In this article we are going to understand how to calculate molar mass from freezing point.

**In this method of calculating molar mass from freezing point we are going to make use of colligative properties. So first of all let us derive a relation between molar mass of solute and depression point:**

**ΔTf = is the depression ( in freezing point)**

**ΔTf ∝ m**

**ΔTf = Kfm … equation 1**

**Where , Kf is the molal depression constant.**

Consider,

**m = number of moles of solute/ weight of solvent (kg)**

**m = w2/m2 × 1000/w1 …equation 2**

Note: If kg comes into picture there there is no need to use 1000, but if given in grams 1000 should be written.

**To calculate molar mass from freezing point:**

So,

**w1 = is the weight of solvent**

**w2 = is the weight of solute**

**M2 = is the molecular weight of solute**

Substituting equation 2 in equation 1

**ΔTf = Kf × w2/M2 × 1000/w1**

**M2 = Kf × w2 × 1000 / ΔTf × w1**

So, this is the basic relation.

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There are more 2 properties from which we can determine molar mass:

**How to determine molar mass from freezing point depression?**

We can understand this concept by solving some examples:

**1.26.4g sample of an unknown compound is dissolved in 75.0g water and the resulting solution has a freezing point of -5.10 degrees Celsius. So calculate the molar mass of the unknown substance. The freezing constant of the water is 1.86 degrees Celsius/m.**

**Solution:**

Consider the equation for freezing point depression.

**ΔTf = KfM**

where m = mol (solute)/kg (solvent)

and we know Molar mass = g/mol

Rearranging the above equation:

**M = ΔTf / Kf …equation 1**

where,

ΔTf = freezing point and Kf = freezing constant

So we are provided with: ΔTf = 5.10 degrees Celsius and Kf = 1.86 degrees Celsius/m

Substituting this values in equation 1

M = 5.10 degrees Celsius / 1.86 degrees Celsius/m = 2.74 m

Now,

2.74 mol / kg × 0.07500 kg = 0.206 mol

Molar mass = g/mol = 26.4g/0.206mol = 128g/mol

**2.When 12.5 g of a certain sugar is dissolved in 1.25g of water the freezing point of the solution decreases by 0.543 degrees Celsius. Determine the molar mass of this sugar.**

**Solution:**

Consider the equation for freezing point depression.

ΔTf = KfM

Where m = mol (solute)/kg (solvent)

And we know Molar mass = g/mol

Rearranging the above equation:

M = ΔTf / Kf …equation 1

Where,

ΔTf = freezing point and Kf = freezing constant

So we are provided with: ΔTf = 0.543 degrees Celsius and Kf = 1.86 degrees Celsius/m

Substituting this values in equation 1

M = 0.543 degrees Celsius / 1.86 degrees Celsius/m = 0.292 m

Now,

0.292mol / kg × 0.125 kg = 0.0365 mol

Molar mass = g/mol = 12.5g/0.0365 mol = 342.465 g/mol

**3.When 12g of an unknown nonelectrolyte compound are dissolved in 400g of benzene, the freezing point of the resulting solution is 3.90 degrees Celsius. The freezing point of pure benzene is 5.44 degrees Celsius. Calculate the molar mass of the unknown compound ( Kf for benzene = 5.12 degrees Celsius/m )**

**Solution:**

Consider the equation for freezing point depression.

ΔTf = KfM

Where m = mol (solute)/kg (solvent)

And we know Molar mass = g/mol

Rearranging the above equation:

M = ΔTf / Kf …equation 1

Where,

ΔTf = freezing point and Kf = freezing constant

ΔTf = 5.44 degrees Celsius- 3.90 degrees Celsius = 1.54 degrees Celsius

1.54 degrees Celsius = 1 × 5.12 degrees Celsius/m × 12g /m × 1000/400g

1.54/1 = 5.12 × 12 × 100/ 400 M

M = 5.12 × 12 × 1000 / 400 × 1.54 = 61440/616 = 99.74 g/mol

**4.When 5.71g of naphthalene is added to 152g of benzene ( FP of pure benzene = 5.46 degrees Celsius and Kf of naphthalene = 5.07 degrees Celsius/ m ) the solution freezes at 3.98 degrees Celsius. What is the molar mass of naphthalene ?**

**Solution:**

Consider the equation for freezing point depression.

ΔTf = KfM

Where m = mol (solute)/kg (solvent)

And we know Molar mass = g/mol

Rearranging the above equation:

M = ΔTf / Kf …equation 1

Where,

ΔTf = freezing point and Kf = freezing constant

ΔTf = 5.46 degrees Celsius- 3.98 degrees Celsius = 148 degrees Celsius

ΔTf = KfM

1.48 = 5.07 M = 0.292 M = Mol. Naphthalene / 0.152 kg = 0.0447 Mol naphthalene

Molar mass = 5.7g / 0.0447 mol = 127 g/mol

**Read more about: How To Find Mass From Moles And Molar Mass: Detailed Explanations**

**How to Calculate molar mass from percent composition?**

The basic formula of percent composition that is related to molar mass is:

**% X = Total atomic mass of X / Molar mass which contains X**

So by rearranging above equation we get :

**Molar mass ( X ) = Total atomic mass of X / % X**

By using this formula we can find molar mass from percent composition.