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
To calculate the cost of treating 1000 lb of ice on a surface using NaCl and urea, we need to find the mass of each chemical needed first.
First, let's calculate the mass of NaCl required. We know that the freezing point depression constant (Kf) for water is 1.86 °C/m. The change in temperature (delta T) is the difference between the desired freezing point (-3.9 °C) and the normal freezing point of water (0 °C), which is -3.9 - 0 = -3.9 °C.
Now, rearranging the formula ΔT = mKf, we can find the mass of NaCl:
m = ΔT / Kf
m = -3.9 °C / 1.86 °C/m
m ≈ -2.1 m
Since mass cannot be negative, we take the absolute value of -2.1, which is 2.1 m.
The cost of NaCl can be calculated by multiplying the mass of NaCl (2.1 m) by the unit cost per pound ($0.033/lb):
Cost of NaCl = (2.1 m) * ($0.033/lb)
Similarly, let's calculate the mass of urea required. The change in temperature (delta T) remains the same (-3.9 °C). The freezing point depression constant (Kf) for urea is given as 20.0 °C/m.
m = ΔT / Kf
m = -3.9 °C / 20.0 °C/m
m ≈ -0.195 m
Taking the absolute value, we have 0.195 m.
The cost of urea can be calculated by multiplying the mass of urea (0.195 m) by the unit cost per pound ($0.10/lb):
Cost of urea = (0.195 m) * ($0.10/lb)
Thus, we have calculated the cost of treating 1000 lb of ice on a surface to produce a solution that melts at -3.9 degrees Celsius using NaCl and urea.