Question

1. A student performed a freezing point determination and calculated the molar mass of an unknown like you did in this experiment. The only difference in procedure was that when determining the freezing point of the unknown-naphthalene mixture, they started with a clean empty test tube. If the following errors occurred, how would each affect the calculated molar mass of the solute (too high, too low, or no change)? Explain your answers.

a. The thermometer used actually read 2.0 celcius too low for all measurements.

b. The test tube was put flat on the lab bench and some naphthalene spilled out. The student did not reweigh the test tube, proceeded to determine both the freezing point of pure naphthalene and the freezing point of the unknown-naphthalene mixture.

c. The student after weighing out 1.02 g of the unknown accidentally spilled a small amount onto the floor when pouring the unknown into the test tube containing the pure naphthalene. The test tube was not reweighed.

d. After mixing the unknown with the naphthalene, the student put the test tube flat on the lab bench while getting a clamp from the lab drawer. After melting the mixture, the student realized some of the mixture had spilled onto the benchtop.

Answer 1

ANSWER:

The freezing point equation is

where T_fsolvent= freezing point of pure solvent, T_fsolution= freezing point of solution, m = molality of solution and k_f =freezing point constant

And the molality is defined as

where MM_solute = molar mass of solute

Then, the freezing point equation is rewritten as

And the molar mass of solute is

Now, we can determine the effect of each error in the molar mass determination:

Part a: Temp readings 2 ºC too low for all measurements

• For calculation we use the freezing point depression (T_fsolvent - T_fsolution). As all measurements of temperature has the same error, the freezing point depression is not affected. Then, the calculated molar change won't change

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Part b: Naphthalene spilled out and test tube not reweighed

• Spilling the naphthalene decrease the mass of naphthalene used to determine both freezing points (pure naphthalene and mixture). The freezing point of pure naphthalene is not affected. However, the freezing point of solution changes:

Less amount of napthalene = higher molality = lower freezing point of solution

• A lower freezing point of solution cause a higher freezing point depression. Then, the calculated molar mass of solute will be too low

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Part c: Unknown spilled out and test tube not reweighed

• Spilling the unknown decrease the mass of solute used to determine freezing point of mixture. This, means that freezing point of solution changes:

Less amount of unknown (solute) = lower molality = higher freezing point of solution

• A higher freezing point of solution produces a smaller freezing point depression. Then, the calculated molar mass of solute will be too high

Part d: Mixture spilled out

• Spilling the mixture decrease the mass of solute and the mass of naphthalene used to determine freezing point of mixture. However, the freezing point of mixture is not affected by this error => the mixture is a homogeneous solution that has the same concentration. This means that even some of mixture is spilled onto the benchtop, the molality of the remaining mixture in the test tube does not change.

not change in molality = not change in freezing point depression

• Then, the calculated molar mass of solute won't change

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