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Answer :
Final answer:
To find the molar mass of the solute, we first determine its molarity from the given osmotic pressure. Then, calculating the moles of solute using the solution's volume, we divide the mass of the solute by its moles to obtain the molar mass, approximately 342.5 g/mol. The correct answer is option e ) none of the above.
Explanation:
1. Molarity (M) from Osmotic Pressure (π):
We know the relationship between osmotic pressure (π), molarity (M), temperature (T), and the universal gas constant (R) is:
π = M * R * T
We can rearrange the equation to solve for M:
M = π / (R * T)
2. Moles of Solute (n):
Once we have the molarity (M), we can find the total moles of solute (n) using the formula:
n = M * V
where V is the volume of the solution.
3. Molar Mass (M_solute):
Finally, the molar mass of the solute (M_solute) is calculated by dividing the mass of the solute (m) by the number of moles (n):
M_solute = m / n
Steps with Provided Values:
Known Values:
π (osmotic pressure) = 0.196 atm
R (gas constant) = 0.0821 L atm / K mol
T (temperature) = 298 K
V (volume of solution) = 0.3 dm³ = 0.3 L (converted to liters)
m (mass of solute) = 0.822 g
Calculation:
Step 1:
M = π / (R * T) = 0.196 atm / (0.0821 L atm / K mol * 298 K) = 0.0079 mol/L (approximately)
Step 2:
n = M * V = 0.0079 mol/L * 0.3 L = 0.0024 mol (approximately)
Step 3:
M_solute = m / n = 0.822 g / 0.0024 mol ≈ 342.5 g/mol (approximately)
The molar mass of the solute is approximately 342.5 g/mol.
The correct answer is option e ) none of the above.
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