How do yo solve this?

Question

What amount of ice must be added to 540g of water at 25°C to cool the water to 0°C and have no ice remaining?

Enthalpy of melting: 6.02kJ/mol

Answer 1

Let
Q1- heat required to bring water to 0°C
Q(ice) - heat required to melt m2 mass of ice
m1- mass of water
m2 - mass of ice

Q1= m1Cp(T2-T1)

Q(ice)= m2Cf

Q1=Q(ice) so
m1Cp(T2-T1)= m2Cf where
Cf= 333.55 kJ/kg =333.55 J/g
Cp =4.18 J/(g K)=75.327 J/(mol K)

m2= m1Cp(T2-T1)/Cf
m2= 540 x 4.18(25)/333. 550
m2=169 g
or using the constant given
m2= 540 x75.32( 25) /6.02E+3= 169g (confirmed just for fun)