Question

please can answer all the questions and with work clearly

1. According to the Joslin Clinic, healthy individuals without diabetes should have a blood glucose level of no more than 100 mg dL−1 after awaking, before breakfast. What is the molarity of glucose in the blood of a healthy individual whose blood glucose level is 100 mg dL−1 ?

2. One index of toxicity is the LD50, the amount of substance which, when administered to a group of subject, will kill 50% of that group. (LD50 stands for lethal dose of 50%.) It is known that LD50s are different for different species; for example, for aspirin, the LD50 in cats is about 5 mg kg−1 , while in dogs, it is about 11 mg kg −1 , and in rats, it is about 200 mg kg−1 . In a recent editorial, Dr. Bernd Mayer of the University of Graz, Austria, discusses the accepted lethal dose of nicotine in humans. According to Dr. Mayer, the widely accepted value of 800 mcg kg−1 (mcg is a common abbreviation for microgram, µg, and 1 mg = 1000 mcg) is based on a casual statement in a 1906 toxicology text, and is far smaller than the values determined for laboratory animals, which are range from 3.3 (mice) to more than 50 mg/kg (rats).

(a) Assuming that the accepted value is correct, how many more times toxic is nicotine towards humans than rats?

(b) Assuming that the accepted value is incorrect and that nicotine is as toxic in humans as in rats, what is the expected lethal dose, in grams, for a 120 lb woman? For a 180 lb man?

c) Depending on brand, smoking a cigarette results in an uptake of approximately 2 mg of nicotine. How many cigarettes must be smoked by a 120 lb woman to achieve the lethal dose of nicotine? How many for the 180 lb man?

3. It is approximately 59 miles from Indiana to Pittsburgh. According to the EPA, the commercially available vehicle with the highest gas mileage is the BMW i3 BEV, which achieves 124 mpg.

(a) How many gallons of gas are required to drive to Pittsburgh and back?

(b) Assuming gasoline is 100% octane, how many moles of octane are required to drive to Pittsburgh and back?

(c) Assuming complete combustion of the fuel, how many grams of CO2 are produced by driving to Pittsburgh and back?

4. The U.S. EPA currently sets the maximum allowable concentration of lead in public drinking water at 15 µg L−1 .

(a) What is the molarity of Pb, if the concentration of Pb is 15 µg L−1

(b) If you allow one gallon of such water to evaporate to dryness, how many grams of Pb are left behind?

(c) How many gallons of such water must you drink in order to have drunk a mole of lead?

5. On the Moodle site, you will find a file, HydocarbonDensity.xls. This is an Excel file listing the names, number of carbons, molar masses, refractive indices, and densities of 35 unbranched alkanes.

(a) Make a plot of the density of unbranched alkanes versus the number of carbon atoms in the alkane.

(b) Given that commercial polyethylenes have densities between 0.91-0.96 g/mL, use your plot to estimate the number of carbon atoms in commercial polyethylene. You should explain your process in writing.

Answer 1

For 1. 100 mg/dL

We have to turn mg to moles of glucose and deciliters to liters, as follows:

100 mg / dL * (1dL / 0.1L) * (1 gram / 1000 mg) * (1 mol of glucose / 180.16 g of glucose) = 0.00555 mol/L

0.00555 mol/L = 0.00555 M

2. a) We have to convert the accepted value to mg/kg:

800 mcg/kg * (0.001 mg / 1 mcg) = 0.8 mg/kg

50 mg/kg for rats / 0.8 mg/kg for humans = The value for rats is 62.5 times greater, so nicotin is 62.5 times more toxic to humans than to rats.

b) Assuming a toxicity of 50 mg/kg for humans:

Dose for a 120 lb woman:

120 lb * (0.4536 kg/ 1lb) = 54.432 kg woman

50 mg/kg of body * 54.432 kg woman = 2721.6 mg = 2.721 g of nicotin

Dose for a 180 lb man:

180 lb * (0.4536 kg/ 1lb) = 81.648 kg man

50 mg/kg of body * 81.648 kg man = 4082.4 mg = 4.082 g of nicotin

c) 2 mg / cigarette

For a 120 lb woman -> 2721.6 mg / 2 mg/cigarette = 1360.8, which is approx. 1361 cigarettes

For a 180 lb man -> 4082.4 mg / 2 mg/cigarette = 2041.2, which is approx. 2042 cigarettes

3. a) 118 miles for going and back trip

118 miles / 124 miles/gallon = 0.9516 gallons

b) 0.9516 gallons * (3.7854 L / gallon) = 3.6 L

Octane density is 0.703 kg/L

3.6 L * (0.703 kg/L) = 2.5324 kg = 2532.4 g

Molar mass of octane = 114.23 g/mol

2532.4 g * (1 mol / 114.23 g) = 22.17 moles

c) Combustion of octane: 2C₈H₁₈ + 25 O₂ -> 16 CO₂ + 18 H₂O

22.17 moles of C₈H₁₈ * (16 moles of CO₂ / 2 moles of C₈H₁₈) = 177.35 moles of CO₂

177.35 moles of CO₂ * (44 g/mol) = 7803.5 grams = 7.8 kg of CO₂

4. a) 15 micrograms/L * (0.000001 g/microgram) * (1mol / 207.2 g) = 7.2394 x 10^-8 mol/L = 7.2394 x 10^-8 M

b) 7.2394 x 10-8 mol/L * (3.7854 L) = 2.7404 x 10^-7 moles of Pb

2.7404 x 10^-7 moles of Pb * (207.2 g/mol) = 0.00005678 grams of Pb

c) 1 mol of Pb * (1L / 7.2394 x 10^-8 mol) = 13813299.44 L * (1 gallon / 3.7854L) = 3649099.024 gallons

5. For this one, excel file is missing, I will be glad to help, if you include the file in another question. Hope this is helpful!