JEE Main · 2020 · Shift-IhardMOLE-151

A solution of two components containing n1 moles of 1st component and n2 moles of 2nd component. M1, M2 are molecular…

Some Basic Concepts (Mole Concept) · Class 11 · JEE Main Previous Year Question

Question

A solution of two components containing n1n_1 moles of 1st component and n2n_2 moles of 2nd component. M1M_1, M2M_2 are molecular weights. If dd is density in g/mL, C2C_2 is molarity and x2x_2 is mole fraction of 2nd component, then C2C_2 can be expressed as:

Options
  1. a

    C2=1000x2M1+x2(M2−M1)C_2=\frac{1000x_2}{M_1+x_2(M_2-M_1)}

  2. b

    C2=dx2M1+x2(M2−M1)C_2=\frac{dx_2}{M_1+x_2(M_2-M_1)}

  3. c

    C2=1000dx2M1+x2(M2−M1)C_2=\frac{1000dx_2}{M_1+x_2(M_2-M_1)}

    ✓
  4. d

    C2=dx1M2+x2(M2−M1)C_2=\frac{dx_1}{M_2+x_2(M_2-M_1)}

Correct Answerc

C2=1000dx2M1+x2(M2−M1)C_2=\frac{1000dx_2}{M_1+x_2(M_2-M_1)}

Detailed Solution

🧠 Derive molarity from mole fractions and density Take 11 mole of mixture as base. Solute moles =x2= x_2, solvent moles =1−x2= 1 - x_2. Total mass =(1−x2)M1+x2M2=M1+x2(M2−M1)= (1-x_2)M_1 + x_2 M_2 = M_1 + x_2(M_2 - M_1).

🗺️ Build the formula Volume of solution (in mL) =mass/d=[M1+x2(M2−M1)]/d= \text{mass}/d = [M_1 + x_2(M_2-M_1)] / d. Volume in litres =[M1+x2(M2−M1)]/(1000d)= [M_1 + x_2(M_2-M_1)] / (1000 d).

Molarity: C2=x2V=1000 d x2M1+x2(M2−M1).C_2 = \frac{x_2}{V} = \frac{1000\,d\,x_2}{M_1 + x_2(M_2 - M_1)}.

So option (c) is correct.

⚠️ Common mistake Dropping the factor of 10001000 when converting mL to L. That is exactly what makes options (a) and (b) wrong.

Answer: (c)\boxed{\text{Answer: (c)}}

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