Final Answer:
The chloride concentration after 1 year at a distance of 15 m from the landfill source is approximately 723.5 mg/L. The calculation involves the advection-dispersion equation, considering hydraulic conductivity, hydraulic gradient, and dispersion coefficient. The resulting concentration accounts for the transport of contaminants in the aquifer.
Explaination:
The transport of contaminants in groundwater can be modeled using the advection-dispersion equation. The one-dimensional advection-dispersion equation for solute transport is given by:
![\[ (\partial C)/(\partial t) = -(\partial)/(\partial x)(vC) + D^*(\partial^2 C)/(\partial x^2) \]](https://img.qammunity.org/2024/formulas/chemistry/high-school/4da78hci8ygxde6qiqfqbg4gf2mtcg61i6.png)
where:
-
is the concentration of the solute,
is time,
is the distance along the flow path,
is the average linear groundwater velocity,
is the dispersion coefficient.

To solve this equation, we can use the method of characteristics. The solution for a pulse input of concentration at time
is given by:
![\[ C(x, t) = (C_0)/(2√(\pi D^* t)) \exp\left(-((x-vt)^2)/(4D^*t)\right) \]](https://img.qammunity.org/2024/formulas/chemistry/high-school/il7nu1lsf40rqwtb5n9v0nqb8ehns3vk4l.png)
where
is the initial concentration.
Now, let's calculate the concentration at

Given values:

First, convert the units to be consistent:
![\[ v = k \cdot (dh)/(dl) = (3.0 * 10^(-3) \ \text{cm/s}) * 0.0020 \]\[ t = 1 \ \text{year} = 31,536,000 \ \text{seconds} \]](https://img.qammunity.org/2024/formulas/chemistry/high-school/d4j9ymowpqf0vgp3yzyk6shnf9pdsbrqa4.png)
Now, substitute these values into the concentration equation:
![\[ C(15 \ \text{m}, 31,536,000 \ \text{seconds}) = \frac{725}{2\sqrt{\pi * 1.0 * 10^(-9) * 31,536,000}} \exp\left(-((15 - v * 31,536,000)^2)/(4 * 1.0 * 10^(-9) * 31,536,000)\right) \]](https://img.qammunity.org/2024/formulas/chemistry/high-school/a1lkq6vzlt6kter9lpedwcolc0duqb4p0g.png)
Calculate this expression to find the chloride concentration after 1 year at a distance of 15 m from the source of contamination.