What mass of salt(NaCl)should you add to 1.20 L of water in an ice cream maker to make a solution that freezes at -10.4∘C?

Why did the salt go to school? Because it wanted to be a little salty!

Now, to answer your question, the freezing-point depression of a solution depends on the concentration of the solute. In this case, the solute is salt (NaCl) and the solvent is water. To determine the mass of salt you should add, we need to use the formula:

ΔT = Kf * m

Where:
ΔT is the freezing-point depression (change in temperature)
Kf is the cryoscopic constant for water (-1.86 °C/m)
m is the molality (moles of solute per kilogram of solvent)

Given that the freezing-point depression is 10.4 °C, we can rearrange the formula to solve for m:

m = ΔT / Kf

m = 10.4 °C / (-1.86 °C/m) = -5.59 m

Since molality (m) is defined as moles of solute per kilogram of solvent, we need to convert the volume of water to kilograms:

1.20 L of water = 1.20 kg (since the density of water is 1 g/mL)

Now, we can calculate the moles of NaCl needed:

moles = m * kg of solvent

moles = -5.59 m * 1.20 kg = -6.71

But hold your horses! The number of moles can't be negative. So, you need to add 6.71 moles of salt (NaCl) to 1.20 L of water to make the solution freeze at -10.4 °C.

To determine the mass of salt (NaCl) that you should add to the water in order to make a solution that freezes at -10.4∘C, you need to use the concept of freezing point depression.

The freezing point depression equation is given by:
ΔT = Kf * m

Where:
ΔT is the change in freezing point (in this case, -10.4∘C)
Kf is the cryoscopic constant (a property of the solvent, water, which is 1.86∘C/m)
m is the molality of the solution (the number of moles of solute per kg of solvent)

To calculate the molality (m), we need to know the number of moles of NaCl and the mass of water.

Let's assume the density of water is 1 g/mL, so the mass of 1.20 L of water is:
Mass of water = Volume of water x Density
Mass of water = 1.20 L x 1000 g/L
Mass of water = 1200 g

To find the molality (m), we need to convert the mass of NaCl to moles:
Molar mass of NaCl = 22.99 g/mol (Na) + 35.45 g/mol (Cl)
Molar mass of NaCl = 58.44 g/mol

Now, let's use the following formula to find the molality (m):
m = moles of NaCl / mass of water (in kg)

moles of NaCl = mass of NaCl / molar mass of NaCl

Substituting the known values, we can find the mass of NaCl:

mass of NaCl = moles of NaCl x molar mass of NaCl

Once we have the mass of NaCl, we can add it to the water in the ice cream maker.

Note: The assumptions made here for the density of water and molar mass of NaCl are approximate values and may differ slightly in reality.

Let's calculate the mass of salt (NaCl) required step-by-step:

To determine the mass of salt (NaCl) required to make a solution that freezes at -10.4∘C, you need to use the concept of freezing point depression. The freezing point depression is the difference between the freezing point of the pure solvent (in this case, water) and the freezing point of the solution.

The formula for calculating freezing point depression is:

ΔTf = Kf × m

Where:
ΔTf is the freezing point depression
Kf is the cryoscopic constant (a property of the solvent)
m is the molality of the solution (moles of solute per kilogram of solvent)

First, we need to determine the cryoscopic constant for water (Kf). The Kf value for water is 1.86 °C/molal.

Next, we need to calculate the molality of the solution (m). Molality is defined as the number of moles of solute divided by the mass of the solvent (in kg).

m = (moles of solute) / (mass of water in kg)

To calculate the moles of solute, we need to know the molecular weight of NaCl, which is 58.44 g/mol.

Now let's plug in the values and solve the equation:

1. Start by converting 1.20 L of water to kg. The density of water is 1 g/mL or 1000 kg/m³.

Mass of water = volume × density = 1.20 L × 1000 g/L = 1200 g = 1.2 kg

2. Determine the moles of solute.

moles of solute = mass of NaCl / molecular weight of NaCl

3. Calculate the molality of the solution.

m = (moles of solute) / (mass of water in kg)

4. Finally, determine the freezing point depression (ΔTf) using the formula:

ΔTf = Kf × m

Now, let's plug in the values and calculate the mass of NaCl required.

ΔTf = 10.4 °C (absolute value, as freezing point depression is always positive)
Kf = 1.86 °C/molal
Molecular weight of NaCl = 58.44 g/mol

Rearrange the freezing point depression formula to solve for moles of solute:

moles of solute = ΔTf / Kf

Plug in the values:

moles of solute = 10.4 °C / 1.86 °C/molal = 5.591 mol

Now, calculate the mass of NaCl:

Mass of NaCl = moles of solute × molecular weight of NaCl
= 5.591 mol × 58.44 g/mol
= 326.75 g

Therefore, you need to add approximately 326.75 grams of NaCl to 1.20 L of water to make a solution that freezes at -10.4∘C in an ice cream maker.

delta T = i*Kf*m

You have delta T = 10.4
i is the van't Hoff factor which is 2 for NaCl.
Kf = 1.86 for water. Solve for m.
Then m is molality = mols NaCl/kg solvent. You have kg solvent. Solve for mols.
Then mols = grams/molar mass. You have mols and molar mass NaCl; solve for grams NaCl.