Final answer:
The concentration of the potassium permanganate solution is 3.8 x 10⁻⁵ M when rounded to two significant digits.
Step-by-step explanation:
The concentration of a solution is calculated by dividing the number of moles of the solute by the volume of the solution in liters. To calculate the concentration of potassium permanganate (KMnO₄) in the chemist's solution, you need to use the equation:
C = n / V
where C is the molarity (concentration) in moles per liter (mol/L), n is the number of moles of KMnO₄, and V is the volume of the solution in liters.
In this case, the student already has 3.8 μmol (or 3.8 x 10⁻⁶ mol) of KMnO₄ and the total volume is 100 mL, which is equivalent to 0.1 L. Therefore, the molarity (C) of the solution is:
C = 3.8 x 10⁻⁶ mol / 0.1 L = 3.8 x 10⁻⁵ M
Thus, the concentration of the potassium permanganate solution is 3.8 x 10⁻⁵ M, which can be rounded to two significant digits as 3.8 x 10⁻⁵ M.