Question

0.009 g of CaCO\(_3\) is dissolved in 1 litre of solution. Calculate the concentration of the solution in parts per million (ppm).

• A. 0.009 ppm
• B. 0.9 ppm
• C. 9 ppm
• D. 90 ppm

Hint:

To quickly calculate ppm for any aqueous solution, just remember that 1 ppm = 1 mg/L. Simply convert your solute mass to milligrams and divide by the volume in litres!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Parts per million (ppm) is a unit of concentration used for very dilute solutions. It expresses the mass of a solute present in one million (\(10^6\)) parts by mass of the solution. For aqueous solutions, where the density is approximately \(1 \text{ g/mL}\), \(1 \text{ litre}\) of solution weighs \(1000 \text{ g}\).

Step 2: Key Formula or Approach:
The formula for ppm can be expressed as: \[ \text{ppm} = \frac{\text{Mass of solute (g)}}{\text{Mass of solution (g)}} \times 10^6 \] Alternatively, for dilute aqueous solutions: \[ \text{ppm} = \frac{\text{Mass of solute (mg)}}{\text{Volume of solution (L)}} \]

Step 3: Detailed Calculation:
1. Convert mass of solute from grams to milligrams: Given mass of CaCO\(_3\) = \(0.009 \text{ g}\) Since \(1 \text{ g} = 1000 \text{ mg}\): \[ \text{Mass in mg} = 0.009 \times 1000 = 9 \text{ mg} \] 2. Calculate ppm using the volume of the solution: Given Volume = \(1 \text{ litre}\) \[ \text{Concentration in ppm} = \frac{9 \text{ mg}}{1 \text{ L}} = 9 \text{ ppm} \] Alternatively, using the mass-to-mass formula: Mass of solute = \(0.009 \text{ g}\) Mass of \(1 \text{ L}\) solution \(\approx 1000 \text{ g}\) \[ \text{ppm} = \frac{0.009}{1000} \times 10^6 = 0.009 \times 10^3 = 9 \text{ ppm} \]

Step 4: Final Answer
The concentration of the CaCO\(_3\) solution is 9 ppm.