If you were to weigh out one gram of potassium chloride (KCl), on a milligram precision balance (i.e. 1.000 g or 1,000 mg), and then were to dissolve into a 3 Liter volumetric flask. Using a calculator, one may be tempted to say that the concentration will be of 0.333333333.... grams per liter (g/L) or 33.333333.... mg/L of KCl. Discuss why this is not correct in terms of the precision of the milligram balance. What will be the concentration of the solution with the correct significant figures?

Answer: 3 x 10^-1

Step-by-step explanation

1. Calculate the Concentration:

• Given: gram KCl= 1 gram; liter solvent= 3 Liters
• Concentration= gram/L

                  = 1 gram/ 3 Liters

                  = 0.33333333333

2. The calculated concentration is not the final answer. You should first apply the rule of significant figures, specifically in the division operation.

• Identify the Significant Figures of all the given. 

          (since all the given is whole number, to find the significant figures, we just have to count the number of figures per given)

            1 gram KCl= 1 significant figure

            3 liters solvent= 1 significant figure

• Apply the rule of significant figures to the computed concentration.

RULE: The LEAST number of significant figures determines the number of significant figures in the answer. 

      - Since all the given has an equal number of significant figure which is 1, we, therefore, say that the final concentration should also have 1 significant figure.

            concentration: 0.33333333333

• Transform the calculated concentration to 1 significant figure using SCIENTIFIC NOTATION.

         -From 0.33333333333, we now have 3 x 10-1

3. Therefore, the concentration if 3 x 10^-1 mg/L, which has 1 significant figure because the given values also have 1 significant figure.