How to calculate osmotic pressure of mixture of solvents?
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This example problem demonstrates how to calculate the osmotic pressure of a solution of sucrose (table sugar) in water.
Osmotic Pressure Problem
What is the osmotic pressure of a solution prepared by adding 13.65 g of sucrose (C12H22O11) to enough water to make 250 mL of solution at 25 °C?
Solution:
Osmosis and osmotic pressure are related. Osmosis is the flow of a solvent into a solution through a semipermiable membrane. Osmotic pressure is the pressure that stops the process of osmosis. Osmotic pressure is a colligative property of a substance since it depends on the concentration of the solute and not its chemical nature.
Osmotic pressure is expressed by the formula:
Π = iMRT (note how it resembles the PV = nRT form of the Ideal Gas Law)
where
Π is the osmotic pressure in atm
i = van 't Hoff factor of the solute
M = molar concentration in mol/L
R = universal gas constant = 0.08206 L·atm/mol·K
T = absolute temperature in K
Step 1: - Find concentration of sucrose.
To do this, look up the atomic weights of the elements in the compound:
From the periodic table:
C = 12 g/mol
H = 1 g/mol
O = 16 g/mol
Use the atomic weights to find the molar mass of the compound. Multiply the subscripts in the formula times the atomic weight of the element. If there is no subscript, it means one atom is present.
molar mass of sucrose = 12(12) + 22(1) + 11(16)
molar mass of sucrose = 144 + 22 + 176
molar mass of sucrose = 342
nsucrose = 13.65 g x 1 mol/342 g
nsucrose = 0.04 mol
Msucrose = nsucrose/Volumesolution
Msucrose = 0.04 mol/(250 mL x 1 L/1000 mL)
Msucrose = 0.04 mol/0.25 L
Msucrose = 0.16 mol/L
Step 2: - Find absolute temperature. Remember, absolute temperature is always given in Kelvin. If the temperature is given in Celsius or Fahrenheit, convert it to Kelvin.
T = °C + 273
T = 25 + 273
T = 298 K
Step 3: - Determine the van 't Hoff factor
Sucrose does not dissociate in water; therefore the van 't Hoff factor = 1.
Step 4: - Find osmotic pressure by plugging the values into the equation.
Π = iMRT
Π = 1 x 0.16 mol/L x 0.08206 L·atm/mol·K x 298 K
Π = 3.9 atm
Answer:
The osmotic pressure of the sucrose solution is 3.9 atm.
This example problem demonstrates how to calculate the osmotic pressure of a solution of sucrose (table sugar) in water.
Osmotic Pressure Problem
What is the osmotic pressure of a solution prepared by adding 13.65 g of sucrose (C12H22O11) to enough water to make 250 mL of solution at 25 °C?
Solution:
Osmosis and osmotic pressure are related. Osmosis is the flow of a solvent into a solution through a semipermiable membrane. Osmotic pressure is the pressure that stops the process of osmosis. Osmotic pressure is a colligative property of a substance since it depends on the concentration of the solute and not its chemical nature.
Osmotic pressure is expressed by the formula:
Π = iMRT (note how it resembles the PV = nRT form of the Ideal Gas Law)
where
Π is the osmotic pressure in atm
i = van 't Hoff factor of the solute
M = molar concentration in mol/L
R = universal gas constant = 0.08206 L·atm/mol·K
T = absolute temperature in K
Step 1: - Find concentration of sucrose.
To do this, look up the atomic weights of the elements in the compound:
From the periodic table:
C = 12 g/mol
H = 1 g/mol
O = 16 g/mol
Use the atomic weights to find the molar mass of the compound. Multiply the subscripts in the formula times the atomic weight of the element. If there is no subscript, it means one atom is present.
molar mass of sucrose = 12(12) + 22(1) + 11(16)
molar mass of sucrose = 144 + 22 + 176
molar mass of sucrose = 342
nsucrose = 13.65 g x 1 mol/342 g
nsucrose = 0.04 mol
Msucrose = nsucrose/Volumesolution
Msucrose = 0.04 mol/(250 mL x 1 L/1000 mL)
Msucrose = 0.04 mol/0.25 L
Msucrose = 0.16 mol/L
Step 2: - Find absolute temperature. Remember, absolute temperature is always given in Kelvin. If the temperature is given in Celsius or Fahrenheit, convert it to Kelvin.
T = °C + 273
T = 25 + 273
T = 298 K
Step 3: - Determine the van 't Hoff factor
Sucrose does not dissociate in water; therefore the van 't Hoff factor = 1.
Step 4: - Find osmotic pressure by plugging the values into the equation.
Π = iMRT
Π = 1 x 0.16 mol/L x 0.08206 L·atm/mol·K x 298 K
Π = 3.9 atm
Answer:
The osmotic pressure of the sucrose solution is 3.9 atm.
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