A 5% solution (by mass) of cane sugar is isotonic with 0.877% solution of substance X. Find the molecular weight of X.

Dear student

The two solutions are said to be isotonic if they have same osmotic pressure(Π). Means the osmotic pressure of cane sugar solution is equal to the osmotic pressure of ammonia solution.

Let the osmotic pressure of cane sugar solution is Π1 and osmotic pressure of urea is Π2.

according to the question Π1 =  Π2

Π1 = W1 RT/M1V  and  Π2 = W2 RT/M2V 

W1 = wt. of cane sugar in 100 ml solution, M1 =mol. wt. of cane sugar, W2 = wt. of urea in 100 ml. solution M2= mol. wt. of urea.By the value given in question,

W1 = 5 , W2 =0. 877  V=100ml, M1 is given =342  M2 =?

Π1 =  Π2 , W1 RT/M1V  =  W2 RT/M2V  putting the value of W1 , W2 and M1 we can get the value of M2 = W2/W1 *M1

 = 0.877 * 342gram /5= 60gram

Regards

Arun (askIITians forum expert)