12.522 grams of KOH is dissolved in enough water to make 475 mL of solution. Find the molarity, Molality, Mole Fraction and w/w%

Dear student

Mass of KOH = 12.522g
Volume = 475mL =0.475L
Molarity = no.of moles of solute/ Volume of solution in L
nO.of moles of KOH = mass of KOH given/ molar mass of KOH
                                = 12.522g/56.1056g/mol
                                =0.223 mol
​​​​​​now Molarity = 0.223 mol/0.475L
                     = 0.47M

Molality = Molality = no. of moles / mass of solvent in Kg 
Now, the density of water is 1g/mL
Density = mass/volume
 mass of solution = 1g/mL x 475mL
                          =475g
Now, molality = 0.223/ 0.475
                      = 0.47m

That is 0,47moles dissolved in 1000kg water
Moles of water = weight of water/molecular weight of water
                     = 18/1000
                     =55.55mol
 no.of moles  = weight of water/molar mass
55.55 = weight of water/ 18
Mole fraction = no.of moles of solute/ no.of moles of solute + no.of moles of solvent
                    = 0.47/0.47 + 55.55
                   = 0.0085
Total Mass of solution =  Mass of solute + Mass of solvent
weight(w/w) % = mass of component / total mass of solution x 100
          =   12.522/ 12.522 + 475 x 100
      =  2.57%

Regards