Ammonium nitrate (NH4NO3) is an important agricultural industrial chemical as it provides readily available nitrogen for plant growth, and one can buy 50. pounds of ammonium nitrate for $38. Urea
(CO(NH2)2) is an attractive alternative, and, not being a pre-cursor to an explosive, draws less attention from law enforcement when buying significant quantities.The key component is the nitrogen content (%composition) in the substance that feeds your plants. What will the price of urea be (for 50. Pounds) in order to provide the same amount of nitrogen per
dollar spent?
Calculate %N in NH4NO3.
Calculate %N in urea.
Those are done (mass N/molar mass compound)*100 = %N.
Then amount N in 50 lbs NH4NO3 = 50 lbs x (percent N/100) = ?
And 38/?amount N = cost/lb N.
Amount N in urea = 50 x (percent N/100) = ?
And X/?amount N = cost/lb N.
To determine the price of urea that provides the same amount of nitrogen per dollar spent as ammonium nitrate, we need to compare the nitrogen content of both substances and calculate the cost per pound of nitrogen.
First, let's find out the nitrogen composition of both ammonium nitrate and urea:
1. Ammonium nitrate (NH4NO3):
- Molecular weight: (1 * 14.01) + (4 * 1.01) + (1 * 14.01) + (3 * 16.00) = 80.05 g/mol
- Nitrogen weight: 2 * 14.01 = 28.02 g/mol
- Nitrogen content: (28.02 g/mol / 80.05 g/mol) * 100% = 34.99%
2. Urea (CO(NH2)2):
- Molecular weight: (1 * 12.01) + (1 * 16) + (2 * 14.01) = 60.06 g/mol
- Nitrogen weight: 2 * 14.01 = 28.02 g/mol
- Nitrogen content: (28.02 g/mol / 60.06 g/mol) * 100% = 46.65%
Now, let's calculate the cost per pound of nitrogen for each substance:
1. Ammonium nitrate:
- Cost for 50 pounds: $38
- Nitrogen content per pound: 50 pounds * (34.99% / 100%) = 17.495 pounds
- Cost per pound of nitrogen: $38 / 17.495 pounds = $2.17 per pound of nitrogen
2. Urea:
- Cost per pound of nitrogen: ? (to be calculated)
To calculate the cost per pound of nitrogen for urea, we need to determine how many pounds of urea are needed to provide the same amount of nitrogen as in 50 pounds of ammonium nitrate. Since the nitrogen content of urea is higher, we can assume that the weight of urea needed will be less than 50 pounds.
Let's set up the equation to calculate this:
Nitrogen content in 50 pounds of ammonium nitrate = Nitrogen content in x pounds of urea
17.495 pounds = (x pounds) * 46.65% / 100%
Simplifying the equation:
17.495 pounds = (0.4665 * x pounds)
x = 37.527 pounds
Therefore, to provide the same amount of nitrogen as 50 pounds of ammonium nitrate, we would need approximately 37.5 pounds of urea.
Now, let's calculate the cost of urea for 37.5 pounds:
Cost for 37.5 pounds of urea = (37.5 pounds * $x) / 50 pounds
We don't have the price of urea, so we cannot calculate the exact cost per pound of nitrogen for urea without this information. You would need to check the current market price of urea to determine the cost per pound of nitrogen and compare it to the cost per pound of nitrogen for ammonium nitrate.