Question

1. Based on the measured molality of the solution, what is the solvent mass in kg? 2. How many moles of water is that? 3. How much water remains in the solid? 4. Based on the results of (c), suggest a composition for the residual solid.

It is found that when one mole of sodium acetate trihydrate (NaC2H302 3H2O, FW 136.08 g/mol) was
heated to 58oC, water of hydration was released. The solid dissolved in the water, giving a saturated
solution that was 16.89 m in sodium acetate (see Fig. 1). This 16.89 m solution contained 0.9129 moles
of sodium acetate. The remaining sodium acetate was left as an undissolved solid, but. it is unknown if
this residual solid is a hydrate or not.
The saturated solution and the undissolved solid were separated, and it was found that the dry solid
weighed 7.144 g and had a crystal structure different from that of sodium acetate trihydrate

Answer 1

1. Solvent mass = 0.0540 kg;
2. Solvent amount = 3.00 mol;
3. Water remaining in solid = 0;
4. The solid is `"NaC"_2"H"_3"O"_2`.

Explanation:

`M_text(r):color(white)(mmmm)136.08color(white)(mmmmmm)82.03color(white)(mmm)18.02`
#color(white)(mmm)"NaC"_2"H"_3"O"_2·"3H"_2"O" → "NaC"_2"H"_3"O"_2 +"3H"_2"O"#

1. Solvent mass

`b = "moles of solute"/"kilograms of solvent"`

`16.9 color(red)(cancel(color(black)("mol")))·"kg"^"-1" = (0.9129 color(red)(cancel(color(black)("mol"))))/x`

`x = 0.9129/"16.9 kg"^"-1" = "0.0540 kg"`

2. Moles of water

`"Moles of water" = 54.0 color(red)(cancel(color(black)("g"))) × "1 mol"/(18.02 color(red)(cancel(color(black)("g")))) = "3.00 mol"`

3. Water remaining in solid

1 mol of trihydrate gave 3 mol of water as the solvent.

There is none left to combine with the solid.

There is no water remaining in the solid.

4. Identity of solid

We started with 1 mol of the trihydrate. Of this, 0.9129 mol went into solution.

The amount of solid acetate is then `"(1 - 0.9129) mol = 0.0871 mol"`

`"Molar mass of solid" = "7.144 g"/"0.0871mol" = "82.0 g/mol"`

This is the molar mass of anhydrous sodium acetate.

The solid is `"NaC"_2"H"_3"O"_2`.