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 of the water sample is 0.003 M, which corresponds to option b.

Step-by-step solution

Understanding PPM and Molarity

PPM stands for parts per million, and in terms of hardness, it refers to the concentration of calcium carbonate, \[ ext{CaCO}_3\], in water. If there are 300 ppm of \[ ext{CaCO}_3\], this means there are 300 grams of \[ ext{CaCO}_3\] per million grams (or liters) of water.

Convert PPM to Grams per Liter

Since 1 ppm is approximately equal to 1 mg/L for water, 300 ppm \[ ext{CaCO}_3\] is equivalent to 300 mg/L. We need to convert this to grams per liter, resulting in 300 mg \[ ext{CaCO}_3\] = 0.3 g/L.

Calculate Moles of \\[ ext{CaCO}_3\\]

Find the molar mass of \[ ext{CaCO}_3\], which is approximately 100 g/mol. To find the number of moles in 0.3 g of \[ ext{CaCO}_3\]: \\[\text{moles of } \text{CaCO}_3 = \frac{0.3 \text{ g}}{100 \text{ g/mol}} = 0.003 \text{ mol/L}\].

Determine the Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. From Step 3, we found that the solution contains 0.003 moles of \[ ext{CaCO}_3\] per liter. Thus, the molarity of the solution is 0.003 M.

Key concepts

ppm (parts per million)

Understanding the concept of ppm, or parts per million, is crucial when discussing concentrations in chemistry, especially in water solutions. PPM is a way of expressing very dilute concentrations of substances. It denotes how many parts of a substance are present in one million parts of a solution. Essentially, 1 ppm indicates that there is one part of "something" in one million parts of "something else."

In the context of water hardness, ppm measures the amount of calcium carbonate (CaCO₃) present. For example, if a water sample has 300 ppm of CaCO₃, it implies there are 300 parts of calcium carbonate per one million parts of the water solution. This is equivalent to 300 grams of calcium carbonate in a million grams (or liters) of water. Understanding ppm allows us to translate these measures effectively when performing further calculations, such as determining molarity.

molarity calculation

Calculating molarity involves determining the concentration of a solute in a solution, expressed as moles of solute per liter of solution. To calculate molarity, you'll need:

• The mass of the solute (often obtained from the ppm value converted to grams per liter).
• The molar mass of the solute, which is the mass of one mole of that substance.

For calcium carbonate, first convert ppm to grams per liter. In water, 1 ppm is typically equal to 1 mg/L. So, 300 ppm means 300 mg/L, which converts to 0.3 g/L. The molar mass of calcium carbonate (CaCO₃) is approximately 100 g/mol. We then calculate the number of moles as follows: \[\text{moles of CaCO}_3 = \frac{0.3 \text{ g}}{100 \text{ g/mol}} = 0.003 \text{ mol/L}\]
Thus, the molarity of a solution with 300 ppm of CaCO₃ is 0.003 M, simplifying our understanding of solution concentrations.

calcium carbonate (CaCO₃) concentration

Determining the calcium carbonate concentration in water is vital for understanding water hardness. Calcium carbonate contributes to the hardness of water, which can affect everything from soap efficiency to the health of water plants and animals.The concentration of CaCO₃ in a solution is often measured in ppm, which can then be converted to molarity for more precise calculations. Using the molar mass of CaCO₃, which is approximately 100 g/mol, we can determine its concentration in terms of moles per liter—a more universally understood measurement in chemistry.

If you start with a ppm value, like 300 ppm, you first translate it to grams per liter (0.3 g/L), then divide by the molar mass of calcium carbonate to calculate the molarity:\[\text{Molarity (CaCO}_3\text{)} = \frac{0.3 \text{ g/L}}{100 \text{ g/mol}} = 0.003 \text{ M}\]This calculation tells us how concentrated the calcium carbonate is in the water, giving insight into water quality and its potential effects on plumbing, appliances, and ecosystems.