The following errors occurred when the experiment was carried out. How would each affect the calculated molar mass of the solute(too high, too low, no effect)? Explain.

a. The thermometer used actually read 1.4 centigrade too high.
b. some of the solvent was spilled before the solute was added.
c. some of the solute was spilled after it was weighed and before it was added to the solvent.
d. some of the solution was spilled after the solute and solvent were mixed but before the freezing point was determined.

The question is from Molar Mass by Freezing Point Depression.

To determine how each error would affect the calculated molar mass of the solute, we need to understand the relationship between the molar mass and the freezing point depression. In the context of the molar mass by freezing point depression method, the freezing point depression is directly proportional to the molality of the solution, which is in turn directly proportional to the molar mass of the solute.

Now, let's analyze each error and its effect on the calculated molar mass:

a. The thermometer used actually read 1.4 degrees Celsius too high:
If the thermometer used read higher than the actual temperature during the experiment, it would cause the freezing point depression to be underestimated. Consequently, the calculated molar mass of the solute would be too low, as the molality would be erroneously calculated as lower than it actually is. Therefore, this error would result in a calculated molar mass that is too low.

b. Some of the solvent was spilled before the solute was added:
If some of the solvent is spilled before adding the solute, it would result in a lower mass of the solvent used in the experiment. As a result, the molality of the solution would be overestimated, leading to a higher calculated molar mass of the solute. Therefore, this error would cause the calculated molar mass to be too high.

c. Some of the solute was spilled after it was weighed and before it was added to the solvent:
If some of the solute is spilled after being weighed, it would result in a lower mass of the solute added to the experiment. This lower mass would lead to an overestimation of the molality and, consequently, a higher calculated molar mass of the solute. Thus, this error would cause the calculated molar mass to be too high.

d. Some of the solution was spilled after the solute and solvent were mixed but before the freezing point was determined:
If some of the solution is spilled after the solute and solvent are mixed but before the freezing point determination, it would lead to a lower mass of the solution used in the experiment. This lower mass would, in turn, cause an overestimation of the molality, resulting in a higher calculated molar mass of the solute. Hence, this error would cause the calculated molar mass to be too high.

In summary:
- Error a: The calculated molar mass would be too low.
- Error b: The calculated molar mass would be too high.
- Error c: The calculated molar mass would be too high.
- Error d: The calculated molar mass would be too high.