Science and Cooking: Problem Set 3
Due on Canvas by 11 PM on Thursday, September 25th
Please type or write your answers within this document or on a separate sheet of paper.
Then save your work as either a Microsoft word document (.doc or .docx) or as a PDF
file (.pdf) and upload to Canvas. If you write your answers by hand, you may scan your
work and paste the images into either of these file types, but submissions that are NOT
either of these file types will not upload properly. Your work must be organized and
legible – if your TF can’t understand what you wrote, they won’t give you credit.
Show your work for derivations and calculations. YOU WILL NOT RECEIVE FULL
CREDIT WITHOUT SHOWING YOUR WORK. Be sure to calculate all results fully
(don’t leave numbers in fraction form, or in terms of pi, etc) and to provide answers in
the requested units, if applicable.
Equations of the Week
Uinteraction = CkBT
Concept
Uinteraction
C
kB
T
Description
Interaction energy
A constant which depends on atmospheric pressure
and the molecule it describes
Boltzmann constant (1.38 • 10-23)
Temperature in Kelvin
Triglyceride with Saturated fatty acids
Units
J
No units
J/K
K
Triglyceride with Poly-unsaturated fatty acids
Problem 1: Sorbet (35 points)
a. In Joanne Chang’s lecture this week, she showed a brief experiment in which she
tried making sorbet with different amounts of sugar. By adding more or less sugar, she
could create a sorbet that became much stiffer than normal or much slushier. Which
change (more or less sugar added) corresponds to which texture (stiffer/slushier)?
Why? (6 points)
When you add more sugar, the sorbet becomes slushier.
When you add less sugar, the sorbet becomes stiffer/harder/icier.
This happens because of the phenomenon of freezing point depression, where by
adding solute (sugar) to a solution (water), the temperature at which the mixture freezes
decreases compared to the liquid without something mixed in. Therefore, if you try to
freeze a very sugary sorbet, it will be slushier and there will be more unfrozen liquid.
b. Sorbet is made using sugar and water. Ice cream, on the other hand, replaces the
water with some combination of milk and cream. If you simply replaced the water in
sorbet with milk, what do you think would happen to the freezing point of the resulting
mixture compared to normal sorbet? (3 points)
Because milk is not a pure substance like water (it contains sugar, proteins, minerals,
fats, etc), it already has a lower freezing point than pure water.
By replacing the water with milk, the freezing point of the mixture would be decreased
relative to the normal sorbet made with water.
(For those interested, lactose and mineral content are the primary factors leading to
milk’s depressed freezing point – and this is actually measured in the dairy industry to
determine whether or not milk has been adulterated.)
c. The following info was borrowed from a table on the wikipedia page for “brine”
(http://en.wikipedia.org/wiki/Brine). It lists some properties of salt-water solutions based
on the amount of salt. What would the table look like if the column for “freezing point”
was replaced with one for “boiling point?” (5 points)
NaCl % weight
0
2
6
10
14
18
22
Freezing point (°C)
0
-1.19
-3.7
-6.56
-9.94
-14.04
-19.18
If the column said freezing point instead of boiling point, the boiling point at 0% NaCl
would be 100C, and as the % NaCl increases (2pts), the boiling point would increase.
d. You decided to attempt a bourbon-sorbet recipe yourself using the same technique
we used in the lab this week - i.e. you prepare the ice cream by shaking it in a bag with
ice and salt. In lab, we used 200g of salt with 600g of ice for our freezing medium.
Given these values and the chart above, estimate the freezing point of your salt-ice bag
(no equations needed beyond the % weight – just give a rough estimate). (3 points)
Following the trends of the table, the freezing point should be around -20 to -25C.
e. Regardless of your current age, pretend that today is your 21st birthday and you’re
super-stoked to be able to legally use your special-21st-birthday-125-proof-bourbon in
your ice cream. Since you have been sampling the bourbon while editing your sorbetmaking procedure, you decide to throw caution to the wind and not measure the amount
of bourbon you are adding to the sorbet mixture before mixing. As a result, you are a bit
overzealous with the bourbon pouring, which seems fine until you get to the mixing. You
mix and mix and mix but your mixture refuses to freeze. What happened? Explain
briefly. (5 points)
Bourbon is a mix of ethanol and water.
Ethanol lowers the freezing point of water.
Apparently, you have added enough bourbon that the mixture of ethanol, water, and
sugar in your sorbet can no longer be frozen by your salt and ice mixture.
f. Shown below is a chart that maps the freezing point of a water-ethanol mixture as a
function of the concentration (weight %) of ethanol in the mixture. Using this and your
temperature estimate in part e, what is the lowest possible wt% of ethanol in your
current sorbet? Ignore for now any effects that the sugar in the ice cream has on the
freezing point (i.e. assume your sorbet is just water and ethanol). (5 points)
Based on the estimate in part d, the freezing point of this mixture must be below about 25C.
According to the graph, if the freezing point of an ethanol and water mixture is -25C, the
mixture must be at least 30-35% ethanol. Therefore, your sorbet must have at least this
much ethanol in it.
g. Bourbon is expensive and you don’t want any to go to waste. To get your sorbet to
freeze, you call up your good friend Daniel, the Science and Cooking demo guru, and
ask him for help. He shows up with a dewar of liquid nitrogen (and relevant safety gear),
puts your sorbet in an electric mixer, and pours liquid nitrogen in as it mixes which
creates a delicious bourbon sorbet. Explain briefly why this method works using the
nitrogen and not salt-and-ice mix. (3 points)
The liquid nitrogen is much much colder than the freezing point of even 100% ethanol,
so it can freeze your mostly-bourbon sorbet.
You can mix it in with the sorbet in a mixer because since the liquid nitrogen’s boiling
point is -196C, it will quickly boil away.
If you mixed in your salt and ice with your sorbet, you would end up with a disgusting
salty, bourboney sorbet because the ice and salt will melt instead of evaporating.
h. Upon sampling your bourbon sorbet with your good friend Daniel, you find that upon
melting in your mouth, the flavor and aroma of the bourbon is much stronger than you
remember from drinking it neat (i.e. without anything added). This is due to a
phenomenon that Harold McGee wrote about in the New York Times: diluting an
alcoholic beverage with water before drinking can release more aroma molecules from
the alcohol and strengthen its fruity and floral character. Based on this, what can you
glean about the Uinteraction of these aroma molecules with water compared to their
Uinteraction with ethanol? (5 points)
(Hint: if you get stuck, you can read McGee’s article here:
http://www.nytimes.com/2010/07/28/dining/28curious.html?pagewanted=all)
The sorbet is diluted bourbon when it melts in your mouth. Because the flavor/aroma is
STRONGER for the sorbet, you are releasing MORE aroma molecules as vapor when
there is MORE water present.
This implies that ethanol is “stickier” to aroma molecules than water is, so the Uint for
aromas and ethanol should be HIGHER than that for aromas and water.
Problem 2: Cooking with a rotovap (35 points)
Rotary evaporators, or rotovaps, were originally designed to be used by synthetic
organic chemists to help them purify chemicals from their reaction mixtures. More
recently, rotovaps have been co-opted by chefs for use in the kitchen. You can get
some idea of how chefs use rotovaps by watching two of the optional Joan Roca videos
from the class website, “Lemon Dessert with Rotovap” and “A Super Cool Dessert.”
Make sure you have subtitles set to “ON” if you don’t understand Spanish! Answering
these questions will also be much easier if you watch the “Science of Rotovaps”
supplementary video on the website and/or read the “Science of Rotovaps” section in
the Course Companion.
a.
Why do chefs use rotovaps in their cooking? What advantage do they provide?
(5 points)
Chefs would want to use rotovaps if they wanted to extract the flavor of something
without using high heat. They use low pressure to boil liquids at low temperatures which
prevents the change in flavor that could happen if you boiled the liquid at 1atm of
pressure (100°C)
b.
Above is a picture of a rotovap with the relevant parts labeled. Please write a
short (1-2 sentence) description of the function of each part. Where applicable, be sure
to mention whether the part in question is important for a temperature or pressure
change that results in a phase change. (10 points)
Water Bath – Holds the water that the evaporation flask sits in.
The temperature of the water bath can be controlled, controlling the temperature of the
evaporation flask.
Evaporation flask – This flask holds the sample that is being distilled.
Rotary motor – Spins the evaporation flask, ensuring constant mixing and an even
temperature throughout the flask as well as higher surface area.
Vacuum – A vacuum on the system decreases the pressure.
This decrease in pressure, decreases the boiling point of the liquid in the evaporation
flask, causing a change from a liquid to a gas.
Condenser coils – Ice-cold water (or dry ice and isopropanol) runs through these coils.
When the vapor from the evaporation flask hits these coils, it condenses into a liquid
(despite the low pressure).
Collection flask – Condensed liquid drips into the collection flask where it is collected.
c. In “A Super Cool Dessert,” Joan Roca distilled eucalyptus leaves mixed with water in
the rotovap. Assume the mixture starts at room temp (23°C) and is heated slowly at a
pressure of 0.4atm. Using the phase diagram below, what (roughly) is the highest
temperature the he can reach before the water vaporizes? (10 points)
From the graph, the point at which water will boil at 0.4atm is between 70 and 80
degrees Celsius. The highest temperature he can reach before vaporizing the water is
thus immediately BELOW this boiling point (e.g. 69-79 degrees).
d. At the end of the distillation, which flask would you expect to contain the molecules
with the higher interaction energy, U? Why? (3 points)
The evaporation flask will contain the molecules with a higher U.
For these molecules, the decrease in pressure/increase in temp was not enough for
their sticking energy to become less than their jiggling energy. Therefore, it is more
favorable for them to remain in the liquid in the flask.
e. Using the diagram above, if you saw that the water was boiling when the water bath
was at 40°C, what can you assume that the pressure inside the rotovap was? (3 points)
Should be about 0.1atm.
f. In the rotovap, you can boil liquid at a much lower temperature than you can at 1atm
of pressure. What is the Uinteraction of two molecules of water at their boiling point at
1atm? (4 points)
Uinteraction = CkBT
Uinteraction = (3/2)(1.38 • 10-23J/K)(373K) = 7.72 • 10-21J
g. Extra Credit: Pressure cookers are similar to rotovaps in that they use a change in
pressure to change the way that food is cooked. Describe how a pressure cooker works
in terms of how the temperature and pressure changes and name one reason why a
chef might want to use a pressure cooker. (5 points)
Pressure cookers increase the pressure used when cooking a food.
This increases the boiling point of liquids.
Foods can be cooked at a much higher temperature than they otherwise would be.
This decreases the cooking time (and often the flavor and texture) of the food.
Problem 3: Cooking with fats (yum) (25 points)
Duck fat can replace any kind of butter or shortening in many recipes. It has a rich
savory flavor, is resistant to high temperatures, and gives food an appetizing goldenbrown color. You decide to make some tasty duck fat fries.
(http://www.dartagnan.com/How-to%3A-Duck-FatFries/HowtoDuckFatFries,default,pg.html)
a. Duck fat in the refrigerator (4°C) is a solid, and its melting point is 14°C. “Oils” are
often defined as fats that are liquid at room temperature. Using this definition, is duck fat
an oil? (3 points)
The melting point of duck fat is BELOW any acceptable value for room temperature, so
duck fat is an oil.
b. Tallow is a term for rendered beef fat. Tallow in its edible form melts at temperatures
as low as 41°C. Using the same definition of “oil” as part a, is tallow an oil? (3 points)
Since the melting point of tallow is ABOVE any acceptable value for room temperature,
it is NOT an oil.
c. Two other fats you could use in this recipe are butter and olive oil. Butter has a
melting point around 32-35°C, and olive oil has a melting point around -6°C. If it was a
brisk fall day in Boston (12°C), and you had to bring one of these fats to your friend’s
house to make fries, which would be least likely to leak in your backpack and make a
giant mess? Why? (4 points)
Butter because it has the higher melting point.
It is least likely to melt, become a liquid, and make a mess as I walk to my friend’s
house.
d. Based on the melting point information, which of all 4 fats mentioned so far (duck fat,
tallow, butter, and olive oil) would you expect to have the most saturated fatty acids?
Explain your answer in terms of the equation of the week. (10 points)
Saturated fats pack together better than unsaturated fats because they do not have
kinks in their chains.
Because of this better packing, saturated fats have a higher Uint than unsaturated fats.
Because of this higher Uint for saturated fats, the fat with the highest melting point is
most likely to have more saturated fat compared to fats with lower melting points.
Tallow has the highest melting point, so it would have the most saturated fatty acids.
Fat or Oil
% Saturated
Fatty Acids
% Monounsaturated Fatty
Acids
% Polyunsaturated
Fatty Acids
Duck Fat
38
48
14
Butter
67
29
4
Olive Oil
14
75
11
Lard
40
49
11
e. Lard is a general term for pig fat. Based only on the information in this table, make a
rough estimate for the melting point of lard. Explain your answer. (5 points)
Melting point for fats is higher for fats with more saturated fatty acids.
Lard has a similar % saturated fatty acids as duck fat, so I would expect it to be only
slightly higher than the melting point for duck fat, 14C.
f. Extra Credit: The actual melting point of lard is between 35-45°C. How can this be?
What are some other factors that are important for determining the melting point of fats?
(5 points)
Melting point depends on the % saturated fat, but it also depends on the length of the
fats.
Triglycerides with long chains of fatty acids will have more surface area to interact with
other triglycerides.
This gives them a higher Uinteraction and a higher melting point.