Question

‎In this module we've been discussing fossil fuels and the impacts of their use. One of the impacts is an increase in acid deposition (or acid rain as many people refer to it). An acid can be neutralized by a base (also known as an alkali). Acid deposition can be neutralized by the addition of ‎‎agricultural lime‎‎ (an alkaline rock, not the tasty green fruit). The following exercise asks you to calculate how much ‎‎agricultural lime‎‎ it would take to increase the pH of a small lake. Remember that acids have lower pHs and bases have higher pHs, so that as I add more base, the pH will increase.‎

‎Consider a small lake in the Adirondack region of New York state; Lake Whatchamacallit (surface area = ‎‎2.6 mi‎^‎2‎‎, average depth = ‎‎45 ft‎‎). The pH of Lake Whatchamacallit has been measured to be ‎‎4.0‎‎ (an unfortunate result of acid deposition), which is just a little too acidic to support aquatic life; ‎‎i.e.‎‎ Lake Whatchamacallit is for all intents and purposes, dead.‎

‎Farmer Jones, whose property adjoins the lake, knows that when the soil on her farm is too acidic she adds ‎‎agricultural lime‎‎ (crushed limestone ‎‎i.e.‎‎ calcium carbonate, CaCO‎_‎3‎‎) to it in order to increase the pH of the soil and make it suitable for planting. She gathers all of her neighbors for a meeting with the state's department of natural resources. She proposes that they add ‎‎lime‎‎ to the lake in order to increase its pH and then to restock the lake with new fish.‎

‎How many ‎‎tons‎‎ of lime would have to be added to Lake Whatchamacallit in order to raise the pH from 4.0 to 7.0? Use the following facts to help you determine your answer.‎

‎Use the following information to answer the questions posed below. Round both answers to ZERO places past the decimal, do NOT use commas in your answers, and do NOT use scientific notation.‎

‎1 ‎‎oz‎‎ of lime will raise the pH of 5,700 liters of lake-water from 4.0 to 7.0‎

‎the cost of agricultural lime is about $28 per ton‎

‎when lime dissolves in water heat is given off, such that when 100 g dissolves in water it gives off enough heat to increase the temperature of 3 liters of water by 1 °C‎

‎1 ‎‎mi‎‎ = 5280 ‎‎ft‎‎; 16 ‎‎oz‎‎ = 1 ‎‎lb‎‎; 2000 ‎‎lb‎‎ = 1 ‎‎ton‎‎; 1 ‎‎ft‎^‎3‎‎ lake-water = 28.3 ‎‎liters‎

‎Hint: Start by finding the volume of the lake.‎

‎How many ‎‎tons‎‎ of lime would have to be added to Lake Whatchamacallit in order to raise the pH from 4.0 to 7.0? Answer = ‎‎Blank 1‎ ‎ tons.‎

‎What would the ‎‎cost‎‎ of this much lime be? Answer = $‎‎Blank 2‎

Answer 1

a) Surface area of lake = 2.6 mi²

1 mi = 5280 ft

So, surface area of lake = 2.6*5280*5280 ft²

Height of lake = 45 ft

So, volume of lake = surface area*height = (2.6*5280*5280*45) ft³

1 ft³ lake water = 28.3 liters

So, volume of water in lake = (2.6*5280*5280*45*28.3) liters

Lime used to raise pH of 5700 liters of lake water = 1oz

So, Lime used to raise pH of (2.6*5280*5280*45*28.3) liters of lake water = (2.6*5280*5280*45*28.3)/5700 oz

16 oz = 1 lb

So, (2.6*5280*5280*45*28.3)/5700 oz = (2.6*5280*5280*45*28.3)/(5700*16) lb

2000 lb = 1 ton

So, (2.6*5280*5280*45*28.3)/(5700*16) lb = (2.6*5280*5280*45*28.3)/(5700*16*2000) tons = 506 tons

Answer is 506 tons

b) Cost of 1 ton lime = $28

cost of 506 tons lime = $28*506 = $14168