What mass of sucrose (C12H22O11) would you combine with 5.28 102 g of water to make a solution with an osmotic pressure of 9.14 atm at 298 K? (Assume a density of 1.0 g/mL for the solution.)

I came up with 67.5 but no luck...help please!!

67.5g looks ok to me.

To solve this question, we need to use the formula for osmotic pressure:

π = i * M * R * T

Where:
π = osmotic pressure
i = van't Hoff factor (the number of particles into which a compound dissociates in a solution)
M = molar concentration of solute (in mol/L)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (K)

In this case, we are given the osmotic pressure (π), temperature (T), and the density of the solution. We need to find the molar concentration (M) of the sucrose.

To calculate the molar concentration, we first need to find the number of moles of water we have. We can do this by dividing the mass of water by its molar mass.

The molar mass of water (H2O) is:
(2 * atomic mass of hydrogen) + (1 * atomic mass of oxygen)
= (2 * 1.008 g/mol) + (1 * 16.00 g/mol)
= 18.016 g/mol

Number of moles of water = mass of water / molar mass of water
= 5.28 x 10^2 g / 18.016 g/mol

Next, we need to find the volume of the solution. The density of the solution is given as 1.0 g/mL, which means for every 1 milliliter of the solution, there is 1.0 gram of the solution. Therefore, the volume of the solution is equal to the mass of the solution.

Volume of solution = mass of water + mass of sucrose
= 5.28 x 10^2 g + mass of sucrose

Since the density of the solution is given as 1.0 g/mL, the volume of the solution is also equal to the mass of the solution.

Now we can calculate the molar concentration of sucrose (M) using the formula:

M = moles of solute / volume of solution (in L)

We have already calculated the number of moles of water. Let's call the number of moles of sucrose 'n' for now.

M = n / (5.28 x 10^2 g + n)

Finally, we can substitute the values into the osmotic pressure formula and solve for 'n':

9.14 atm = i * M * R * T
9.14 atm = (1, since sucrose doesn't dissociate) * (n / (5.28 x 10^2 g + n)) * 0.0821 L·atm/(mol·K) * 298 K

Simplifying the equation:

9.14 = (n / (5.28 x 10^2 + n)) * 0.0821 * 298

Now, we can solve this equation for 'n' to find the number of moles of sucrose:

9.14 * (5.28 x 10^2 + n) = 0.0821 * 298 * n

After solving this equation for 'n', you can calculate the mass of sucrose (in grams) by multiplying the number of moles of sucrose by its molar mass (342.3 g/mol).

I hope this helps! Let me know if you have any more questions.