Concentration of PbNO3

Calculus Level pending

Question: A tank contains 65 L of a solution composed of 80% of water and 20% of PbNO3. A second solution containing 25% of water and 75% of PbNO3 is added to the tank at the rate of 2L/hr. The volume of solution is constant since the tank is draining at the same rate.

Answer Submission: What is the amount of PbNO3, in volume, in the solution after 3 hrs? Round your answer to the nearest integer.


The answer is 16.

S. P. by S. P. , 16, USA

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1 solution

Steven Chase
May 3, 2020

Here is a time simulation of the inflow and outflow. The inflow has a fixed composition, and the outflow has the composition from the tank at that time. We expect the water fraction to begin at 0.8 0.8 and asymptotically approach 0.25 0.25 over time. It takes about 200 200 hours to reach a steady state. 

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import math

Vw = 65.0*0.8   # initial water volume
Vp = 65.0*0.2   # initial PbNO3 volume

dt = 10.0**(-5.0)  # time step in hours

t = 0.0
count = 0

while t <= 200.0:            

    fracw = Vw/(Vw+Vp)     # fraction of tank that is water

    dV = 2.0*dt            # infinitesimal volume = flow rate * time step

    Vw = Vw - dV*fracw        # outflow has composition of tank
    Vp = Vp - dV*(1.0-fracw)

    Vw = Vw + dV*0.25          # inflow has fixed composition
    Vp = Vp + dV*0.75

    t = t + dt
    count = count + 1

    if count % 10000 == 0:
        print t,fracw,Vp

2 Helpful 2 Interesting 2 Brilliant 0 Confused

@Steven Chase Solve it anaylitically . Please

A Former Brilliant Member - 1 year, 1 month ago

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