what is the osmotic pressure at 20 C of a solution made by dissolving 0.69 grams of sucrose C12 H22 O11 in 100 mL of water
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To find the osmotic pressure of a solution, you can use the formula:
π = iCRT
Where:
- π is the osmotic pressure (in atmospheres)
- i is the Van't Hoff factor (which depends on the number of particles generated per unit of solute, in this case, sucrose)
- C is the molar concentration of the solute (in moles per liter)
- R is the ideal gas constant (0.0821 L·atm/mol·K)
- T is the temperature in Kelvin (20°C = 293.15 K)
To calculate the osmotic pressure, follow these steps:
Step 1: Convert grams of sucrose to moles.
The molar mass of sucrose (C12H22O11) is approximately 342.3 g/mol. Divide 0.69 grams by the molar mass to find the number of moles.
0.69 g / 342.3 g/mol = 0.002015 moles
Step 2: Convert milliliters to liters.
Divide 100 mL by 1000 to convert it to liters.
100 mL / 1000 = 0.1 L
Step 3: Calculate the molar concentration (C).
Divide the number of moles by the volume in liters.
C = 0.002015 moles / 0.1 L = 0.02015 M
Step 4: Determine the Van't Hoff factor (i).
Sucrose does not dissociate in water; therefore, the Van't Hoff factor (i) is 1.
Step 5: Convert the temperature to Kelvin.
20°C + 273.15 = 293.15 K
Step 6: Calculate the osmotic pressure (π).
Use the formula:
π = iCRT
π = (1)(0.02015 M)(0.0821 L·atm/mol·K)(293.15 K)
π ≈ 4.95 atm
Therefore, the osmotic pressure at 20°C of the solution containing 0.69 grams of sucrose dissolved in 100 mL of water is approximately 4.95 atm.