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 ppm, so the answer is (d).

Step 1: Understand Parts Per Million (ppm)

Understand that ppm is a way to express very dilute concentrations of substances. 1 ppm means 1 part of solute (carbonate in this case) per 1 million parts of the solution. Mathematically, this can be expressed as \( \text{ppm} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 10^6 \).

Step 2: Insert Values into the ppm Formula

The given values are 10 g of carbonate as solute and 1000 g of the total solution. Inserting these into the ppm formula, we have \( \text{ppm} = \frac{10}{1000} \times 10^6 \).

Step 3: Calculate the ppm

Perform the division and multiplication: \( \text{ppm} = 0.01 \times 10^6 = 10,000 \).

Step 4: Choose the Correct Option

The calculated concentration is 10,000 ppm. Thus, option (d) \(10,000 \mathrm{ppm}\) is correct.

Key Concepts

Understanding Parts Per Million

The term "parts per million" (ppm) is a way to specify very dilute concentrations of substances. It is similar to other fraction-based measurements like percentages or parts per billion, but ppm is specifically used when dealing with minute amounts of one component within a vast amount of another.

This unit is commonly used in chemistry and environmental science when measuring pollutant levels, solute measurements in solutions, or even in atmospheric sciences.

• 1 ppm implies that there is 1 part of solute per 1 million parts of the solution.
• Mathematically, it translates to: \( ext{ppm} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 10^6 \).

Using ppm allows for expressing very small concentrations in a manageable and comparable manner. Whenever you hear about ppm, think of it as a tiny part spread throughout a million parts of a whole.

Exploring Solute Concentration

The solute concentration determines how much solute is present in a solution compared to the amount of solvent. A solute is the substance dissolved, while the solvent is what it's dissolved into. For instance, in a sugar-water mixture, sugar is the solute, and water is the solvent.

Concentration can be expressed in various forms like molarity, mass percentage, or ppm—each depending on how dilute or concentrated the solution is.

• Low concentrations often use ppm, especially when the solute's presence is barely perceptible.
• To calculate solute concentration in ppm: you use the formula \( ext{ppm} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 10^6 \).

Accurate solute concentration measurement is crucial in fields ranging from chemistry labs to environmental monitoring, where precise data can influence critical decisions.

Introduction to Calcium Carbonate Solutions

Calcium carbonate is a common chemical compound found in rocks as minerals like calcite or limestone. It is often encountered in various applications ranging from industrial uses to food additives.

In aqueous solutions, calcium carbonate can dissolve slightly but remains mostly as a suspension or precipitate due to its low solubility in water.

• In scientific studies, it is crucial to determine its concentration precisely, often using ppm, especially when evaluating solubility or biological effects.
• In the provided exercise, a solution of calcium carbonate was used, highlighting the way ppm can specify its concentration in a large mixture.

Understanding how to measure and interpret the concentration of calcium carbonate in solutions can lead to insights in fields such as geochemistry and environmental studies, where its effects play a significant role.