2.56g of sulphur in 100ml solution shows osmotic pressure of 2.463 atm at 27 degree celcius .how many sulphur atoms associated in colloidal solution ? ( solution constant=0.0821atm)

To determine the number of sulfur atoms associated in the colloidal solution, we can use the principles of osmotic pressure and the ideal gas law. The osmotic pressure of a solution is related to the concentration of solute particles in that solution. Here’s how we can break it down step by step.

Understanding Osmotic Pressure

Osmotic pressure (\( \Pi \)) can be described by the formula:

\( \Pi = i \cdot C \cdot R \cdot T \)

Where:

• \( \Pi \) = osmotic pressure (in atm)
• i = van 't Hoff factor (number of particles the solute dissociates into)
• C = molarity of the solution (in mol/L)
• R = ideal gas constant (0.0821 atm·L/(mol·K))
• T = temperature in Kelvin (K)

Step 1: Convert Temperature to Kelvin

The temperature given is 27 degrees Celsius. To convert this to Kelvin, we add 273.15:

\( T = 27 + 273.15 = 300.15 \, K \)

Step 2: Calculate Molarity (C)

We need to find the molarity of the sulfur solution. First, we calculate the number of moles of sulfur:

\( \text{Moles of S} = \frac{\text{mass}}{\text{molar mass}} \)

The molar mass of sulfur (S) is approximately 32.07 g/mol. Thus:

\( \text{Moles of S} = \frac{2.56 \, g}{32.07 \, g/mol} \approx 0.0799 \, mol \)

Next, we calculate the molarity (C) of the solution:

\( C = \frac{\text{moles}}{\text{volume in L}} = \frac{0.0799 \, mol}{0.1 \, L} = 0.799 \, mol/L \)

Step 3: Substitute Values into the Osmotic Pressure Equation

Now we can substitute the values into the osmotic pressure equation. We know \( \Pi = 2.463 \, atm \), \( R = 0.0821 \, atm·L/(mol·K) \), and \( T = 300.15 \, K \):

\( 2.463 = i \cdot 0.799 \cdot 0.0821 \cdot 300.15 \)

Step 4: Solve for the van 't Hoff Factor (i)

Rearranging the equation to solve for \( i \):

\( i = \frac{2.463}{0.799 \cdot 0.0821 \cdot 300.15} \)

Calculating this gives:

\( i \approx 0.099 \)

Step 5: Determine the Number of Sulfur Atoms

The van 't Hoff factor \( i \) indicates how many particles the solute dissociates into. In this case, since sulfur typically exists as individual atoms in a colloidal solution, we can assume that \( i \) represents the number of sulfur atoms per molecule. Therefore, if \( i \) is approximately 0.099, it suggests that each sulfur molecule contributes about 0.099 sulfur atoms to the solution.

To find the total number of sulfur atoms in the solution, we can multiply the number of moles of sulfur by Avogadro's number (\( 6.022 \times 10^{23} \, atoms/mol \)):

\( \text{Total atoms} = 0.0799 \, mol \times 6.022 \times 10^{23} \, atoms/mol \approx 4.8 \times 10^{22} \, atoms \)

Thus, the total number of sulfur atoms associated in the colloidal solution is approximately \( 4.8 \times 10^{22} \) atoms. This calculation illustrates how osmotic pressure can be used to infer the behavior of solute particles in a solution.