Question

3. Professor Best is entertaining guests one Saturday night and decides to serve a green salad dressed with his special vinaigrette. He adds honey, lemon, oil, and vinegar in a ratio of 1:2:4:8 and whisks the mixture until it emulsifies. He then sets it in the refrigerator to chill. a. How many degrees of freedom does this mixture have immediately after mixing? b. After twenty minutes, Professor Best rescues the dressing from the refrigerator and notices that it tastes horrible. Upon consideration, he realizes that the oil to vinegar ratio should have been 3:1. How much oil should be added to the mixture if each unit of measurement is 1 TBSP? (How many more TBSPs?) C. Upon adding the additional oil, the mixture separates into three layers. How many degrees of freedom does the mixture have now?

Answer 1

From Gibbs phase rule ,

F = C - P + 2

Where F = no of degrees of freedom , C = no of components in the system

P = no of phases.

Professor has mixed honey, lemon, oil and vinegar in a 1:2:4:8 ratio. The unit of measurement is 1 TBSP. So he have mixed 1 TBSP of honey, 2 TBSP of lemon, 4 TBSP of oil,l and 8 TBSP of vinegar primarily to prepare the dressing.

a. Immediately after mixing there are four components in the system and the phases are four as the components don't mix together immediately. Hence, F = 4 - 4 + 2 = 2.

So the degrees of freedom immediately after mixing the components is 2.

b. To make oil to vinegar ratio 3:1 we have to mix three times more oil than vinegar for ex. if we have mixed 1 TBSP of vinegar then we have to take 3 TBSP of oil.

Now Professor best have already mixed 8 TBSP of vinegar and 4 TBSP of oil together to prepare the dressing. Now if he have to make oil to vinegar ratio 3:1 then he have to mix 24 TBSP of oil in it. But he already have mixed 4 TBSP of oil. So he have to add 20 extra TBSP of oil in the dressing.

c. Now there is three layers after the addition of excess oil in the dressing. So no of phases (P) is 3. Now in the mixture there are four components are in total.

Hence, F = 4 - 3 + 2 = 3.

So the no of degrees of freedom is 3.