PROBLEM SET 1
*QUESTIONS ONLY - DUE: MONDAY, SEPTEMBER 19, 2011
DEFINING SYSTEMS
Question 1:
a)
Define the terms: mass flow rate, volumetric flow rate, density, mass fraction
b)
What is conserved in a chemical reaction?
c)
Define closed, open and isolated systems.
d)
What is the material balance equation for an individual chemical species “A” in an open system?
Which terms
become zero if you have: a closed system, no reaction, or steady-state?
MASS BALANCES
Question 2:
The kidneys carry out a separation process where blood enters
at a rate of 1200 mL/min and is split into two streams: filtered
blood and urine. We are specifically interested in the details of
the separation of urea and a drug
circulating in the patient’s
blood by the patient. What is known is given in the figure. Find
the unknown quantities in the filtered blood and urine streams.
Find the unknown quantities in the filtered blood and urine
streams. Assume density of all streams is the same as water = 1
kg/L. Note that 1 uM = 1 micromole per liter.
*Question 3:
You are preparing a mixture of methanol (MeOH) by combining two
solutions of MeOH. More specifically, you are adding 200 g of
solution A and 150 g of solution B. The mass fraction of MeOH in A is
0.4 and the mass fraction of MeOH in B is 0.7. What is the mass
fraction MeOH in the final mixture C (see figure)?
Question 4:
You have designed a centrifuge system to
separate cells from a solution. A mixture of
water and cells enters the centrifuge system at a
rate 1000 L/h and contains 500 mg cells/L. You
can assume that the density is that of water (1
g/cm
3
). The inlet stream or feed (F), is separated
to a cell-free supernatant (S), and a pellet (P)
consisting of a solution containing water and
cells. The mass fraction of cells in the pellet is
0.5. Using the data in the figure, calculate the
mass flow rates
m
P
(g/hr) and m
S
(g/hr).
Kidney
Blood
Filtered
Blood
Urine
V
B
= 1200 mL/min
C
urea, B
= 10 mg/dL
C
drug, B
= 100 uM
V
F
= ?
C
urea, F
= ?
C
drug, F
= 90 uM
V
U
= 1.5 mL/min
C
urea, U
= 500 mg/dL
drug, U
= ?
C
A
200 g
x
M, A
= 0.400
150 g
x
M, B
= 0.700
B
Centrifuge
Feed (F)
Supernatant (S)
Pellet (P)
V
F
= 1000 L/h
= 1.0 g/cm
3
C
cells, F
= 500 mg cells/L
C
cells, S
= 0
X
cells, P
= 0.5
X
water, P
= 1- X
cells, P
= 0.5
F