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Q.

At 10°C, the osmotic pressure of urea solution was formed to be 500 mm. The solution is diluted 'x' times and the temperature raised to 25°C when the osmotic prssure was noticed to be 105.3mm, then 'x' is

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a

3

b

4

c

5

d

12

answer is C.

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Detailed Solution

I(before dilution)                           II(after dilution)

 

π1= 500mm                                    π2= 105.3mm

T1 = (10+273)K                                T2 = (25+273)K

V1 = 1 lit                                            V2 = x lit

large pi =CST\\frac{pi_1}{pi_2}=frac{C_1T_1}{C_2T_2}
large because

the amount of urea remains constant , Wt. and GMW of urea remain constant

large therefore frac{pi_1}{pi_2} =frac{(frac{w}{GMW}Xfrac{1}{1})XT_1}{(frac{w}{GMW}Xfrac{1}{x})XT_2}
large frac{pi_1}{pi_2}=frac{xT_1}{T_2}\frac{500}{105.3}=frac{x(283)}{298}
large x=frac{500X298}{105.3X283}

x=5

large therefore

the solution  is diluted by 5 times

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