Explanation:
As the given data is as follows.
Volume = 1.06 L, [tex]\Delta T = -11.0^{0}C[/tex]
[tex]k_{f}[/tex] for water = 1.853 ^{0}C m, density = 1.00 g/mL
Relation between temperature change and [tex]k_{f}[/tex] is as follows.
[tex]\Delta T = c \times i \times k_{f}[/tex]
where, c = concentration
i = Van't Hoff factor
[tex]k_{f}[/tex] = 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.
[tex]\Delta T = c \times i \times k_{f}[/tex]
[tex]11 ^{0}C = c \times 2 \times 1.853 ^{0}C/m}[/tex]
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.
[tex]1.06 L \times \frac{2.96 \text{mol of NaCl}}{1 kg} \times \frac{58.5 g NaCl}{1 mol}[/tex]
= 183.54 g
Thus, we can conclude that mass of NaCl that should be added is 183.54 g.
