A farmer applies 13.50 kg of a fertilizer that contains 10.0% nitrogen to his fields each year. Fifteen (15.0%) percent of the fertilizer washes into a river that runs through the farm.
If the river flows at an average rate of 0.265 cubic feet per second. What is the additional concentration of nitrogen (expressed in milligrams of nitrogen per liter) in the river water due to the farmer's fertilizer?
To find the additional concentration of nitrogen in the river water, we need to calculate the amount of nitrogen that washes into the river.
Step 1: Calculate the amount of nitrogen in the fertilizer applied.
The fertilizer contains 10.0% nitrogen.
Therefore, the amount of nitrogen in the fertilizer is:
13.50 kg x 0.10 = 1.35 kg
Step 2: Calculate the amount of nitrogen that washes into the river.
Fifteen (15%) percent of the fertilizer washes into the river.
Therefore, the amount of nitrogen that washes into the river is:
1.35 kg x 0.15 = 0.2025 kg
Step 3: Convert the mass of nitrogen into milligrams (mg).
1 kg is equal to 1,000,000 mg.
Therefore, the mass of nitrogen that washes into the river is:
0.2025 kg x 1,000,000 mg/kg = 202,500 mg
Step 4: Find the volume of water passing through the river per second.
The river flows at an average rate of 0.265 cubic feet per second.
Step 5: Convert the volume to liters.
There are 7.48052 liters in 1 cubic foot.
Therefore, the volume of water passing through the river per second is:
0.265 cubic feet/second x 7.48052 liters/cubic foot = 1.98148 liters/second.
Step 6: Calculate the additional concentration of nitrogen in the river water.
Concentration is given by the amount of nitrogen divided by the volume of water.
Therefore, the additional concentration of nitrogen in the river water is:
202,500 mg / 1.98148 liters = 102,382.49 mg/L
So, the additional concentration of nitrogen in the river water due to the farmer's fertilizer is approximately 102,382.49 mg/L.
To find the additional concentration of nitrogen in the river water due to the farmer's fertilizer, we need to follow these steps:
Step 1: Calculate the total amount of nitrogen applied to the fields each year.
- The fertilizer contains 10.0% nitrogen, meaning that 10.0% of the total weight is nitrogen.
- Therefore, the total amount of nitrogen applied is 13.50 kg multiplied by 10.0%, which is equal to 1.35 kg.
Step 2: Calculate the amount of nitrogen that washes into the river.
- Fifteen (15.0%) percent of the fertilizer washes into the river.
- Therefore, the amount of nitrogen that washes into the river is 1.35 kg multiplied by 15.0%, which is equal to 0.2025 kg.
Step 3: Convert the mass of nitrogen that washes into the river to milligrams (mg).
- There are 1000 milligrams in a gram. Therefore, 1 kg is equal to 1,000,000 milligrams.
- Hence, 0.2025 kg equals 0.2025 kg multiplied by 1,000,000 mg/kg, which is equal to 202,500 mg.
Step 4: Calculate the volume of water that flows through the river in a year.
- The river flows at an average rate of 0.265 cubic feet per second.
- This rate needs to be converted to cubic feet per year.
- There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.
- Additionally, there are 365 days in a year.
- Therefore, the volume of water that flows through the river per year is 0.265 cubic feet per second multiplied by 60 seconds/minute multiplied by 60 minutes/hour multiplied by 24 hours/day multiplied by 365 days/year, which is equal to 8,356.4 cubic feet per year.
Step 5: Convert the volume of water that flows through the river to liters (L).
- There are 28.3168466 liters in a cubic foot.
- Hence, 8,356.4 cubic feet equals 8,356.4 cubic feet multiplied by 28.3168466 L/cubic foot, which is equal to 236,557.3 liters per year.
Step 6: Calculate the additional concentration of nitrogen in the river water.
- Divide the amount of nitrogen that washed into the river (202,500 mg) by the volume of water that flows through the river (236,557.3 L) to find the concentration in milligrams per liter (mg/L).
- 202,500 mg divided by 236,557.3 L is approximately 0.856 mg/L.
Therefore, the additional concentration of nitrogen in the river water due to the farmer's fertilizer is approximately 0.856 milligrams of nitrogen per liter.