A rock salt NaCl ice and water mixture is used to cool milk and cream to make homemade ice cream. How many grams of rock salt must be added to water to lower the freezing point 10.0C?
See response to your earlier post.
To lower the freezing point of water by 10.0°C, we need to calculate the amount of rock salt (NaCl) required. The freezing point depression constant (Kf) for water is approximately 1.86°C/m.
The equation for calculating the freezing point depression is:
ΔT = Kf * i * m
Where:
ΔT = change in freezing point (10.0°C)
Kf = freezing point depression constant (1.86°C/m)
i = Van't Hoff factor (ionization factor for NaCl, which is 2)
m = molality of the solution
We need to convert the change in freezing point (ΔT) to Celsius per molality before proceeding:
ΔT = 10.0°C / m
Next, we need to solve for the molality (m) in terms of grams of rock salt (NaCl).
The molar mass of NaCl is approximately 58.5 g/mol. The molality (m) is calculated as follows:
m = (moles of solute) / (mass of solvent in kg)
Assuming we're using 1 kg of water, we can calculate the moles of NaCl using its molar mass.
moles of NaCl = mass of NaCl / molar mass of NaCl
Now, we can substitute the values into the equation:
10.0°C / m = 1.86°C/m * 2 * (mass of NaCl / molar mass of NaCl)
Rearranging the equation, we can solve for the mass of NaCl:
mass of NaCl = (10.0°C * molar mass of NaCl) / (1.86°C/m * 2)
Substituting the molar mass of NaCl (58.5 g/mol) into the equation:
mass of NaCl = (10.0°C * 58.5 g/mol) / (1.86°C/m * 2)
Simplifying the equation:
mass of NaCl = 294.6 g / (1.86°C/m)
Therefore, approximately 294.6 grams of rock salt (NaCl) must be added to water to lower the freezing point by 10.0°C.
To calculate the amount of rock salt (NaCl) needed to lower the freezing point of water by 10.0°C, we need to use the concept of freezing point depression.
Freezing point depression is the phenomenon where adding a solute (in this case, rock salt) to a solvent (water) lowers the freezing point of the resulting solution. The amount of depression depends on the concentration of the solute particles.
The formula to calculate freezing point depression is ΔTf = Kf * m * i, where:
- ΔTf is the change in freezing point
- Kf is the cryoscopic constant for the solvent (water in this case)
- m is the molality of the solute
- i is the van't Hoff factor (a measure of the number of moles of particles formed when the solute dissolves)
For water, the cryoscopic constant (Kf) is 1.86°C/molal.
Since NaCl dissociates into two ions (Na+ and Cl-), the van't Hoff factor (i) for NaCl is 2.
We can rearrange the formula to solve for the molality of the solute (m): m = ΔTf / (Kf * i)
In this case, ΔTf is given as 10.0°C, Kf is 1.86°C/molal, and i is 2.
Substituting these values, we have: m = 10.0°C / (1.86°C/molal * 2)
Simplifying the equation gives us the molality (m) of the solute.
To convert from molality to mass (grams) of the solute, we need to use the molecular weight of NaCl, which is 58.44 g/mol.
The final step is to calculate the mass of the rock salt (NaCl) needed by multiplying the molality by the molecular weight: mass = molality * molecular weight.
Let's perform the calculations:
m = 10.0°C / (1.86°C/molal * 2)
m ≈ 2.688 molal
mass = 2.688 molal * 58.44 g/mol
mass ≈ 156.95 grams
Therefore, approximately 157 grams of rock salt (NaCl) must be added to water to lower the freezing point by 10.0°C.