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1) The molecular mass of a substance was determined by the freezing point depression technique. The minimum data required for the determination are:

a) delta T and Kf only
b) delta T, Kf, and mass of solute
c) delta T, Kf, mass of solute, and mass of solvent
d) delta T, Kf, mass of solute, mass of solvent, and identity of solvent
e) delta T, Kf, mass of solute, mass of solvent and identity of mass and solvent.

I chose delta T, Kf, and mass of solute.

2)Ethanol and water are both liquids at or near room temperature. When a sample of ethanol is poured into a beaker containing water, the two liquids

a) are miscible because each can hydrogen bond with the other.
b) are immiscible because each has strong hydrogen bonds that cannot be broken.
c) are miscible because both are liquids and all liquids are miscible.
d) are immiscible because organic and non-organic compounds cannot mix.

I chose that they are miscible because each can hydrogen bond with each other.

Are these correct?

b is correct.
I've responded to a before. Your answer is not right. Frankly, I'm not sure the correct answer is one of the choices. Furthermore I think you have an omission in e. "Identity of mass and solvent" doesn't make sense to me.

delta T =i*Kf*m
So delta T,i, Kf, and m are musts. m can be calculated if you have mass solute and mass solvent so the list now is delta T, i, Kf, mass solute and mass solvent. That leaves i. If I knew the identity of the solute and the identity of the solvent, I think I could make a good guess as to i. #e, if it is......identity of solute and solvent... would be the best choice in my opinion If the problem is ignoring i then c is the best choice. You see the problem with "multiple guess" questions, one can't always figure what's in the mind of the author and sometimes the author doesn't take all things into consideration.
e is my choice if it reads, "delta T, Kf, mass solute, mass solvent, identity of solute and solvent."

Was number 2 correct about water and ethanol being miscible?

yes. #2 is correct. I thought I had said that in my original response but on re-reading I see I did not and in fact, what I said may be have been misinterpreted. My first sentence was "b is correct." I should have said, "#2 is correct." That first sentence had everything to do with question #2 and nothing to do with question #1. Sorry if I misled you.

If i was being ignored wouldn't the right answer be D because you need the identity of solvent in order to know the Kf?

Actually just realized why it is not D because Kf is already provided so don't need to know the identity of solvent.

So since identity of solvent is not required then wouldn't answer E be incorrect as well?