M.

CaCO3

Calcium carbonate, or CaCO3, is a white insoluble solid found naturally as limestone, chalk, and marble. It is a common substance encountered in chemistry, geochemistry, and even in daily life as an active ingredient in agricultural lime.
CaCO3 is crucial for determining the hardness of water, which can affect household water systems and industrial processes. The molar mass of CaCO3 is 100 g/mol, which means one mole of calcium carbonate weighs 100 grams.
In water hardness calculations, it's essential to convert the mass of CaCO3 from milligrams to grams, then into moles by using its molar mass. This way, you can determine the concentration of CaCO3 in a solution, which helps in determining its molarity and assessing water quality.

conversion of units

Converting units is an important skill in chemistry to convert one measurement into another for accurate calculations. This process can involve changing one unit of measurement to another or even converting one form of data into something entirely different, such as weight to moles.
In this exercise, we are converting water hardness from ppm to molarity, requiring a few conversion steps:

• Convert ppm to mg/L, recognizing that 1 ppm = 1 mg/L.
• Convert mg to grams, knowing that there are 1000 mg in a gram.
• Convert grams to moles using the molar mass of the substance (e.g., for CaCO3, it's 100 g/mol).
• Determine molarity using the formula: \(M = \frac{n}{V}\), where \(n\) is moles and \(V\) is volume in liters.

By mastering unit conversions, you'll be better equipped to tackle a variety of analytical and experimental problems in chemistry.