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) \(10,000 \mathrm{ppm}\)

Short answer

The concentration of the solution is 10,000 ppm (option d).

Step-by-step solution

Understanding ppm

The term 'ppm' stands for 'parts per million' and is used to describe the concentration of a substance in a solution. 1 ppm corresponds to 1 milligram of solute per kilogram of solution.

Define the Mass of Solution

According to the problem statement, the total mass of the calcium carbonate solution is given as 1000 grams.

Identify the Mass of Solute

From the problem, the mass of the carbonate (solute) in the solution is given as 10 grams.

Convert Grams to Milligrams

Since 1 ppm is equivalent to 1 mg of solute per kilogram of solution, convert the mass of the solute from grams to milligrams. We know that 1 gram = 1000 milligrams, so 10 grams = 10,000 milligrams.

Calculate Concentration in ppm

Using the definition of ppm from Step 1, the concentration can be calculated as follows: \[ \text{Concentration (ppm)} = \frac{\text{mass of solute (mg)}}{\text{mass of solution (g)}} \times 10^6 \]Therefore, \[ \text{Concentration (ppm)} = \frac{10,000 \, \text{mg}}{1000 \, \text{g}} \times 10^6 = 10,000 \, \text{ppm} \]

Conclusion

Based on the calculation, the concentration of the solution is 10,000 ppm. Therefore, the correct answer is (d) 10,000 ppm.

Key concepts

Calcium Carbonate Solution

A calcium carbonate solution is a mixture where calcium carbonate is dissolved or suspended in a solvent, usually water. Calcium carbonate itself is a chemical compound with the formula \( \text{CaCO}_3 \), commonly found in rocks, and is the main component of shells of marine organisms. When creating a chemical solution, it usually involves adding a solute, in this case, calcium carbonate, to a solvent, resulting in the solution.

• Components: The main components of a calcium carbonate solution are the solute, calcium carbonate, and the solvent, typically water.
• Purpose: Such solutions are often used in various applications, including industrial processes, water treatment, and as dietary supplements.
• Characteristics: The properties of the solution, such as its concentration, depend largely on the amounts of solute and solvent used. For example, the 1000 g solution mentioned contains 10 g of calcium carbonate.

Understanding the role and form of calcium carbonate within a solution context is crucial for various computations, especially in determining concentrations.

Parts Per Million (ppm)

Parts per million (ppm) is a measure of concentration that signifies the number of parts of a solute per million parts of the solution. This is a very helpful unit when dealing with small concentrations.

• Definition: 1 ppm equates to 1 milligram of solute per kilogram of solution. This implies that for every 1,000,000 units of the solution, there's 1 unit of solute.
• Usage: Ppm is commonly used in environments such as chemistry, environmental science, and engineering to express dilute concentrations of substances.
• Relevance: In the context of the given exercise, calculating ppm aids in understanding the specific amount of calcium carbonate present within a much larger quantity of liquid solution.

In practice, understanding ppm allows you to interpret how much of a particular substance is in a larger sample, such as pollutants in water or chemicals in air.

Conversion of Grams to Milligrams

Often, when working with chemical solutions, you need to convert between different units of measurement like grams and milligrams.

• Basic Conversion: 1 gram is equal to 1000 milligrams. This simple conversion is crucial for chemical calculations.
• Importance in Calculations: In order to compute concentration in ppm, it's essential to first convert the mass of a solute from grams to milligrams. This is because ppm is defined with milligrams corresponding to grams of solution.
• Example from Exercise: In the exercise, 10 grams of calcium carbonate is present in 1000 grams of solution. Converting 10 grams to milligrams involves multiplying by 1000, resulting in 10,000 milligrams, which is then used in the ppm calculation.

This conversion step simplifies the process of solving problems related to concentration and ensures that all measurements are in compatible units for calculations.