SPU27: Problem Set 1
Due in your TF’s homework box before class on Thursday, September 11th
You are encouraged to work in groups, but all submitted work must be your own. If you
work with others, please note who they are on the front page of your problem set.
Please type or write your answers on a separate sheet of paper. 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. 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
1 mole (mol) of molecules = 6.022•1023 molecules
pH = -log10[H+]
Concept
pH
[H+]
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Description
A measure of acidity
Concentration of protons or H+ ions in a solution in moles
of protons per liter
www.wolframalpha.com
http://en.wikipedia.org/wiki/Coca-Cola_formula
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http://www.wikihow.com/Make-OpenCola
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Units
None
M (mol/L)
Problem 1 - New England Clam Chowder (30 points)
INGREDIENTS: Light Cream, Water, Clams, Potatoes, All Purpose Flour (Bleached Wheat Flour, Malted
Barley Flour, Niacin, Reduced Iron, Thiamine Mononitrate, Riboflavin, Folic Acid), Diced Celery, Diced
Onions, Clam Base (Cooked Clams, Natural Clam Juices, Salt, Sugar, Maltodextrin, Yeast Extract, Disodium
Inosinate/Disodium Guanylate, Onion Powder, Potato Starch, Corn Oil, Anchovy Dried Whey, Dried Soy
Sauce (Soybeans, Salt), Clam Extract, Natural Flavoring (Soy Lecithin).), Canola Oil, Rendered Bacon Fat,
Chablis, Clam Broth (Dehydrated clam broth,maltodextrin), Water, Corn Starch (Derived from Waxy Maize),
Tabasco Sauce (Distilled Vinegar, Red Pepper, Salt.), Ground Black Pepper, Ground Bay Leaves, Thyme,
Ground Cayenne Pepper
Above is a recipe from Harvard University Dining Services for the Clam Chowder that
was served in the dining halls around campus this week. Thank you to Martin Breslin,
Executive Director at HUDS, who sent us this recipe (Martin Breslin is the visiting chef
in the week covering viscosity at the end of October). Each ingredient is listed on the
right with a given quantity in pounds or quarts corresponding to the amount of that
ingredient per serving. The ingredients are listed below in full to help clarify the table on
the right.
a. Search wolfram alpha1 and look up the nutritional content for (1) “prepared clam”,
(2) “heavy cream”, and (3) “flour”. What are the amounts of each food
component: proteins, fats, carbohydrates, and water? (6pts)
Prepared clam: In 55g there is 2g fat, 3g carbs, 9g protein
Heavy cream: In 1tbsp (15g) there is 5g fat, 0.667g carbs, 0g protein
Flour: In 1C (120g) there is 2g fat, 90g carbs, 13g protein
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b. The majority of the calories in this recipe come from just six ingredients: Bacon
Fat, Canola Oil, All-Purpose Flour, Clams, Potatoes, and Light Cream. Write the
ONE major food component responsible for most of that ingredients’ calories (for
example, cream has carbs, fat, AND protein, but only write the most prevalent
one of those three in your answer). (6pts)
Bacon Fat – Fat
Canola Oil – Fat
All-Purpose Flour – Carb
Clams – Protein
Potatoes – Carb
Light Cream - Fat
c. Consider only the ingredients in the recipe that are principally fats (cream, bacon
fat, canola oil). Compute the total mass of these ingredients. Answer in grams.
Assume the density of all liquids is the same as water (1g/mL), that 1lb = 453.6g,
and that 1 cup = 236.6mL (8pts)
0.1411qt cream • 4C/1qt • 236.6ml/1C • 1g/ml = 133.54g cream
0.0143lbs bacon fat • 453.6g/1lb = 6.49g bacon fat
0.015316lb canola oil • 453.6g/1lb = 6.95g canola oil
133.54g cream + 6.49g bacon fat + 6.95g canola oil = 146.98g
d. Is this more or less than the total amount of fat given in the nutrition facts? Why?
(2pts)
This is more. Cream is not 100% fat. The vast majority is water.
e. Light Whipping Cream is at least 30% fat by mass. Using this value of 30%, how
much fat is added to this recipe by the cream alone? Show your work. (4pts)
Mass of cream from part C = 133.54g
0.3 • 133.54g = 40.06g fat
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f. Recalculate the total weight of the fat-heavy ingredients as before, but use the
fat-only weight of cream calculated in d instead of the full weight of the cream.
Show your work. (4pts)
From part C: mass of bacon fat = 6.49g
From part C: mass of canola oil = 6.95g
From part E: mass of fat in cream = 40.06g
6.49g + 6.95g + 40.06g = 53.5g fat
Problem 2 – Coca Cola (40pts)
The major ingredients of coke are sugar (sucrose), caramel color, caffeine, phosphoric
acid, flavoring, and glycerin2
a. Which ingredient is the primary source of H+ ions? (2pts)
Phosphoric acid
b. The concentration of H+ ions in a can of Coke is 0.00316M. What is the pH?
(5pts)
pH = -log(0.00316M) = 2.5
c. How many H+ ions are there in a 12 fluid oz can? (1 fluid oz = 29.57mL) (5pts)
0.00316M = 0.00316mol/L
12floz • 29.57ml/floz = 354.84ml
354.84ml • 1000ml/L = 0.35484L
0.00316mol/L • 0.35484L = 0.00112mol
0.00112mol • 6.022 • 1023molecules/mol = 6.75 • 1020 molecules H+
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(1pt)
(1pt)
(1pt)
(1pt)
(1pt)
d. It’s a hot summer day, and you have poured your can of coke over 200g of ice.
Unfortunately, before you could drink your coke, the ice melted and has diluted
your drink. What is the pH of your coke now (for water, 1g = 1mL)? (9pts)
200g ice • 1ml/g = 200ml water = 0.2L
pH of water = 7
[H+] = 10-7mol/L
10-7mol/L • 0.2L = 2 • 10-8mol H+ in water
From part C: 0.00112mol H+ in coke
Total moles H+ in drink = 0.00112mol + 2 • 10-8mol = 0.00112mol
New volume of drink = 0.2L + 0.35484L = 0.55484L
Concentration of H+ in drink = 0.00112mol/0.55484L = 0.00203M
pH = -log(0.00203M) = 2.69
e. You have decided to try and make homemade Coke (you can actually do this!) 3
How many H+ ions are in a 3L batch (assuming same pH as commercial Coke)?
(5pts)
From part B: [H+] = 0.00316M
0.00316mol/L • 3L = 0.00948mol
0.00948mol • 6.022 • 1023molecules/mol = 5.71 • 1021molecules
f. The recipe calls for using 17.5ml of a 75% by volume phosphoric acid solution.
What is the molarity of this solution? The molecular weight of phosphoric acid is
98g/mol. The density of phosphoric acid is 1.88g/ml (9pts)
17.5mL solution • 0.75 = 13.125mL phosphoric acid
13.125ml • 1.88g/ml = 24.675g phosphoric acid
24.675g • 1mol/98g = 0.252mol
17.5ml = 0.0175L
Concentration = 0.252mol/0.0175L = 14.39M
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www.wolframalpha.com
http://en.wikipedia.org/wiki/Coca-Cola_formula
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http://www.wikihow.com/Make-OpenCola
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g. Another important ingredient in Coca Cola is sugar (sucrose). The molecular
weight of sucrose is 342.3g/mol. How many molecules of sugar are in a can of
Coke? (5pts)
39g sugar/can
39g • 1mol/342.3g = 0.1139mol
0.1139mol • 6.022 • 1023molecules/mol = 6.86 • 1022molecules
Problem 3 – Chocolate Chip Cookies (30pts)
a. The Nestle Toll House Chocolate Chip cookie recipe also contains sugar.
Assuming this recipe makes 60 small cookies, how many cookies have the same
amount of sugar as a can of Coke? Ignore the chocolate chips. 1C = 201g for
white sugar and 1C = 220g for brown sugar. (10pts)
0.75C • 201g/C = 150.75g white sugar
0.75C • 220g/C = 165g brown sugar
Total = 150.75g white sugar + 165g brown sugar = 315.75g sugar
Sugar/cookie = 315.75g/60cookies = 5.26g/cookie
From question 2, 39g sugar in coke
39g sugar/5.26g/cookie = 7.41cookies
b. Acids and bases are also important for making cookies. The source of acid in this
cookie recipe is the brown sugar. Which ingredient is the source of base? (3pts)
Baking soda
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c. When the acid and base in this recipe mix together, carbon dioxide gas is
produced. Write a hypothesis for why this is important for baking cookies. (7pts)
Cookies usually have small bubbles that contribute to the cookie’s texture and
mouth feel. I hypothesize that the carbon dioxide produced by this reaction is
important for producing these air bubbles.
d. Write out an experimental plan for testing your hypothesis? Make sure to
describe what you will vary and how you will measure your data. (10pts)
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www.wolframalpha.com
http://en.wikipedia.org/wiki/Coca-Cola_formula
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http://www.wikihow.com/Make-OpenCola
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