# Answer a Chemistry Question: Rock Salt & Ice Cream

• MHB
• WMDhamnekar
In summary: In both cases we are using the same unit, the kelvin.The two ways of expressing a freezing point depression (in degrees Celsius or kelvins) are completely equivalent. They both give the same answer, which is 232 grams of NaCl.
WMDhamnekar
MHB
Hello,

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 14.7°C? (Assume that there is 1 kg of water.)

How to answer this question? Answer provided is 231 grams. Is that correct?

If any member knows the correct answer to this question may reply.

From wiki's Freezing-point depression:

If the solution is treated as an ideal solution, the extent of freezing-point depression depends only on the solute concentration that can be estimated by a simple linear relationship with the cryoscopic constant (Charles Blagden's Law):
$$ΔT_F = K_F \cdot b \cdot i,$$
where:
• $ΔT_F$, the freezing-point depression.
• $K_F$, the cryoscopic constant, which is dependent on the properties of the solvent, not the solute. For water, $K_F = 1.853\,K·kg/mol$.
• $b$ is the molality (moles solute per kilogram of solvent).
• $i$ is the Van 't Hoff factor (number of ion particles per individual molecule of solute, e.g. $i = 2$ for $\ce{NaCl}$, $3$ for $\ce{Ba Cl2}$).

Hello,

There is error in your wikipedia link. $K_F$ shuld be $K_F=1.853^\circ C \cdot kg/mol$

Dhamnekar Winod said:
Hello,

There is error in your wikipedia link. $K_F$ shuld be $K_F=1.853^\circ C \cdot kg/mol$

It's the same thing.
The kelvin is the same unit as the degree Celsius except for the choice of its zero.
In this case we're talking about a change in temperature so that the zero of the scale does not matter.

Klaas van Aarsen said:
It's the same thing.
The kelvin is the same unit as the degree Celsius except for the choice of its zero.
In this case we're talking about a change in temperature so that the zero of the scale does not matter.
Hi,
I have answer to this question from another chemistry expert.

Molar mass of NaCl = 23.0 + 35.5 = 58.5 g/mol

van't Hoff factor for NaCl = 1 (1 mol NaCl = 1 mol Na⁺ + 1 mol Cl⁻)
Cryoscopic constant for water, $K_F = 1.853 ^\circ C\cdot kg/mol$
Freezing point depression, ΔTF = 14.7°C
Molality, b = ? mol/kg

$\Delta T_F = K_F\cdot b\cdot i$
14.7 = 1.853 × b × 2
Molality, b = 14.7 / (1.853 × 2) = 3.967 mol/kg water

(3.967 mol NaCl / 1 kg water) × (1 kg water) × (58.5 g NaCl / 1 mol NaCl)
= 232 g NaCl

In the above answer, $1.853^\circ C$ is used to arrive at the final answer 232 grams of NaCl. But you are saying it doesn't make any difference whichever units of temperature are used. How is that? In my opinion, we have to convert either degree Celsius into Kelvin or vice versa. Would you explain your standpoint in this regard?

Dhamnekar Winod said:
In the above answer, $1.853^\circ C$ is used to arrive at the final answer 232 grams of NaCl. But you are saying it doesn't make any difference whichever units of temperature are used. How is that? In my opinion, we have to convert either degree Celsius into Kelvin or vice versa. Would you explain your standpoint in this regard?

Consider that we calculate a freezing point depression $\Delta T_F$, which is a change in temperature of the freezing point.
In $^\circ C$ the freezing point of water happens to be at $0\,^\circ C$ while in $K$ it is at $273.15\,K$.

If we calculate the freezing point depression with $^\circ C$ we find $\Delta T_F=14.7\,^\circ C$, which means that the freezing point of water is not at $0\,^\circ C$ but at $-14.7\,^\circ C$.
If instead we calculate with $K$ we find $\Delta T_F=14.7\,K$, which means that the freezing point of water is not at $273.15\,K$ but at $273.15\,K-14.7\, K$.
See how these statements are the same?

## 1. What is rock salt and how does it work in making ice cream?

Rock salt, also known as halite, is a mineral composed primarily of sodium chloride (NaCl). In making ice cream, rock salt is used to lower the freezing point of water. When ice cream ingredients are placed in a container surrounded by ice and rock salt, the salt causes the ice to melt, creating a brine solution. This brine solution has a lower freezing point than plain water, allowing the ice cream mixture to freeze at a lower temperature, resulting in a smoother and creamier texture.

## 2. Is rock salt the same as table salt?

No, rock salt and table salt are not the same. While both are primarily composed of sodium chloride, table salt is finely ground and has added iodine, while rock salt is in larger crystal form and does not contain iodine. Additionally, table salt typically has anti-caking agents added, while rock salt does not.

## 3. Can I use any type of salt to make ice cream?

Technically, any type of salt can be used to make ice cream, but rock salt is the most commonly used because of its larger crystals and lower cost. Other types of salt, such as sea salt or kosher salt, may also work but may not be as effective in lowering the freezing point of water.

## 4. How much rock salt should I use when making ice cream?

The amount of rock salt needed depends on the amount of ice cream mixture and the size of the container. As a general rule, you should use about 1 cup of rock salt for every 4 cups of ice. However, it is always best to follow the specific instructions for your ice cream maker or recipe.

## 5. Can I reuse rock salt for making ice cream?

Yes, you can reuse rock salt for making ice cream. After use, simply allow the salt to dry out and store it in an airtight container for future use. However, keep in mind that the salt may become contaminated with small amounts of ice cream mixture, so it is recommended to only reuse the salt a few times before replacing it.

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