It's January in Nashville and your local weather station just informed you that the temperature outside is -4.37 degrees Celcius. You estimate the amount of ice on your driveway to be approximately 30kg. What is the minimum amount of sodium chloride in kilograms (kg) needed to lower the freezing point of the water so that the ice melts
delta T = i*Kf*m
delta T = 4.37 C. You might want to make that 4.38 to add just a wee bit more.
i for NaCl = 2
Kf for water = 1.86
Substitute and solve for m = molality
Then m = mols/kg solvent
You know m and kg (30) solvent. Solve for mols.
Then mol = grams/molar mass
You know mol and molar mass, solve for grams.
To calculate the minimum amount of sodium chloride (NaCl) needed to lower the freezing point of the ice on your driveway, you can use the concept of freezing point depression. Freezing point depression refers to the phenomenon where adding a solute, such as sodium chloride, to a solvent, such as water, lowers the freezing point of the solution.
To calculate the amount of sodium chloride required, we need to know the molal freezing point depression constant (Kf) for water and the freezing point depression desired.
1. Determine the freezing point depression desired:
The freezing point depression desired is the difference between the freezing point of pure water (0 degrees Celsius) and the temperature outside (-4.37 degrees Celsius). Therefore, the freezing point depression desired would be: 0 - (-4.37) = 4.37 degrees Celsius.
2. Find the molal freezing point depression constant (Kf):
The molal freezing point depression constant (Kf) for water is a constant value, which is 1.86 degrees Celsius/m. This value represents the change in the freezing point of the solvent per molal concentration (moles of solute per kilogram of solvent).
3. Calculate the molality (m):
Molality (m) is defined as the number of moles of solute (NaCl) per kilogram of solvent (water). To calculate molality, we need to convert the mass of ice on your driveway from kilograms to moles, using the molar mass of water (18 g/mol). Let's assume the molar mass of NaCl is 58.5 g/mol.
Mass of ice (mice) = 30 kg
Moles of water (nwater) = mice / (molar mass of water)
Moles of NaCl (nNaCl) = moles of water
Mass of NaCl (mNaCl) = nNaCl * (molar mass of NaCl)
4. Calculate the minimum amount of sodium chloride:
Now, using the molality (m), freezing point depression (ΔT), and the molal freezing point depression constant (Kf), we can calculate the minimum amount of sodium chloride (NaCl) needed.
ΔT = Kf * m
Rearranging the equation:
m = ΔT / Kf
mNaCl = mwater
mNaCl = ΔT / Kf
mNaCl = 4.37 / 1.86
Finally, the mass of sodium chloride (mNaCl) required would be 4.37 / 1.86 kg.
Therefore, the minimum amount of sodium chloride needed to lower the freezing point of the water and melt the ice on your driveway is approximately 2.35 kg (rounded to two decimal places).