Answer
Verified
397.8k+ views
Hint: It has been observed that a solution containing non-volatile solute freezes at a temperature lower than that of the pure solvent. This decrease in the freezing point is directly proportional to the mole fraction of the solute in the solution.
Complete answer:
Freezing point is the temperature at which solid and liquid states of a substance co-exist, i.e. they have the same vapour pressure. In addition a non-volatile solute is added in a solvent as its freezing point decreases. This is called the depression in freezing point. If \[{{T}_{f}}\] and \[{{T}_{o}}\] are the freezing points of the solution containing non-volatile solute and the pure solvent, respectively. Then, the depression in freezing point (\[\Delta {{T}_{f}}\]) is given as: \[\Delta {{T}_{f}}={{T}_{o}}-{{T}_{f}}\]
\[\Delta {{T}_{f}}\] is directly proportional to the amount of non-volatile solute added per kg of the solvent. Molality is the number of moles of solute present in one kg of the solvent.
$ \Delta {{T}_{f}}\propto molality(m)$
$\Delta {{T}_{f}}={{K}_{f}}m$
$\text{or }{{K}_{f}}=\dfrac{\Delta {{T}_{f}}}{m}$
Here, \[{{K}_{f}}\] is the molal freezing point depression constant of the solvent or cryoscopic solvent. Cryoscopic constant is, therefore, defined as the ratio of the depression in freezing point to the molality of the solution. Its basic unit is \[\text{K kg mo}{{\text{l}}^{-1}}\].
If we take molality of the solution as unity, we get
$m=1$
$\Delta {{T}_{f}}={{K}_{f}}\times 1$
$\Delta {{T}_{f}}={{K}_{f}}$
We can also define a cryoscopic constant as the freezing point of the solution when one mole of the solute is dissolved in one kg of the solvent. In some cases, \[{{K}_{f}}\] may also be calculated from the thermodynamically derived equation:
\[~{{K}_{f}}=\dfrac{RT_{f}^{2}}{1000\times {{L}_{f}}}\]
where \[{{L}_{f}}\] is the latent heat of fusion per gram of the solvent.
Additional Information \[\Delta {{T}_{f}}\] of a solution is a colligative property. It depends on the mole fraction of solute and is independent of the nature of the solute. Molar mass of the solute can be determined from it. Let \[{{M}_{2}}\] be the molar mass of the solute and \[{{w}_{1}}\], \[{{w}_{2}}\] be the weights of the solute and the solvent in grams, respectively. Using the expression for molality, we get
$m=\dfrac{{{n}_{2}}}{{{w}_{1}}}$
$m=\dfrac{{{w}_{2}}\times 1000}{{{M}_{2}}\times {{w}_{1}}(g)}$
$\Delta {{T}_{f}}={{K}_{f}}m$
$\Delta {{T}_{f}}={{K}_{f}}\dfrac{{{w}_{2}}\times 1000}{{{M}_{2}}\times {{w}_{1}}(g)}$
$\text{then, }{{M}_{2}}=\dfrac{{{K}_{f}}\times {{w}_{2}}\times 1000}{\Delta {{T}_{f}}\times {{w}_{1}}(g)}$
Note: Cryoscopic constant has a specific value for any given solvent. Physical quantities without appropriate units have no significance. So, never write \[{{K}_{f}}\] without units and use proper symbols for different physical quantities.
Complete answer:
Freezing point is the temperature at which solid and liquid states of a substance co-exist, i.e. they have the same vapour pressure. In addition a non-volatile solute is added in a solvent as its freezing point decreases. This is called the depression in freezing point. If \[{{T}_{f}}\] and \[{{T}_{o}}\] are the freezing points of the solution containing non-volatile solute and the pure solvent, respectively. Then, the depression in freezing point (\[\Delta {{T}_{f}}\]) is given as: \[\Delta {{T}_{f}}={{T}_{o}}-{{T}_{f}}\]
\[\Delta {{T}_{f}}\] is directly proportional to the amount of non-volatile solute added per kg of the solvent. Molality is the number of moles of solute present in one kg of the solvent.
$ \Delta {{T}_{f}}\propto molality(m)$
$\Delta {{T}_{f}}={{K}_{f}}m$
$\text{or }{{K}_{f}}=\dfrac{\Delta {{T}_{f}}}{m}$
Here, \[{{K}_{f}}\] is the molal freezing point depression constant of the solvent or cryoscopic solvent. Cryoscopic constant is, therefore, defined as the ratio of the depression in freezing point to the molality of the solution. Its basic unit is \[\text{K kg mo}{{\text{l}}^{-1}}\].
If we take molality of the solution as unity, we get
$m=1$
$\Delta {{T}_{f}}={{K}_{f}}\times 1$
$\Delta {{T}_{f}}={{K}_{f}}$
We can also define a cryoscopic constant as the freezing point of the solution when one mole of the solute is dissolved in one kg of the solvent. In some cases, \[{{K}_{f}}\] may also be calculated from the thermodynamically derived equation:
\[~{{K}_{f}}=\dfrac{RT_{f}^{2}}{1000\times {{L}_{f}}}\]
where \[{{L}_{f}}\] is the latent heat of fusion per gram of the solvent.
Additional Information \[\Delta {{T}_{f}}\] of a solution is a colligative property. It depends on the mole fraction of solute and is independent of the nature of the solute. Molar mass of the solute can be determined from it. Let \[{{M}_{2}}\] be the molar mass of the solute and \[{{w}_{1}}\], \[{{w}_{2}}\] be the weights of the solute and the solvent in grams, respectively. Using the expression for molality, we get
$m=\dfrac{{{n}_{2}}}{{{w}_{1}}}$
$m=\dfrac{{{w}_{2}}\times 1000}{{{M}_{2}}\times {{w}_{1}}(g)}$
$\Delta {{T}_{f}}={{K}_{f}}m$
$\Delta {{T}_{f}}={{K}_{f}}\dfrac{{{w}_{2}}\times 1000}{{{M}_{2}}\times {{w}_{1}}(g)}$
$\text{then, }{{M}_{2}}=\dfrac{{{K}_{f}}\times {{w}_{2}}\times 1000}{\Delta {{T}_{f}}\times {{w}_{1}}(g)}$
Note: Cryoscopic constant has a specific value for any given solvent. Physical quantities without appropriate units have no significance. So, never write \[{{K}_{f}}\] without units and use proper symbols for different physical quantities.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE