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A solution containing \[25.6{\rm{ }} gm\] of sulphur dissolved in \[1000{\rm{ }}gm\] of naphthalene gave a freezing point lowering of \[0.680\],then molecular formula of sulphur is:
(A)\[{S_2}\]
(B)\[{S_4}\]
(C)\[{S_6}\]
(D)\[{S_8}\

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Last updated date: 17th Jun 2024
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Answer
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Hint: We know that the freezing point lowering can be determined by the specific formula that is the depression in freezing point due to the addition of non-volatile solute in the volatile solvent.

Complete Step by step answer:To decide the solvent and solute in the given question we know that the one which is higher in amount is solvent and the one which is lesser in amount is solute. It seems clear that the non-volatile solute is sulphur and the volatile solvent is naphthalene. To find the molecular formula of the sulphur, the molecular weight is needed for that the substitution of all the given values will lead us to find the molecular mass.
Now, let’s find the mass to choose the correct option.
As we know that,
\[\Delta {T_f} = {K_f}.m\]
\[{K_f} = \]molal depression constant or Cryoscopic constant.
\[
m = \;molality{\rm{ }}of{\rm{ }}solution\;\\
m = \dfrac{{molecular\;mass\;of\;solute}}{{mass\;of\;solute}} \times \dfrac{{1000}}{{mass\;of\;solvent(in\;gm)}}
\]
Mass of dissolved sulphur (solute)\[ = 25.6g\].
Mass of solvent (Naphthalene)\[ = 100g\].
Depression in freezing point\[ = 0.68\]℃.
Molecular mass of solute=M (Assumed)
Substituting in the known formula:
\[\Delta {T_f} = {K_f}.m\]
\[
{\therefore 0.68 = 6.8 \times \left( {\dfrac{{25.6}}{M} \times \dfrac{{1000}}{{1000}}} \right)}\\
{ \Rightarrow M = 256}
\]
Therefore, Molecular Mass of Sulphur \[ = {\rm{ 32}}\;g\]
So, the number of sulphur atoms present in a formula is calculated as shown below.
$\dfrac{{256\;{\rm{g}}}}{{32\;{\rm{g}}}} = 8$
Hence, the formula of sulphur \[ = \;{S_8}\]

Therefore, the correct answer is (D) that is \[{S_8}\].

Note: The value of solute and solvent should be selected from the question in the appropriate way. The molar mass is calculated by using the molality from the formula of depression in freezing point.