Commodity prices of NaCl and urea are about $0.033/lb for NaCl (as rock salt) and about $0.10/lb for urea. Calculate the cost of treating 1000 lb of ice on a surface to produce a solution that melts at -3.9 degrees Celsius with each chemical. I know you use to delta T= mkfi but after i find m idk what to do next please help
delta T = i*Kf*molality
Plug in 3.9 for delta T, i = 2 for NaCl (i - 1 for urea), Kf, and solve for molality.
molality = mols/kg solvent.
You have m and kg solvent(convert 1000 lb to kg) and solve for mols.
mol = grams/molar mass. You have mols and molar mass; solve for grams.
I would convert cost/lb to cost/gram, and grams urea x cost/g = total cost.
grams NaCl x cost/g = total cost.
THANK YOU SO MUCH!!!
To calculate the cost of treating 1000 lb of ice using NaCl and urea, you first need to determine the amount of each chemical required to achieve the desired freezing point.
1. NaCl (rock salt):
The first step is to calculate the amount of NaCl required to lower the freezing point of the ice to -3.9 degrees Celsius. The formula you mentioned, delta T = m * k * fi, can be used.
Let's assume the freezing point constant (k) for NaCl is 1.86 degrees Celsius/mass percent. The initial freezing point (fi) of water is 0 degrees Celsius.
delta T = -3.9 - 0
m * 1.86 * 1 = -3.9
Now, solve for m (mass of NaCl):
m = delta T / (k * fi)
m = -3.9 / (1.86 * 1)
m ≈ -2.10
Since mass cannot be negative, this indicates that you need to use approximately 2.10 lbs of NaCl to lower the freezing point by -3.9 degrees Celsius.
Next, calculate the cost of 2.10 lbs of NaCl:
Cost of treating 2.10 lbs of NaCl = 2.10 lbs * $0.033/lb
2. Urea:
Follow the same steps as above to calculate the required mass of urea. Assuming the freezing point constant (k) for urea is 1.86 degrees Celsius/mass percent:
delta T = -3.9 - 0
m * 1.86 * 1 = -3.9
Now, solve for m (mass of urea):
m = delta T / (k * fi)
m = -3.9 / (1.86 * 1)
m ≈ -2.10
Again, since mass cannot be negative, this indicates that you need to use approximately 2.10 lbs of urea to lower the freezing point by -3.9 degrees Celsius.
Finally, calculate the cost of 2.10 lbs of urea:
Cost of treating 2.10 lbs of urea = 2.10 lbs * $0.10/lb
Now, you will have the cost of treating 1000 lbs of ice with NaCl and urea, respectively. Multiply the cost of treating 2.10 lbs of each chemical by the factor 1000/2.10 to find the final cost.