What is the melting point of a mixture of 2.00 lb of NaCl and 12.00 pounds of ice if exactly half of the ice melts? Assume that all the NaCl disolves in the melted ice and that the van't Hoff factor for resulting solution is 1.44.
-15.3
-15.3
-15.280 degrees Celsius
6 lbs melted ice x 454 g/lb = ? grams H2O as the solvent.
2 lbs NaCl x 454 = ? grams NaCl.
delta T = i*Kf*m
i = 1.44
Kf = 1.86
You need m to solve for delta T.
mol NaCl = grams NaCl/molar mass NaCl
molality = moles NaCl/kg solvent.
delta T = i*Kf*m
Subtract delta T from 0 C to find melting point.
To find the melting point of this mixture, we need to first calculate the amount of heat required to melt half of the ice.
The heat of fusion (ΔHfus) is the amount of heat required to melt a given amount of substance. For water, the heat of fusion is 334 J/g.
Step 1: Calculate the amount of ice that is melted.
Since half of the ice melts, we need to find the amount of heat required to melt only 6.00 pounds (12.00 pounds / 2) of ice.
To convert pounds to grams, we need to know the conversion factor. 1 pound is equal to 453.59237 grams.
So, 6.00 pounds is equal to 6.00 * 453.59237 grams.
Step 2: Calculate the heat required to melt 6.00 pounds of ice.
We can use the heat of fusion (ΔHfus) to calculate the heat required to melt the ice:
Heat = mass * heat of fusion
Heat = (6.00 pounds * 453.59237 g/pound) * 334 J/g
Step 3: Calculate the heat produced by the NaCl dissolving.
Since the total heat absorbed by the mixture is equal to the heat produced by NaCl dissolving, we can calculate it using the heat produced by dissolving 1 mole of NaCl:
ΔHdiss = -n * R * T
The van't Hoff factor (i) for NaCl is given as 1.44, which means we need to consider 1.44 moles of NaCl.
R is the ideal gas constant, which is 8.314 J/(mol K).
T is the temperature we want to find, the melting point in Kelvin.
By rearranging the formula, we can solve for T:
T = (-ΔHdiss) / (n * R)
Step 4: Calculate the heat produced by dissolving 1 mole of NaCl.
We need to convert the given weight of NaCl to moles:
2.00 lb of NaCl * (453.59237 g/pound) * (1 mol/58.44 g) = x moles of NaCl
ΔHdiss = x moles * R * T
Step 5: Combine the equations to solve for T.
Using the values calculated from Steps 2 and 4, we can substitute them into the equation to solve for T:
T = (-ΔHdiss) / (n * R)
After calculating T, convert it back to Celsius by subtracting 273.15, which is the conversion factor from Kelvin to Celsius.
This will give you the melting point of the mixture.