What mass of sucrose should be combined with 524 g of water to make a solution with an osmotic pressure of 8.50 atm at 270 K? I keep working this and end up with 68.81g but it is not right, any help?
Assuming the density of water is 1.00 g/cc (which it is not at this concn of sugar solution), 68.81 g is correct. The problem may be that you are reporting to 4 significant figures and you are allowed only three. Try 68.8 g. If that doesn't take care of it, you need the density of water.
To calculate the mass of sucrose needed to make a solution with a specific osmotic pressure, you need to use the formula for the osmotic pressure of a solution:
Π = (n/V)RT
Where:
Π = osmotic pressure
n = number of moles of solute
V = volume of solvent (in liters)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
In this case, the osmotic pressure (Π) is given (8.50 atm) along with the temperature (270 K). Also, since the solution is prepared by dissolving sucrose in water, the number of moles of sucrose will be equal to the number of moles of water, as they are both the solute and solvent.
First, let's convert the given mass of water to its volume using the density of water at this temperature. The density of water at 270 K is approximately 0.994 g/mL.
524 g of water * (1 mL / 0.994 g) = 527.66 mL = 0.52766 L
Now, let's substitute the values into the formula and solve for the number of moles:
8.50 atm = (n / 0.52766 L) * 0.0821 L·atm/(mol·K) * 270 K
Simplifying the equation, we have:
8.50 = (n / 0.52766) * 0.0821 * 270
Let's solve for n:
n = (8.50 * 0.52766) / (0.0821 * 270)
n ≈ 1.152 mol
Since the number of moles of sucrose is equal to the number of moles of water, we can use the molar mass of sucrose (342.3 g/mol) to calculate the mass:
Mass of sucrose = number of moles * molar mass
Mass of sucrose ≈ 1.152 mol * 342.3 g/mol
Mass of sucrose ≈ 394.11 g
Therefore, the mass of sucrose that should be combined with 524 g of water to make a solution with an osmotic pressure of 8.50 atm at 270 K is approximately 394.11 g, not 68.81 g.