Question

What mass of salt (NaCl) should you add to 1.06 L of water in an ice cream maker to make a solution that freezes at -11.0 ∘C ? Assume complete dissociation of the NaCl and density of 1.00 g/mL for water.

Answer 1

Step-by-step explanation:

As the given data is as follows.

Volume = 1.06 L,
`\Delta T = -11.0^(0)C`

`k_(f)` for water = 1.853 ^{0}C m, density = 1.00 g/mL

Relation between temperature change and
`k_(f)` is as follows.

`\Delta T = c * i * k_(f)`

where, c = concentration

i = Van't Hoff factor

`k_(f)` = cryoscopic constant

When NaCl dissolves in water then it results in formation of sodium ions and chlorine ions. In means two ions are formed so, i = 2. Therefore, putting the given values into the above formula as follows.

`\Delta T = c * i * k_(f)`

`11 ^(0)C = c * 2 * 1.853 ^(0)C/m}`

c = 2.96

As molality is defined as number of moles of solute per kg of solvent.

So, mass of NaCl that should be added is calculated as follows.

`1.06 L * \frac{2.96 \text{mol of NaCl}}{1 kg} * (58.5 g NaCl)/(1 mol)`

= 183.54 g

Thus, we can conclude that mass of NaCl that should be added is 183.54 g.