Please do all steps, show work, and explain. 6. Fizzle. a. Let?s say that the He
ID: 908065 • Letter: P
Question
Please do all steps, show work, and explain.
6. Fizzle. a. Let?s say that the Henry?s Law constant for N2 is 1.56 x 10^5 kPa . Kg(H2O)/ mol(N2). How much N2 is in a diver?s blood (a person has about 5L of blood = 5 kg) at 100 m depth (which means that the diver is under 10.0 atms of pressure). Please answer in moles of gas. b. Now the diver rapidly resurfaces to 1 atm of pressure;how much N2 will come out of the diver?s blood in Liters using the perfect gas law? Hint: the reason you?re calculating 0.795 L and not 0.715 L is that you forgot that some gas will be retained in the blood at 1 atm pressure. C. Can you also show that the perfect gas law volume is basically identical to the same predicted by the van der Waal s equation? (Hint, show that a volume of 0.715 L give s a pressure o f 101.3 kPa using the van der Waals equation for 0.0292 moles of N2). Assume the temperature is a constant 25 degree C. (12 pts)Explanation / Answer
ANSWER:
(a) Henry's constant for N2 is, H = 1.56E5 kPa. kg(H2O)/mol(N2).
Assuming only N2 is present in gas.
pN2 = total pressure
At pressure of 10 atm, pN2 = 10 atm
1 atm = 101.3 kPa
pN2 = 7.8 atm = 10*101.3 kPa = 1013kPa
xN2 = pN2/H = 1013/1.56E5 = 0.0065 mol(N2)/kg(H2O)
Kg of H2O, W = kg of blood = 5 kg
Moles of N2, nN2 = xN2*W = 5 kg*0.0066 mol(N2)/kg(H2O) = 0.0325 moles
(b)
Now the diver rapidly resurfaces to 1 atm of pressure; how much N2 will come
out of the diver's blood in Liters using the perfect gas law?
Hint: the reason you're calcuating 0.795L and not 0.715L is that you forgot that
some gas will be retained in the blood at 1 atm pressure.
pN2 = 1 atm = 101.3 kPa
xN2 = pN2/H = 101.3/1.56E5 = 0.00065 mol(N2)/kg(H2O)
Kg of H2O, W = kg of blood = 5 kg
Moles of N2, nN2 = xN2*W = 5 kg*0.00065 mol(N2)/kg(H2O) = 0.00325 moles
no of moles of N2 come out of the diver's blood = 0.0325 - 0.00325 = 0.03 moles
R = 0.0821 L atm/mol K; T = 25+273 = 298 K; P = 1 atm
Volume of N2 in liters, V = n*R*T/P = 0.03*0.0821*298/1 = 0.715 L