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# 2.56g of Sulphur in 100g of$\text{C}{{\text{S}}_{2}}$ has depression in freezing point 0f $\text{0}\text{.010}{}^\circ \text{C}$. Atomicity of sulphur is $\text{C}{{\text{S}}_{2}}$ is:(Given, ${{\text{K}}_{f}}=\ \text{0}\text{.1}{}^\circ \text{ mola}{{\text{l}}^{1-}}$)A. 2B. 4C. 6D. 8

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Hint: Atomicity tells us about the total number of atoms that are present in the molecule. For example, a monatomic molecule consists of one type of atom. Depression in freezing point tells us about the decrement in the freezing point of a solvent when a non-volatile solute is added.

Complete answer:
-To find the value of atomicity we will assume it as 'n'. So, the molecular formula will become ${{\text{S}}_{n}}$.
-Now, we all know that the molecular mass of the sulphur is 32 so the mass of the compound of sulphur will be 32n.
-Here, 32 is the mass of sulphur and n is the mass of an atom whose value we have to find.
-Now, let's apply the formula depression in freezing point i.e.
$\Delta {{\text{T}}_{f}}\text{ = }\dfrac{100\text{ w }{{\text{K}}_{f}}}{\text{mW}}$
-Here, ${{\text{K}}_{f}}$ expresses the molal freezing point constant, $\Delta {{\text{T}}_{f}}$ is the depression in the freezing point or the difference between the freezing point of pure solvent and the freezing point of the solution.
-Whereas w is the weight of the solute in gram, W is the weight of solvent in kg and m is the molecular weight of solute.
-It is given that the value of depression in freezing point is $\text{0}\text{.010}{}^\circ \text{C}$, w is the mass of sulphur i.e.2.56g and w is the mass of compound 100g. We have to find the value m that is atomicity.
-Now, by applying the formula of depression in freezing point we will get:
$0.010\ \text{= }\dfrac{1000\ \times \text{ 2}\text{.56 }\times \text{ 0}\text{.1}}{\text{m }\times \text{ 100}}$
$\text{m}\ \text{= }\dfrac{1000\ \times \text{ 2}\text{.56 }\times \text{ 0}\text{.1}}{\text{0}\text{.010 }\times \text{ 100}}$
$32\text{n = 256}$
$\text{n = }\dfrac{\text{256}}{32}\text{ = 8}$
-Therefore, the atomicity of sulphur is 8 and the molecular formula will be ${{\text{S}}_{8}}$.

Note: A sulphur molecule with a molecular formula of ${{\text{S}}_{8}}$ have a crown structure and consists of the covalent bond and the length all bonds are equal. It is commonly known as octal sulphur. It is considered as one of the allotropes of sulphur.