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A 4% solution of non volatile solute is isotonic with 0.702% urea solution calculate molar mass of nin volatile solute?
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A 4% solution of non volatile solute is isotonic with 0.702% urea solu...
Solution:

Given,
4% solution of non-volatile solute is isotonic with 0.702% urea solution

To find out: Molar mass of non-volatile solute

Let's start solving the problem step by step.

What is an isotonic solution?
- An isotonic solution is a solution having the same osmotic pressure as of the other solution with which it is being compared.

What is Osmotic pressure?
- Osmotic pressure is the pressure that needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane.

Formula to calculate osmotic pressure:
π = (n/V)RT
Where,
π = osmotic pressure
n = number of moles of solute
V = volume of solution
R = Universal gas constant
T = Temperature in Kelvin

What is non-volatile solute?
- Non-volatile solute is a solute which does not evaporate or vaporize on heating.

Let's calculate the osmotic pressure of the given solution.

Osmotic pressure of the solution containing non-volatile solute:
π1 = (n1/V1)RT

Osmotic pressure of the urea solution:
π2 = (n2/V2)RT

As the solutions are isotonic, both the solutions have the same osmotic pressure.
π1 = π2

Therefore,
(n1/V1)RT = (n2/V2)RT

n1/V1 = n2/V2

Given,
4% solution of non-volatile solute = 4 g of solute in 100 mL of solution
0.702% urea solution = 0.702 g of urea in 100 mL of solution

We have to calculate the molar mass of non-volatile solute, which can be calculated as follows:

Molar mass of non-volatile solute = (1000 x mass of solute in grams) / (volume of solution in mL x number of moles of solute)

To calculate the number of moles of solute, we will use the formula:
Number of moles = mass of solute / molar mass

From the given data, we can calculate the number of moles of urea as follows:

Number of moles of urea = 0.702 / 60 = 0.0117

As both the solutions are isotonic, the number of moles of non-volatile solute in 100 mL of the solution will be equal to the number of moles of urea in 100 mL of the solution.
Number of moles of non-volatile solute = 0.0117

Now, let's substitute the values in the formula to calculate the molar mass of non-volatile solute.

Molar mass of non-volatile solute = (1000 x 4) / (100 x 0.0117)
Molar mass of non-volatile solute = 342.74 g/mol

Therefore, the molar mass of the non-volatile solute is 342.74 g/mol.

Conclusion:
- The molar mass of the non-volatile solute is 342.74 g/mol.
- The solution containing 4% of non-volatile solute and 0.702% of urea is isotonic.
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