[emissivity]

hi I have a problem with this concept.

I will analyse the partial molar volume of the solution (from pure water, 90% water+10% ethanol, ···, to pure ethanol) anyway, as you can see(image I uploaded)

eq. (11) is derived from '1kg water.' so 55.51 is used. and 55.51 in eq. (13) is there. and I have a problem with these things.

eq. (14) comes from density = mass / volume

so the number 1000 in eq. (14) means '1kg water' right? but what is the number, 1000 in the eq. (15) ? I don't know the meaning of 1000...

and, in equation (17), you can see 'apparent molar volume, Φ' this equation comes from eq. (14) and (15). then 1kg water continues even in this equation. and Is the m in the eq. (17) 'molality' or 'the number of moles of solute'?

and, eq. (18), (19) also come from eqation (11) and (12) 1kg water continues... at last, we obtain equation (21) and (22) from eqation (18) and (19).

but 55.51(moles of 1kg water) continues in equation (22). the m in equation (21) and (22) is 'molality' isn't it? and equation (22) is not linear function..  ehhh... I really don't know from top to the bottom.  I have studies this document for about 6 hours....  you can see the problem I have. and additional question is this.

1. if I don't use 1kg of water(for example 30ml of water+ 20ml ethanol), can I use the equations above this? (eq 17, 21, 22)

2. the m in eq 17 is the number of moles of solute right?

3. to take partial molar volume,should I calculate all the molality and Φ?

    a. and If I plot those molality(m) and Φ, can I get partial molar volume?

4. the book said Φ vary linearly with (m)^(1/2), but equation (21),(22) is not linear funtion.  the degree is (1/2), 3/2. that is not line function..

but how can I get the partial molar volume? please help me... I think I can't achieve this without your help..

*{MOD Edit --  remove excess whitespace}*

[Borek]

No time to dig in, but in general whenever you see 1000 in such places it is some kind of conversion factor between kg and g (or L and mL), often put there as we define some quantities for kg and L and we want to do the calculations for g and mL.