A sample of seawater taken from the Atlantic Ocean freezes at –2.14 °C and a sample from the Arctic Ocean freezes at –1.96 °C. Assume i = 2.
What is the molality of the Atlantic Ocean sample?
What is the molality of the Arctic Ocean sample?
Two problems here. For each,
dT = i*Kf*m
Plug in and solve for m for each.
How do you solve for Kf in this problem?
Kf is something you look up. It's value for water is 1.86 C/m.
To find the molality of each sample, we will use the equation:
ΔT = i * Kf * m
Where:
ΔT is the change in freezing point temperature,
i is the vant Hoff factor,
Kf is the cryoscopic constant of the solvent, and
m is the molality of the solution.
Given that i = 2, Kf = -1.86 °C/m (for water), and the change in freezing point temperature (ΔT) is known, we can rearrange the equation to solve for m:
m = ΔT / (i * Kf)
Let's calculate the molality for each sample now.
1. Atlantic Ocean sample:
ΔT = 0 °C - (-2.14 °C) = 2.14 °C
m = 2.14 °C / (2 * -1.86 °C/m) = 2.14 / -3.72 ≈ -0.58 mol/kg
Therefore, the molality of the Atlantic Ocean sample is approximately -0.58 mol/kg.
2. Arctic Ocean sample:
ΔT = 0 °C - (-1.96 °C) = 1.96 °C
m = 1.96 °C / (2 * -1.86 °C/m) = 1.96 / -3.72 ≈ -0.53 mol/kg
Thus, the molality of the Arctic Ocean sample is approximately -0.53 mol/kg.