Answer
See the answer below.
Work Step by Step
Per kg of solvent:
The number of moles of solute $10.7\ mol/kg\times 1\ kg=10.7\ mol$
The number of moles of solvent: $1000\ g\div 18.015\ g/mol=55.51\ mol$
a) Mole fraction: $10.7/(10.7+55.51)=0.162$
Mass of solute: $10.7\ mol\times 40.00\ g/mol=428\ g$
b) Weight percent: $428/(1000+428)\times 100\%=30\%$
The volume of the solution: $(1000+428)g\div1.33\ g/cm^3\times 1\ L/1000\ cm^3=1.074\ L$
c) Molarity: $10.7\ mol\div 1.074\ L=10.0\ M$