What mass of sucrose should be combined with 491 g of water to make a solution with an osmotic pressure of 8.70 atm at 270 K? (Assume the density of the solution to be equal to the density of the solvent.)
pi = MRT
Substitute for pi, R, and T. Solve for molarity = M.
Then M = moles/L.]
You know L and M, solve for moles.This assumes that the volume of the solution is the same as the volume of the solvent.
Then moles = grams/molar mass. You know moles and molar mass, solve for grams.
65.995
To find the mass of sucrose needed to make a solution with a specific osmotic pressure, we need to use the formula for osmotic pressure and apply it to the given information.
First, let's outline the necessary steps:
1. Convert the given osmotic pressure from atm to Pa.
2. Calculate the molar concentration of the sucrose solution.
3. Use the molar concentration to find the molarity of the sucrose solution.
4. Convert the molarity to moles of sucrose.
5. Convert the moles of sucrose to mass using the molar mass of sucrose.
Let's start by converting the osmotic pressure from atm to Pa:
1 atm = 101325 Pa
Therefore, the osmotic pressure is 8.70 atm * 101325 Pa/atm = 882442.5 Pa.
Next, we need to calculate the molar concentration of sucrose. The formula for osmotic pressure is:
π = MRT
where:
π = osmotic pressure
M = molar concentration
R = ideal gas constant (0.0821 L*atm/mol*K)
T = temperature in Kelvin
We can rearrange this formula to solve for the molar concentration:
M = π / (RT)
Now, substituting the given values:
M = 882442.5 Pa / (0.0821 L*atm/mol*K * 270 K) = 38.16 mol/L
Since we are dealing with a solution, we need to convert the molar concentration to moles of solute per liter of solution. Since the density of the solution is assumed to be equal to the density of the solvent (water), the volume of the solution is equal to the volume of the water, which can be calculated using its mass and density.
Use the density of water to determine the volume:
density of water = 1 g/mL = 1 g/cm^3
volume of water = mass of water / density of water = 491 g / 1 g/cm^3 = 491 mL = 0.491 L
Now, let's calculate the number of moles of sucrose needed in the solution:
moles of sucrose = M * volume of solution = 38.16 mol/L * 0.491 L = 18.73 mol
Finally, we can convert the moles of sucrose to mass using the molar mass of sucrose:
The molar mass of sucrose (C12H22O11) is:
12.01 g/mol (C) + 1.01 g/mol (H) + 16.00 g/mol (O) * 11 = 342.34 g/mol
mass of sucrose = moles of sucrose * molar mass of sucrose = 18.73 mol * 342.34 g/mol ≈ 6,419 g
Therefore, approximately 6,419 grams of sucrose should be combined with 491 grams of water to make a solution with an osmotic pressure of 8.70 atm at 270 K.