Molality and mole fraction

Exercise 1

We want to prepare an $0.200\;m$ ($m$ = molal) aqueous solution of sodium chloride. Calculate the mass of $NaCl $ to be dissolved in $500\;g$ water!

$\mu_{NaCl}$ $=$ $\frac{n_{NaCl}\cdot 1000}{m_{H_2O}}$ $n_{NaCl}$ $=$ $\frac{\mu_{NaCl}\cdot m_{H_2O}}{1000}$ $m_{NaCl}$ $=$ $M_{NaCl}\frac{\mu_{NaCl}\cdot m_{H_2O}}{1000}$ $=$ $5.84\;g$