Explain why .100 m NaCl in water does not have a freezing point equal to
a) -0.183 degrees Celsius
b) -0.366 degrees Celsius
To understand why .100 m NaCl in water does not have a freezing point equal to -0.183 degrees Celsius or -0.366 degrees Celsius, we need to consider the concept of freezing point depression.
When a solute, such as salt (NaCl), is dissolved in a solvent, such as water, it affects the freezing point of the solvent. This phenomenon is known as freezing point depression.
The freezing point of a solution is lower than that of the pure solvent. This occurs because the solute particles disrupt the formation of the crystal lattice structure of the solvent, which is required for freezing.
The extent of freezing point depression depends on the concentration of the solute. In the case of NaCl in water, a .100 m (molar) concentration means that there are .100 moles of NaCl dissolved in one liter of water.
Now, to calculate the freezing point depression, we can use the formula:
∆T = Kf * m
∆T represents the change in freezing point, Kf is the cryoscopic constant specific to the solvent (which is 1.86 degrees Celsius/molal for water), and m is the molal concentration of the solution.
a) For a .100 m NaCl solution:
∆T = (1.86 degrees Celsius/molal) * (.100 molal)
∆T = 0.186 degrees Celsius
So, the freezing point of the .100 m NaCl solution would be lowered by 0.186 degrees Celsius, not -0.183 degrees Celsius as stated in option a).
b) Similarly, for -0.366 degrees Celsius:
∆T = (1.86 degrees Celsius/molal) * (.100 molal)
∆T = 0.186 degrees Celsius
Therefore, the actual freezing point depression for the .100 m NaCl solution remains the same, at 0.186 degrees Celsius, and it does not match the given values of either -0.183 or -0.366 degrees Celsius.