Final answer:
To calculate the mass of CH₃OH needed to lower the freezing point of water by 12.0 °C, you can use the formula: ΔT = Kf x m. Rearrange the formula and solve for m to find the molarity of the solution. Convert the molarity to moles and then to grams using the molar mass of CH₃OH.
Step-by-step explanation:
Answer:
To calculate the mass of CH₃OH needed to lower the freezing point of water, we can use the formula:
ΔT = Kf x m
In this case, we know that ΔT is -12.0 °C, Kf for water is 1.86 °C/m, and we want to find the molarity of the solution. Rearranging the formula, we can solve for m:
m = ΔT / Kf = -12.0 °C / 1.86 °C/m = -6.45 m
Since molarity (m) is defined as moles of solute per liter of solution, we need to convert the molarity to moles:
moles of solute = m x liters of solution
First, we convert the mass of water to liters using its density of 1 g/mL:
380.1 g x (1 mL/1 g) x (1 L/1000 mL) = 0.3801 L
Now, we can calculate the moles of solute:
moles of solute = -6.45 m x 0.3801 L = -2.454 moles
Finally, we can convert moles of solute to grams using the molar mass of CH₃OH:
mass of solute = moles x molar mass = -2.454 moles x 32.04 g/mol = -78.52 g
Since we can't have a negative mass, it seems there may be an error in the calculation.
Double-check the given values and calculations to ensure accuracy.
If the given values are correct, then the calculated mass should be positive instead of negative.