How to Calculate Mole Fractions and Molar Volume in a Thermodynamic System?

[MathematicalPhysicist]

Homework Statement

This question is problem 1.3.1 from Herbert Callen's textbook in Thermodynamics, second edition.

One tenth of a kilogram of NaCl and 0.15 kg of sugar ($C_{12} H_{22}O_{11}$ are dissolved in 0.5 Kg of pure water. The volume of the resultant thermodynamic system is $0.55\times 10^{-3}m^3$. What are the mole numbers of the three components of the system? What are the mole fractions? What is the molar volume of the system?

In the answers I have the following: Mole fraction of NaCl = 0.057, molar volume =$18\times 10^{-6} m^3/mole$.

How did they arrive at these answers? did they multiplied the ratios with Avogadro's number?

Homework Equations

Relative mole fraction is given by: $$N_k/\sum_{j=1}^r N_j$$ if we have a mixture of $r$ substances, where this is defined as the molar fraction;
Molar volume is defined as $$V/\sum_{k=1}^r N_k$$.

The Attempt at a Solution

How do extract the moles of each substance here?

It's not written in the text.

 

[Borek]

If you are attacking thermodynamics you should already know how to convert between masses and numbers of moles, this is GenChem101 which is prerequisite.

Do you know what the molar mass is?

 

[MathematicalPhysicist]

I have taken undergraduate thermal physics years ago, so I might have forgotten some stuff.

Anyhow, I solved it, thanks; I checked molar mass in wiki and it solved my problem.