# Material Balance Lead in a lake

1. Mar 18, 2014

### dimens

1. The problem statement, all variables and given/known data

Question 2.
Tetraethyl lead was used in early model cars to help reduce engine knocking, boost octane ratings, and help with wear and tear on valveseats within the motor. In Australia, our petrol
contained lead between approximately 1950 and 2002. Consider the impact of lead in petrol on a lake used for drinking water supply. The lake has a steady state water volume of 8.2 x 107m3 with an inflow and outflow of 6.0 x 107m3/year. From 1950, the lead concentration in the lake inflow water was 40 ppb and the deposition rate of lead onto the lake surface was 120 kg/y. Assume the lead concentration in the lake water was zero when lead first started being added to petrol and that the lake is completely mixed.

the lake water (in μg/L) for the time period when lead was included in petrol.

2. Relevant equations
I was thinking since output rate = reaction rate... QC = G-kCV

3. The attempt at a solution

We've got pretty much all of the variables.. Except for C and k...

Rearranging for C...

C = G / (Q + kV)

To find k... k = G/VC

(120kg/year) / 8.2x10^7 * 40 ppb

= 120 kg/year / 8.2*10^10L * 4x10^-8 kg/L
= 120/year / 3936
= 0.0366/year

...

c = 120 kg/year / 6.0*10^7 m3/year + 0.0366/year * 8.2*10^7m3

However I get some ridiculous number.

2. Mar 18, 2014

### SteamKing

Staff Emeritus
It's hard to follow your calculations because you omit so many units.

3. Mar 18, 2014

### Staff: Mentor

There is no reaction taking place, so forget that. You need to do a transient (time dependent) material balance on the lead in the lake.

Let Q = volumetric water flow rate into and out of the lake.
Let C0 = concentration of lead in the water flowing into the lake.
Since the lake is well-mixed, let C = concentration of lead in the water exiting the lake, and also the concentration of lead within the lake (at any time t)
Let R be the rate of lead being deposited into the lake from above.
Write a time dependent differential mass balance for the lead in the lake.

Chet

4. Mar 18, 2014

### dimens

input rate = output rate + deposition
Qin*C0 = Qout * C + Rt
C(t) = (Qin*C0 - Rt) / Qout

Something like this?

5. Mar 13, 2018 at 3:31 AM

Hi Chester, i made an account just for this as i have the same question.

i have converted the kg of lead being deposited onto the lake into litres, 12.346 per year and have included that into the inputs. I have calculated the concentration of the water exiting the lake at year 1 as 4.22x10^-5 μg/L, however I am still struggling to find the correct equation as i do not think i have think that is correct answer. The equation i used was (Qin x Cin + Rin)/Qout = Cout. Any help would be appreciated.

6. Mar 13, 2018 at 7:02 AM

### Staff: Mentor

Why did you convert the lead deposited into liters?

Your equation omits the rate of accumulation of lead in the lake. Why did you think they told you the volume of the lake?