Midterm Review Questions
month?
Jello Swimming Pool
After pulling triple sevens on a $20 slot machine,
you decide to fulfill your lifelong dream of filling an
Olympic size pool (50 m x 25 m x 2m) with cherry
Jello. You must mix enough of the Jello powder into
the water to make a 1% solution.
• How many kilograms of Jello will you need?
A “1% solution” means that the mass of the powder
should be 1% of the mass of the water. We can use
the volume and density of the water to calculate the
water’s mass:
V = 50 m ⋅ 25 m ⋅ 2 m = 2500 m3
ρ = 1g/mL
mw = V ⋅ ρ
1000 L 1000 mL 1 g
⋅
⋅
1 m3
1L
1 mL
= 2.5 × 109 g
= 2500 m3 ⋅
m p = 0.01 ⋅ mw = 2.5 × 10 g
7
After adding in the Jello and stirring carefully to
no avail, you remember that you are supposed to boil
the water.
• How much heat, in Joules, do you need to raise
the water from 25° C to 100° C?
q = mc p ∆T
= 2.5E9 g ⋅ 4.18
J
⋅ (100° C − 25° C)
g⋅ C
Start by determining how many Joules are
in a kiloWatt hour:
1 kWh ⋅
1000 W 1 J/s 3600 s
⋅
⋅
= 3.6 ⋅ 106 J
1 kW 1 W
1h
Determine how many kWh it will take to heat
the pool:
7.8 × 1011 J ⋅
1 kWh
= 2.2 × 105 kWh
3.6 ⋅ 106 J
Since you’re paying $0.10 per kWh, your bill
will be $22,000. (Good thing you’re rich now!)
Once the Jello solidifies, you belly flop into the pool.
You have average dimensions (height 1.7 m, weight
80 kg, shoulder width 0.5m). The elastic modulus of
Jello is 100 Pa.
• Calculate ∆L. Will the Jello support your weight
by depressing elastically?
F = mg = 80 kg ⋅ 9.8m/s2 = 784 N
A = 1.7 m ⋅ 0.5m = 0.85 m2
F/A
E =
∆L/L
F/A
∆L =
E/L
784 N/0.85 m2
=
= 18 m
100 Pa/2 m
Clearly Jello two meters deep cannot compress by
eighteen meters. The reason that the equation fails is
= 7.8 × 1011 J
that you will simply fall through the Jello. Since you
cannot swim through Jello, your best hope of survival
• If you’re paying $0.10 per kWh to run your is to stand on your tiptoes and eat until you reach the
pool heater, what will your electric bill be next air.
°
Hipster ice
Hipsters will pay anything for a cocktail made with
fancy ice. You propose to get rich quick by selling
amorphous ice to upscale clubs. Amorphous ice
differs from the plebeian variety in that it is made
from many small, randomly-arranged seed crystals.
The lack of long-range order gives it an opaque
appearance.
• Given what you know about ice cream making,
how can you favor the production of many
small seed crystals in freezing water?
Rapid freezing and thorough mixing (so
that the middle doesn’t stay warm while the rest
freezes) both help to make many small water
crystals in ice cream mix.
• What type of equipment would you need for
this process?
You would need a vacuum to lower the
pressure of the water vapor, since sublimation is
not possible at atmospheric pressure. You also
need to cool the water vapor and the surface
that it will be deposited onto. (The water vapor
must be able to cool enough on contact with the
surface that it can cross the phase boundary.)
Calcium Catastrophe
A clever way to form amorphous ice is deposition
Excited by your experience in lab, you decide to
(the opposite of sublimation) of water vapor onto a
perorm inverse spherification with your roommates.
cold surface at constant pressure.
You search Amazon for calcium chloride. The top
result is for sidewalk de-icing pellets.
• Draw the phase diagram of water.
• Draw potential start and end points of the deposition process. Use an arrow to indicate the
direction of the process.
• How do salts like calcium chloride help de-ice
sidewalks?
Salts lower the freezing point of water. The
freezing point is the temperature at which as
many H2 O molecules are melting into water as
there are freezing into ice. This delicate balance
keeps the ice crystal at constant size. When we
add salt, it mixes into any melted water present.
As you know from experience, it’s easier to
soda), when the carbonate neutralizes acid, it
mix to things together than it is to separate
releases CO2 gas. Your lemon juice fizzled on
them again. Water must separate themselves
contact because the acid in lemon juice was
from the dissolved salt to crystallize, which is
neutralized by the carbonate, releasing gas. The
energetically unfavorable. Therefore, adding
lemon flavor was mainly contributed by the
salt makes it less likely that water molecules
acid, so the drops become bland.
will freeze, tilting the balance towards melting.
This freezing point depression causes the ice Meringues
to melt on your sidewalk even as the outside
Your recipe for white meringues calls for heavily
temperature stays constant.
whipping 500g of sugar into 120g of egg whites,
Repulsed by the association of calcium chloride with piping the mixture into three dozen meringues, and
antifreeze, your roommate suggests dissolving the baking at 200 degrees Fahrenheit for three hours.
antacid Tums in water instead. Each tablet of Tums
contains 500 mg of calcium carbonate (molecular
weight 100 g/mol).
• Estimate the number of Calories per meringue.
State your assumptions.
• How many tablets of Tums would you need
to dissolve in 1 L of water to make a 0.05 M
solution of calcium (like we used in class)?
The sugar is pure carbohydrate.
Assume
that the egg white is pure protein. The 4:4:9 rule
tells us there are 4 Calories per gram of carbs or
protein and 9 Calories per gram of fat.
500
mg
1g
1mol
mol
⋅
⋅
= 0.005
tablet 1000 mg 100 g
tablet
1 L ⋅ 0.05
mol
= 0.05 moles needed
L
We need to dissolve ten tablets in 1 L of water.
You decide to make “lemon drop” spheres by mixing
alginate into lemon juice and releasing droplets into
the calcium bath. When the lemon juice hits your
calcium bath, it starts to fizzle. The resulting lemon
drop comes out bland.
• What happened?
Calcium carbonate is in antacid: it’s a base
that reacts with the acid in your stomach to
neutralize it, relieving your heartburn. Like
the more familiar sodium bicarbonate (baking
(4
Cal
Cal
⋅ 500 g + 4
⋅ 120 g) /36
g
g
= 70 Cal per meringue
Please remember: the Calories listed on US
nutrition labels (“2000 Calorie diet”) are not
the same as calories to chemists (1 calorie
raises 1 g of water by 1 degree Celsius). A
“Calorie” is 1000 calories. You may have noticed
that imported candy bars often give the energy value in “kcal”: this is the same as a Calorie.
• After baking, the meringues are crispy. Which
ingredient is responsible for this change?
200 degrees Fahrenheit (93 degrees Celsius)
is below the boiling point of water, so the
meringues have not simply dried out. Table
sugar caramelizes at 160 degrees Celsius, and the
meringues are still white, so caramelization has You set out to make your white bread more elastic
not taken place. The crispiness is due to the de- by substituting all-purpose flour with whole wheat
naturation and coagulation of proteins in the egg flour, which has 50% more gluten.
whites, which we know happens around 63 degrees Celsius, well below our cooking tempera• How do you expect the elastic modulus and
ture.
crosslink distance to change?
Bread
The equation of the week tells us that the
elastic modulus is a density of bond energy.
If we add 50% more gluten and all of it forms
into polymers, then we expect the bond energy
density to go up by 50%, so the elastic
√ modulus
should go up by 50%. Since l ∝ 3 1/E, l will
decrease by 13%.
Glutenin is the protein found in wheat that’s responsible for the elasticity of bread. Glutenins can
break and form intermolecular bonds (250 kJ/mol)
freely in water, but these covalent bonds become
permanent when the dough dries in the presence of
oxygen. Glutenins have a tendency to form aligned
Moonshine
linear polymers when kneaded.
In your morning rush, you drink straight from the
• What is the temperature of phase transition for Welch’s carton and accidentally leave it sitting on
bread?
your sunlit desk. You discover days later that the
grape juice has fermented. Ever the opportunist, you
The phase transition occurs when the dough decide to distill it into hootch. Pure ethanol boils at
goes from flexible to stiff. In the case of glutenin, 78° C; water at 100° C.
that occurs when the water boils off, leaving
the glutenin permanently bonded. The phase
• Which has a greater interaction energy: ethanol
transition temperature is thus 100 degrees
or water?
Celsius.
Some baked goods require more elasticity than
others.
• Rank the following products from least to
greatest elastic modulus: bagel, sponge cake,
wheat bread, white bread.
A greater elastic modulus means that the
food deforms less when the same force is applied (the food is stiffer). The order is therefore
sponge cake, white bread, wheat bread, bagel.
U = ckb T
Water has a higher boiling point (the “T” in
this equation) than ethanol, so it has a higher
interaction energy.
• Do you think the boiling point of ethanol is an
ethanol:water mixture is higher, lower, or the
same? Explain.
Adding salt to water makes it more difficult for the water to leave the solution by either
freezing or boiling off: this leads to freezing
point depression and boiling point elevation.
The phenomenon is not unique to salt: it is also
entropically favorable for ethanol and water to
mix. Therefore, the boiling point of ethanol will
be higher when it has been mixed with water.
first few ounces of condensate they collect to
get rid of the methanol. Don’t drink it: you’ll go
blind.
Pasteurization
In the U.S., milk is usually treated by “pasteuriza• Describe how you could take advantage of the
tion”: raising the temperature to 70 degrees Celsius
difference in boiling points to concentrate the
for a minimum of twenty seconds. Pasteurization
ethanol using only typical kitchen supplies.
kills most, but not all, of the bacteria present in milk.
The key is to heat the fermented juice to a
• Why not simply boil the milk and kill all of the
temperature just above where ethanol boils. The
bacteria?
trick is to collect the ethanol vapor. You can do
this by placing a lid above the pot and tilting
Boiling the milk would cause it to curdle.
the lid so that as ethanol condenses onto the lid,
it will drip down the side and into a ell-placed
bowl. The lid must be kept cold for vapor to Pasteurization destroys vitamin C, a molecule
condense on the lid: placing a bag of frozen naturally present in milk that is essential for the
production of collagen.
peas on top would suffice.
• Describe how you could use the rotovap in lab
to accomplish the same feat.
In the rotovap, we can keep the temperature constant and lower the pressure until the
ethanol, but not the water, boils off and collects
on the condenser.
You notice that something is already condensing out
of the vapor as you heat the grape juice to 70° C.
• What do you think this is? Should you drink it
and find out?
Besides ethanol and water, there are some
toxic compounds in the fermented grape juice.
One of them is methanol, which has a boiling
point well below that of ethanol and therefore is
first to evaporate. Still operators throw out the
• What type of macromolecule is collagen?
Where is it found in the body?
Collagen is a protein found in connective
tissues. It makes up 2% of the weight of your
muscles. It’s also the source of gelatin.
• What is the role of collagen in a well-done steak?
In a well-done steak, collagen has broken
down to produce gelatin, contributing to the
steak’s texture.
• Is pasteurized milk a suitable replacement for
breast milk or formula? Explain.
No: pasteurized milk lacks vitamin C. Infants that drink pasteurized milk develop
vitamin C deficiency (“scurvy”), a serious
illness due to the importance of collagen in
muscle/connective tissues.
Ca2+ vs. H+
The role of calcium and hydrogen ions in cooking is
easily confused.
• Which ion(s) increases the acidity of the solution?
Only H+ can increase the acidity of a solution.
No other positively-charged ion contributes to
pH (although some pH meters can be fooled by
the very small Li+ ion).
• Which ion(s) can neutralize charge? What kind
of bond does this entail? Give an example of its
use in lab.
When the [H+ ] is large enough that the
pH falls below the pKa of a negatively charged
group, protons will form covalent bonds with
the negative charge, neutralizing (eliminating)
the negative charge completely. No other positively charged ion can neutralize charge. We
used a very low pH to neutralize the charges of
casein to cause curdling in the ricotta cheese lab.
• Which ion(s) can shield negative charges?
When have we used that property in lab?
All positively-charged ions can shield negative charges through ionic interactions with
the charge. Shielding negative charges allows
gellan molecules to get close enough together
to entangle and make a gel. We saw in the
elasticity lab that either protons or calcium ions
can shield the negative charges of gellan and
improve its gelation.
• Which ion(s) can crosslink negative charges?
What gel type made in lab requires crosslinking
specifically?
Calcium ions, but not protons, can form
crosslinks between alginate polymers. Like
shielding, crosslinking involves ionic bonding
between the positively-charged ion and the
negative charge on the gelling agent polymer.
However, in crosslinking, the positively-charged
ion must form two ionic bonds: this results in
two alginate polymers being held together by
one calcium ion.