Questions: Open Response Questions- Kf(H2O)=1.86°C/m, Kb(H2O)=0.52°C/m, 760 mm Hg=1.0 atm 13) Sea water is primarily composed of 42.3 g of NaCl/kg water. Calculate the freezing point of the oceans.

Open Response Questions- Kf(H2O)=1.86°C/m, Kb(H2O)=0.52°C/m, 760 mm Hg=1.0 atm
13) Sea water is primarily composed of 42.3 g of NaCl/kg water. Calculate the freezing point of the oceans.

Transcript text: Open Response Questions- $\mathrm{K}_{\mathrm{f}}\left(\mathrm{H}_{2} \mathrm{O}\right)=1.86{ }^{\circ} \mathrm{C} / \mathrm{m}, \mathrm{K}_{\mathrm{b}}\left(\mathrm{H}_{2} \mathrm{O}\right)=0.52{ }^{\circ} \mathrm{C} / \mathrm{m}, 760 \mathrm{~mm} \mathrm{Hg}=1.0 \mathrm{~atm}$ 13) Sea water is primarily composed of 42.3 g of $\mathrm{NaCl} / \mathrm{kg}$ water. Calculate the freezing point of the oceans. Previous Next

Solution

Solution Steps

Step 1: Determine the Molality of the NaCl Solution

First, we need to calculate the molality of the NaCl solution. Molality ($m$) is defined as the moles of solute per kilogram of solvent.

The molar mass of NaCl is approximately $58.44 \, \text{g/mol}$.

\[ \text{Moles of NaCl} = \frac{42.3 \, \text{g}}{58.44 \, \text{g/mol}} = 0.724 \, \text{mol} \]

Since the solution is per kilogram of water, the molality is:

\[ m = 0.724 \, \text{mol/kg} \]

Step 2: Calculate the Freezing Point Depression

The freezing point depression ($\Delta T_f$) can be calculated using the formula:

\[ \Delta T_f = i \cdot K_f \cdot m \]

where:

$i$ is the van 't Hoff factor for NaCl, which is 2 (since NaCl dissociates into Na$^+$ and Cl$^-$),
$K_f$ is the cryoscopic constant for water, $1.86 \, ^\circ \text{C/m}$,
$m$ is the molality of the solution.

Substituting the values:

\[ \Delta T_f = 2 \cdot 1.86 \, ^\circ \text{C/m} \cdot 0.724 \, \text{mol/kg} = 2.6923 \, ^\circ \text{C} \]

Step 3: Determine the Freezing Point of the Ocean

The normal freezing point of pure water is $0 \, ^\circ \text{C}$. The freezing point of the ocean is lowered by the freezing point depression:

\[ \text{Freezing point of ocean} = 0 \, ^\circ \text{C} - 2.6923 \, ^\circ \text{C} = -2.6923 \, ^\circ \text{C} \]