Problem 37 - A Complete Resource Book in Chemistry for JEE Main

Question

\(1000 \mathrm{~g}\) calcium carbonate solution contains \(10 \mathrm{~g}\) carbonate. The concentration of solution is (a) \(10 \mathrm{ppm}\) (b) \(100 \mathrm{ppm}\) (c) \(1000 \mathrm{ppm}\) (d) \(10,000 \mathrm{ppm}\)

Step-by-Step Solution

Answer

The concentration of the solution is \(10,000 \mathrm{ppm}\).

Step 1: Understanding ppm

PPM stands for parts per million and is a measure of concentration. It is equivalent to mg/L or mg/kg when dealing with solutions. In this exercise, we are asked to find the amount of carbonate in parts per million within the given solution.

Step 2: Identify Key Quantities

We have a total mass of the solution, which is 1000 g, and the mass of the carbonate in this solution, which is 10 g.

Step 3: Convert Grams to ppm

To convert grams of carbonate to parts per million, use the formula:\[\text{ppm} = \left( \frac{\text{mass of solute in grams}}{\text{mass of solution in grams}} \right) \times 10^6\]Plug in the known values:\[\text{ppm} = \left( \frac{10 \, \text{g}}{1000 \, \text{g}} \right) \times 10^6\]

Step 4: Calculate the ppm Value

Perform the calculation:\[\text{ppm} = \left( \frac{10}{1000} \right) \times 10^6 = 0.01 \times 10^6 = 10,000 \, \text{ppm}\]

Key Concepts

Understanding Concentration in Solutions

Concentration tells us how much of a substance (solute) is present in a given quantity of a solvent or mixture. It is an essential concept in chemistry because it allows us to quantify how strong or weak a solution is.
Common units for expressing concentration include parts per million (ppm), molarity, and percentage by mass. PPM is a unit that describes the number of parts of solute per million parts of solution. This unit is particularly useful for very dilute solutions. For instance, if a solution has a concentration of 10 ppm, it means that there are 10 parts of solute in every 1,000,000 parts of the solution.
Understanding concentration is important in fields like environmental science, where pollutants are often measured in ppm, and in medicine, which uses ppm to determine doses for treatments such as homeopathic medicines.

The Role of Carbonates

Carbonates are salts or esters of carbonic acid, characterized by the presence of the carbonate ion, \({\text{CO}_3^{2-}}\). They are crucial in the Earth's geology, chemistry, and biology. Carbonates form the bases of many structures like corals and shells, playing a vital role in marine life.
When dissolved in solutions, carbonate ions can react with acids to release carbon dioxide gas, which is a principle behind the formation of caves through the process of chemical weathering. Carbonates are also significant in industries like glass making, cement manufacturing, and as a pH regulator in some processes.
Understanding the behavior of carbonates in solutions helps in fields like water treatment, where bicarbonate levels may indicate water hardness, and thus, necessary treatments to soften water.

Significance of Calcium Carbonate

Calcium carbonate, \({\text{CaCO}_3}\), is one of the most common and widely used compounds on Earth. It forms the primary component of natural substances like limestone, chalk, and marble. In industries, calcium carbonate is essential in the production of cement, lime, and as a filler in various products.
Apart from its industrial significance, calcium carbonate plays a key role in biological systems. For instance, it's vital for bone formation in vertebrates and the structural integrity of shells and exoskeletons in marine organisms. In water systems, calcium carbonate acts as a buffering agent, helping to maintain stable pH levels.
In food, it serves as a calcium supplement, contributing to dietary requirements for healthy bones. Understanding its presence in solutions, like calculating its concentration in ppm, can help in applications ranging from food science to ecological studies.