Land growing continuous grain corn as a cash crop loses soil at a rate of

14.0 metric tonnes ha-1 yr-1. This is a fertile soil, which has an organic matter content of 3.8% and nitrogen content of 0.35% (both by mass).

a)Calculate how long it will take to erode the entire Ah horizon of this soil. Assume an initial Ah thickness of 7 inches and a bulk density of 1.25 g cm-3 prior to the onset of cultivation .

b)If the entire Ah horizon is lost, calculate how many kg of manure you would need to add per hectare in order to replace the lost organic matter if manure is assumed to be 100% organic matter.

c)If nitrogen (as ammonium nitrate) sells for $0.70 kg-1, calculate the dollar value of nitrogen that would have to be added per hectare in order to replace the lost nitrogen.

a) To calculate how long it will take to erode the entire Ah horizon of this soil, we need to convert the thickness of the Ah horizon from inches to centimeters and then calculate the volume of soil lost per hectare annually.

1. Convert the initial Ah thickness from inches to centimeters:
7 inches = 17.78 cm

2. Calculate the volume of the Ah horizon per hectare:
Volume = Area x Thickness
Since 1 hectare is equal to 10,000 square meters, the volume will be:
Volume = 10,000 m² x 17.78 cm = 1,778,000 cm³

3. Convert the volume to cubic meters (m³):
1,778,000 cm³ = 1.778 m³

4. Calculate the mass of soil lost per hectare annually:
Mass = Volume x Bulk Density
Mass = 1.778 m³ x 1.25 g/cm³ = 2.2225 metric tonnes

5. Use the given soil erosion rate to calculate the time it takes to erode the entire Ah horizon:
Time = Total Loss / Rate
Time = 100 metric tonnes / 2.2225 metric tonnes/year = 45.02 years

Therefore, it will take approximately 45 years to erode the entire Ah horizon of this soil.

b) To calculate the amount of manure needed to replace the lost organic matter, we first need to determine the amount of organic matter lost per hectare annually:

1. Calculate the mass of organic matter lost per hectare annually:
Mass = Area x Loss Rate
Mass = 100 metric tonnes x 0.038 = 3.8 metric tonnes

2. Since manure is assumed to be 100% organic matter, the amount of manure needed to replace the lost organic matter is equal to the mass of organic matter lost:
Manure needed = 3.8 metric tonnes

Therefore, you would need to add 3.8 metric tonnes of manure per hectare annually to replace the lost organic matter.

c) To calculate the dollar value of nitrogen that would have to be added per hectare to replace the lost nitrogen:

1. Calculate the mass of nitrogen lost per hectare annually:
Mass = Area x Loss Rate
Mass = 100 metric tonnes x 0.0035 = 0.35 metric tonnes

2. Calculate the dollar value of nitrogen needed:
Value = Mass x Price per unit
Value = 0.35 metric tonnes x $0.70/kg = $0.245 per hectare

Therefore, the dollar value of nitrogen that would have to be added per hectare to replace the lost nitrogen is $0.245.