What is the osmotic pressure of a solution containing 25.7 g of sugar (C12H22O11) in one liter of solution at 20°C?
pi = MRT
Then M = moles/L and
moles = grams/molar mass.
To calculate the osmotic pressure of a solution, you can use the formula:
π = i * M * R * T
Where:
- π represents the osmotic pressure
- i is the van't Hoff factor
- M is the molarity of the solute in mol/L
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
First, let's determine the molarity of the solution.
Molar mass of C12H22O11 (sugar) = (12 * 12.01 g/mol) + (22 * 1.01 g/mol) + (11 * 16.00 g/mol)
= 144.12 g/mol
Now, we can calculate the molarity (M):
M = (mass of solute)/(molar mass)
= 25.7 g / 144.12 g/mol
≈ 0.1785 mol/L
Next, convert the temperature to Kelvin:
T(K) = T(°C) + 273.15
= 20°C + 273.15
= 293.15 K
Now, we will substitute the values into the osmotic pressure formula:
π = i * M * R * T
Since sugar does not dissociate into ions in water, the van't Hoff factor (i) for sugar is 1.
Substituting the values into the formula:
π = 1 * 0.1785 mol/L * 0.0821 L·atm/(mol·K) * 293.15 K
Calculating:
π ≈ 4.16 atm
Therefore, the osmotic pressure of the solution containing 25.7 g of sugar in one liter of solution at 20°C is approximately 4.16 atm.
To find the osmotic pressure of a solution, we can use the formula:
π = MRT
Where:
- π represents the osmotic pressure
- M represents the molarity of the solution
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
First, we need to calculate the molarity (M) of the solution. Molarity is defined as the number of moles of solute per liter of solution.
To determine the number of moles of sugar (C12H22O11) in 25.7 g, we need to know the molar mass of sugar.
The molar mass of C12H22O11 can be calculated by adding up the atomic masses of carbon (12.01 g/mol), hydrogen (1.01 g/mol), and oxygen (16.00 g/mol) according to the chemical formula.
Molar mass of C12H22O11 = (12 * 12.01) + (22 * 1.01) + (11 * 16.00) = 342.34 g/mol
Now we can calculate the number of moles using the formula:
Moles of sugar = Mass of sugar / Molar mass of sugar
Moles of sugar = 25.7 g / 342.34 g/mol
Next, we convert the temperature of 20°C to Kelvin:
Temperature in Kelvin = 20°C + 273.15
Lastly, we can substitute the values into the osmotic pressure equation:
π = MRT
π = (moles of sugar / volume of solution) * (0.0821 L·atm/(mol·K)) * (temperature in Kelvin)
Since we have 25.7 g of sugar in 1 liter of solution, the volume of the solution is 1 L.
π = (moles of sugar / 1 L) * (0.0821 L·atm/(mol·K)) * (temperature in Kelvin)
Now plug in the values you calculated to find the osmotic pressure (π).