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Example 1: If C(1/5KMnO4) = 0.01 mol/L, then 0.01 × 158 = 1.58 g; this means 1.58 grams of potassium permanganate is dissolved to make 1 liter of solution.
Example 2: 1/5KMnO4 = 158/5 = 31.6. If C(1/5KMnO4) = 0.1 mol/L, then 0.1 × 31.6 = 3.16 grams of potassium permanganate is needed to make 1 liter of solution. In other words, 0.1 × 31.6 = 3.16 grams of potassium permanganate must be dissolved to obtain 1 liter of solution
Example 2 is correct. For a specific explanation, I’ve copied information from Baidu for your reference. Definition of mole: A mole is the amount of substance in a system whose number of elementary units is equal to the number of atoms in 0.012 kilograms of carbon-12. If the number of basic units contained in a system is 6.022*10 to the 23rd power, this quantity is called 1 mole. The basic units in this context can be: atoms, molecules, ions, electrons, and other particles or combinations of them. 1/5KMnO4=0.1mol/l actually represents the volume molar concentration of the potassium permanganate solution; the proper way to write it is C(1/5KMnO4)=0.1mol ; It is calculated based on 1/5 molecule of potassium permanganate as the basic unit, because when a potassium permanganate solution participates in a reaction, the Mn ion generally changes from +7 to +2, and one molecule of potassium permanganate gains 5 electrons. 1/5KMnO4 indicates that 1 electron is obtained per basic unit molecule used in the reaction; in other words, (1/5 mol of KMnO4 molecules) is equivalent to 1 mol of electrons, and 1 mol of electrons can be obtained during the reaction. The concentration is calculated as C(1/5KMnO4) = mass of KMnO4 / (molecular weight of 1/5 potassium permanganate) / volume of the solution. For example: 3.161 grams of potassium permanganate dissolved in 1 liter of water ; What is the volume molar concentration of this solution? C(1/5KMnO4) = 3.161 g / (1/5 * 158.03) / 1 = 0.1 mol/L; C(KMnO4) = 3.161 g / 158.03 / 1 = 0.02 mol/L.