Pesticide is applied to a 10 ha (hectare) field at an average rate of 1 kg/ha every
month. The soil is regarded as 20 cm deep and well-mixed. The pesticide evaporates
at a rate of 2% of the amount present per day and it degrades microbially with a
rate constant of 0.05 day-1
. What will be the steady state concentration of pesticide
in g/m3
and in unit of g/g, assuming the soil density as 2500 kg/m3. (10 marks)
To find the steady state concentration of pesticide in both g/m3 and g/g, we need to understand the different processes affecting the concentration of pesticide in the soil.
The first process is the application rate, where 1 kg/ha of pesticide is applied to a 10 ha field every month. To determine the pesticide amount applied each month, we multiply the application rate (1 kg/ha) by the area (10 ha), resulting in 10 kg of pesticide applied per month.
The second process is evaporation, which occurs at a rate of 2% of the pesticide amount present per day. To calculate the daily evaporation rate, we multiply 2% by the pesticide amount applied per month (10 kg) and divide it by the number of days in a month. Assuming an average of 30 days in a month, the daily evaporation rate would be (0.02 * 10 kg) / 30 = 0.0067 kg/day.
The third process is microbial degradation, which happens at a rate constant of 0.05 day-1. This means that 5% of the remaining pesticide amount degrades each day. To calculate the daily microbial degradation rate, we multiply the remaining pesticide amount by the degradation rate constant. Initially, the remaining pesticide amount is equal to the amount applied (10 kg). Thus, the daily degradation rate would be 0.05 * 10 kg = 0.5 kg/day.
Now, let's calculate the steady state concentration of the pesticide:
Step 1: Calculate the amount of pesticide remaining in the soil after microbial degradation.
Since microbial degradation occurs at a constant rate, the remaining pesticide amount will reduce linearly over time. At steady state, the degradation rate must be balanced by the application rate. So, the daily degradation rate (0.5 kg/day) should equal the daily application rate (10 kg/month / 30 days) plus the daily evaporation rate (0.0067 kg/day).
0.5 kg/day = (10 kg/month / 30 days) + 0.0067 kg/day
0.4933 kg/day = 0.3333 kg/day + 0.0067 kg/day
0.4933 kg/day = 0.34 kg/day
This equation is not balanced, so we need to adjust the application rate.
Step 2: Adjust the application rate to achieve a balanced equation.
To balance the equation, we increase the monthly application rate until the degradation balanced with the evaporation rate.
Let's assume the adjusted monthly application rate is X kg.
0.5 kg/day = (X kg/month / 30 days) + 0.0067 kg/day
0.4933 kg/day = (X/30) kg/day + 0.0067 kg/day
0.4866 kg/day = (X/30) kg/day
X/30 = 0.4866 kg/day
X = 0.4866 kg/day * 30
X = 14.598 kg/month
So, to achieve a balanced equation, the monthly application rate should be approximately 14.598 kg.
Step 3: Calculate the steady state concentration in g/m3 and g/g.
The steady state concentration is calculated by dividing the remaining pesticide amount by the volume of soil.
First, we need to calculate the remaining pesticide amount at steady state. Since the application rate has been adjusted to balance degradation and evaporation, the system reaches a steady state where the remaining pesticide amount is constant.
The remaining pesticide amount is equal to the monthly application rate (14.598 kg).
Next, we calculate the volume of soil that this amount is spread over.
The volume of soil is calculated by multiplying the area (10 ha) by the depth (20 cm).
First, convert the area to m2: 10 ha * 10,000 m2/ha = 100,000 m2.
Then, convert the depth to m: 20 cm * 0.01 m/cm = 0.2 m.
Now, the volume of soil is calculated:
Volume = area * depth = 100,000 m2 * 0.2 m = 20,000 m3.
Finally, we calculate the steady state concentration in g/m3 by dividing the remaining pesticide amount by the volume of soil:
Concentration (g/m3) = remaining pesticide amount (g) / volume of soil (m3)
Concentration (g/m3) = 14.598 kg * 1000 g/kg / 20,000 m3
Concentration (g/m3) = 729.9 g / 20,000 m3
Concentration (g/m3) ≈ 0.036495 g/m3
To calculate the concentration in g/g, we need to convert the remaining pesticide amount to g/g by dividing it by the total mass of soil. The total mass of soil is calculated by multiplying the volume of soil by the soil density (2500 kg/m3).
Total mass of soil (kg) = volume of soil (m3) * soil density (kg/m3)
Total mass of soil (kg) = 20,000 m3 * 2500 kg/m3 = 50,000,000 kg
Concentration (g/g) = remaining pesticide amount (g) / total mass of soil (kg)
Concentration (g/g) = 14.598 kg * 1000 g/kg / 50,000,000 kg
Concentration (g/g) = 14,598 g / 50,000,000 kg
Concentration (g/g) ≈ 0.00029196 g/g
Therefore, the steady state concentration of pesticide is approximately 0.036495 g/m3 and 0.00029196 g/g in the given conditions.