Mass Balance and Enviromental Reactor

[interxlocking]

Homework Statement

1) A spill of 5kg of a soluble pesticide takes place into a well-mixed pond. The pesticide is subject to volatilization that can be characterized by the first order flux J=VvC, where Vv = volatilization mass-transfer coefficient of 0.01m/d. Other parameters for the pond are:

Surface area, m2 = 0.1x106
Mean depth, m = 5
Outflow, m3/d = 1x106
a) Predict the concentration in the pond as a function of time. Present your results as a plot (60 marks)
b) Determine the 95% response time for the system (20 marks)
c) Calculate the time required for the concentration to be reduced to 0.1µg/L (20 marks)

Homework Equations

V dc/dt = QC_i-QC-Vk_dC+K_gV

The Attempt at a Solution

I'm stumped because there is no rate for the flow in. Would I just ignore the first part. and just use
V dc/dt = -QC-Vk_dC+K_gV.

I just need a kick in the right direction. Any time of help would be appreciated. Thanks

 

[KataKoniK]

!

Hi there,

It seems like you are trying to solve a problem related to environmental chemistry and transport. To solve this problem, you will need to use a mass balance equation, which is the basis of environmental engineering and science. The mass balance equation states that the rate of change of mass in a system is equal to the sum of all the inputs and outputs of mass in that system. In this case, the system is the pond and the mass is the pesticide.

So, let's start by writing the mass balance equation for this system:

V(dc/dt) = QCi + Vin - QCo - Vout - VvC

Where:
V = volume of the pond (m3)
dc/dt = rate of change of concentration (kg/m3/d)
Q = flow rate (m3/d)
Ci = initial concentration (kg/m3)
Co = final concentration (kg/m3)
Vin = mass input due to volatilization (kg/d)
Vout = mass output due to outflow (kg/d)
Vv = volatilization mass-transfer coefficient (m/d)
C = concentration (kg/m3)

Now, let's substitute the given values into the equation:

V(dc/dt) = 0 + 0 - (1x106)(Ci) - (1x106)(Co) - (0.01)(0.1x106)(C)

Simplifying:

V(dc/dt) = -1x106(Ci + Co + 0.001C)

This is a first-order differential equation, which can be solved using separation of variables. The general solution is:

C = C0e^(-kt)

Where:
C0 = initial concentration
k = rate constant (1/d)

Now, let's solve for the 95% response time, which is the time it takes for the concentration to decrease by 95%. To do this, we can use the half-life formula for first-order reactions:

t1/2 = ln(2)/k

Since we want the 95% response time, we can solve for t by setting the concentration equal to 0.05C0 (95% decrease):

0.05C0 = C0e^(-kt)

Solving for t:

t = ln(20)/k

Finally, to calculate the time required for the concentration to be reduced to 0.1µg/L, we can set the concentration equal