SPU7: Problem Set 1 Due in your TF s homework box before class on Thursday, September 11 th 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 = 6.0 10 3 molecules ph = -log 10 [H + ] Concept Description Units ph A measure of acidity None [H + ] Concentration of protons or H + ions in a solution in moles of protons per liter 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 alpha 1 and look up the nutritional content for (1) prepared clam, () 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 g fat, 3g carbs, 9g protein Heavy cream: In 1tbsp (15g) there is 5g fat, 0.667g carbs, 0g protein Flour: In 1C (10g) there is g fat, 90g carbs, 13g protein
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 = 36.6mL (8pts) 0.1411qt cream 4C/1qt 36.6ml/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? (pts) 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
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 Coca Cola (40pts) The major ingredients of coke are sugar (sucrose), caramel color, caffeine, phosphoric acid, flavoring, and glycerin a. Which ingredient is the primary source of H + ions? (pts) 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) =.5 c. How many H + ions are there in a 1 fluid oz can? (1 fluid oz = 9.57mL) (5pts) 0.00316M = 0.00316mol/L (1pt) 1floz 9.57ml/floz = 354.84ml (1pt) 354.84ml 1000ml/L = 0.35484L (1pt) 0.00316mol/L 0.35484L = 0.0011mol (1pt) 0.0011mol 6.0 10 3 molecules/mol = 6.75 10 0 molecules H + (1pt)
d. It s a hot summer day, and you have poured your can of coke over 00g 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) 00g ice 1ml/g = 00ml water = 0.L ph of water = 7 [H + ] = 10-7 mol/l 10-7 mol/l 0.L = 10-8 mol H + in water From part C: 0.0011mol H + in coke Total moles H + in drink = 0.0011mol + 10-8 mol = 0.0011mol New volume of drink = 0.L + 0.35484L = 0.55484L Concentration of H + in drink = 0.0011mol/0.55484L = 0.0003M ph = -log(0.0003m) =.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 6.0 10 3 molecules/mol = 5.71 10 1 molecules 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 = 13.15mL phosphoric acid 13.15ml 1.88g/ml = 4.675g phosphoric acid 4.675g 1mol/98g = 0.5mol 17.5ml = 0.0175L Concentration = 0.5mol/0.0175L = 14.39M
g. Another important ingredient in Coca Cola is sugar (sucrose). The molecular weight of sucrose is 34.3g/mol. How many molecules of sugar are in a can of Coke? (5pts) 39g sugar/can 39g 1mol/34.3g = 0.1139mol 0.1139mol 6.0 10 3 molecules/mol = 6.86 10 molecules 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 = 01g for white sugar and 1C = 0g for brown sugar. (10pts) 0.75C 01g/C = 150.75g white sugar 0.75C 0g/C = 165g brown sugar Total = 150.75g white sugar + 165g brown sugar = 315.75g sugar Sugar/cookie = 315.75g/60cookies = 5.6g/cookie From question, 39g sugar in coke 39g sugar/5.6g/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
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)