HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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# Derive the Relationship Between Relative Lowering of Vapour Pressure and Molar Mass of Nonvolatile Solute. - HSC Science (Computer Science) 12th Board Exam - Chemistry

ConceptColligative Properties and Determination of Molar Mass Relative Lowering of Vapour Pressure

#### Question

Derive the relationship between relative lowering of vapour pressure and molar mass of nonvolatile solute.

#### Solution

Let W2 g of solute of molar mass M2 be dissolved in W1 g of solvent of molar mass M1 . Hence number of
mole of solvent n1 and number of mole of solute n2 in solution.

n_1=W_1/M_1  and  n_2=W_2/M_2 (because "Number of moles (n)"="mass of the substance"/"molar mass of the substance")

The mole fraction of solute x2 is given by

x_2=n_2/(n_1+n_2)

x_2=(W_2/M_2)/(W_1/M_1+W_2/M_2) .....(1)

For a solution of two components A1 and A2 with mole fraction x1 and x2 respectively, if the vapour pressure of pure component A1 is

P_1^0  and that of component A2 is p_2^0 The relative lowering of vapour pressure is given by,

(Deltap)/p_0^1=(p_1^0-p)/p_1^0

(Deltap)/p_0^1=(p_1^0x_2)/p_1^0

(Deltap)/p_0^1=x_2 .....(2)

Combining equations (1) and (2)

(Deltap)/p_0^1=(p_1^0-p)/p_1^0=x_2=(W_2/M_2)/(W_1/M_1+W_2/M_2)

For dilute solutions n1 >> n2. Hence n2 may be neglected in comparison with n1 in equation (1) and thus equation (3) becomes

(Deltap)/p_0^1=n_2/n_1=(W_2/M_2)/(W_1/M_1)=(W_2M_1)/(W_1M_2)

Knowing the masses of non-volatile solute and the solvent in dilute solutions and by determining experimentally vapour pressure of pure solvent and the solution, it is possible to determine molar mass of a non-volatile solute.

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#### APPEARS IN

2012-2013 (March) (with solutions)
Question 2.7 | 2.00 marks
2016-2017 (March) (with solutions)
Question 2.4 | 2.00 marks

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Solution Derive the Relationship Between Relative Lowering of Vapour Pressure and Molar Mass of Nonvolatile Solute. Concept: Colligative Properties and Determination of Molar Mass - Relative Lowering of Vapour Pressure.
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