When we know that the solubility of KMnO4 is 6.4 g/100mL
so 6.49 g → solve in 100mL
? ← solve in 500mL
the amount of KMO4 soluble in 500mL = (500X 6.49) /100 = 32.45 g
and when we have the molar mass of the KMnO4 = 158/mol
we can get the number of moles of KMnO4 = mass of KMnO4 / molar mass of KMnO4
no.of moles of KMnO4 = 32.45 / 158 = 0.2 mol
when the no.of moles is less than 0.35 ∴KMnO4 will not dissolve because the number of moles is less than 0.35 mol that given in the question.