Question

A 5% solution (wt/volume) of cane sugar is isotonic with 0.877% (wt/volume) of urea solution.Find the molecular weight of urea,if molecular weight of sugar is 342.

Answer 1

Answer : The molecular weight of urea is, 60 g/mole

Solution :

Isotonic solutions have same osmotic pressure at same temperature.

$\pi_1=\pi_2\\\\\frac{n_1RT}{V_1}=\frac{n_2RT}{V_2}\\\\\frac{n_1}{V_1}=\frac{n_2}{V_2}\\\\C_1=C_2\\\\\frac{w_1}{M_1V_1}=\frac{w_2}{M_2V_2}$

where,

n = number of moles

w = mass

M = molar mass

V = volume

R = gas constant

T = temperature

Formula used :

$\frac{w_1}{M_1V_1}=\frac{w_2}{M_2V_2}$

where,

$w_1$ = mass of cane sugar = 5 g

$V_1$ = volume of cane sugar = 100 ml = 0.1 L

$M_1$ = molecular weight of cane sugar = 342 g/mole

$w_2$ = mass of urea = 0.877 g

$V_2$ = volume of urea = 100 ml = 0.1 L

$M_2$ = molecular weight of urea = ?

Now put all the given values in the above formula, we get the molecular weight of urea.

$\frac{5g}{342g/mole\times 0.1L}=\frac{0.877g}{M_2\times 0.1L}$

$M_2=59.99g/mole\approx 60g/mole$

Therefore, the molecular weight of urea is, 60 g/mole

Answer 2

Answer:

The molar mass of urea is 60 g/mol.

Explanation:

5g of cane sugar in 100ml of solution

we know that .

For isotonic solution,

Osmotic .Pressure of  sugar cane =P  1

Osmotic .Pressure of  urea  = P 2

When two solutions are isotonic, they have equal osmotic pressures ( π / P)   i.e (P 1 = P 2)

Given -  

molar mass of cane sugar = 342 g

mass of cane sugar = 5 g

0.877 g of urea in 100 ml of solution

molar mass of urea = ?

mass of urea = 0.877

​Let the molecular mass of urea be M (say )

 $P =\frac{n R T }{V} \\ \\P= \frac{W_{b} \\ \\ RT }{{M_{b} \\} V} \\\\W.K.T \\\\ n = \frac{W_{b} \\}{M_{b} \\}\\P_{1} = \frac{W_{b1} \\ \\ RT }{{M\\_{b1} \\} V} \\\\\\P_{2} = \frac{W_{b2} \\ \\ RT }{{M_{b2} \\} V} \\\\\\P_{1} = P_{2}\\\ \frac{W_{b1} \\ \\ RT }{{M_{b1} \\} V} = \frac{W_{b2} \\ \\ RT }{{M_{b2} \\} V} \\\\\\\\\frac{W_{b1} }{M_{b1} } } = \frac{W_{b2} \\ \\ }{{M_{b2} \\} } \\\\\\\\\frac{5}{342} = \frac{0.877}{M} \\\\M = \frac{0.877 * 342}{5}\\M = 59.9$

M = 59.9 g/ mole  ≅ 60 g/mole

for more convenience see the attached attachment