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Question

A solution of two components containing n1moles of the 1st component and n2 moles of the second component is prepared. M1and M2 are the molecular weights of component 1 and 2 respectively. If d is the density of the solution in gmL-1, C2 is the molarity and x2 is the mole fraction of the 2nd component, then C2 can be expressed as:


A

C2=1000x2M1+x2M2-M1

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B

C2=dx2M2+x2M2-M1

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C

C2=dx1M2+x2M2-M1

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D

C2=1000dx2M1+x2M2-M1

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Solution

The correct option is D

C2=1000dx2M1+x2M2-M1


  1. Given quantities for the 1st component - number of moles - n1, molecular weight - M1

Given quantities for the 2nd component (solute) - number of moles - n2, molecular weight - M2, mole fraction - x2

2. Calculation of molarity of 2nd component C2 -

Molarity=numberofmolesofsolutevolumeofsolutioninmL×1000(1)

Step 1 - Calculation of moles of 2nd component-

Let the total number of moles present in the solution be 1.

n1+n2=1

We know, x2=n2n1+n2

So, x2=n2 (number of moles of solute / 2nd component)

and 1-x2=n1

Step 2 - Calculation of mass of solution and solute -

Number of moles of solute / 2nd component =x2

So, mass =x2M2 g

Mass of 1st component =1-x2M1 g

Mass of the solution =x2M2+1-x2M1 g

Step 3 - Calculation of volume of the solution -

volume=massdensity

Volume of solution =x2M2+1-x2M1d mL

Step 4- Calculation of molarity of 2nd component C2 - Putting the values of the number of moles of solute and volume of solution in equation 1, we get-C2=1000dx2M1+x2M2-M1

Hence, option D is the correct answer.


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