Solution:

Identification of given values:

- Aqueous solution of non-electrolyte CnH2nO
- Temperature (T) = 27°C = 300 K (conversion factor: 1°C = 273 K)
- Osmotic pressure (π) = 24.63 atm

Calculation of Van't Hoff factor (i):

The Van't Hoff factor (i) is the ratio of the observed osmotic pressure to the expected osmotic pressure of an ideal solution, which is calculated using the formula:

π = iMRT

where M is the molarity of the solution and R is the gas constant.

Since the given solution is 6% by weight, we assume that 100 g of the solution contains 6 g of the solute. Therefore, the molarity of the solution (M) can be calculated as follows:

M = (6 g / molecular weight of solute) / (100 g of solution / 1000 mL of solution)

= 0.06 / (molecular weight of solute)

Assuming that the solute dissociates into n particles in solution, the expected osmotic pressure (π0) of an ideal solution can be calculated using the formula:

π0 = nMRT

Since the given solute is a non-electrolyte, n = 1. Therefore, we have:

π0 = MRT

Substituting the given values, we get:

π0 = (0.06 / molecular weight of solute) x R x 300

i = π / π0

Substituting the given and calculated values, we get:

i = 24.63 / [(0.06 / molecular weight of solute) x R x 300]

Calculation of molecular weight:

The molecular weight (Mw) of the non-electrolyte can be calculated using the formula:

Mw = [(RT) / (πV2)] x i

where V is the volume of the solution in liters.

Assuming that 100 g of the solution has a volume of 100 mL, we have:

V = 100 mL / 1000 mL/L

= 0.1 L

Substituting the given and calculated values, we get:

Mw = [(R x 300) / (24.63 x 0.12)] x i

Calculation of number of atoms:

The given non-electrolyte is represented by the formula CnH2nO. Therefore, its molecular weight can be expressed as follows:

Mw = n(12.01) + 2n(1.01) + 16.00

Simplifying the above equation, we get:

Mw = 14.02n + 16.00

Equating this expression with the calculated value of Mw, we can solve for n:

14.02n + 16.00 = [(R x 300) / (24.63 x 0.12)] x i

n = {[ (R x 300) / (24.63 x 0.12)] x i - 16.00} / 14.02

Once we have the value of n, we can calculate the total number of atoms in one molecule of the non-electrolyte using the formula:

Total number of atoms = n x (number of

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