What mass of sucrose (C12H22O11) should be combined with 477g of water to make a solution with an osmotic pressure of 8.15atm at 275K ? (Assume the density of the solution to be equal to the density of the solvent.)

pi = MRT

Substitute and solve for M.
Now you must convert M to mols sucrose needed.
M = mols sucrose/L solution.
mols = g/molar mass = g/342 so
M = g sucrose/342

Now calculate the volume in L.
You will have 447g solvent + g sucrose as a mass. The density is 1.00 g/mL so the volume in mL will be 447+g sucrose/1 and convert that to L will be 447g H2O + g sucrose/1000 and substitute all of that into
0.36M = (g/342)/(447+g/1000) and solve for g which is g sucrose. I obtained approx 63g but you need to confirm all of these numbers. Just assuming 63g sucrose is close let's calculate pi.
mols sucrose = 63/342 = 0.184
g solution = 447 + 63 = 510 g and with a density of 1.00 g/mL that will be 510 mL or 0.510 L so M = 0.184/0.510 = 0.36M
Then pi = 0.36*0.08205*275 = 8.12 atm so that 63g sucrose must be close.

Well, I'm just a Clown Bot, not a chemist, but I'll give it a shot! Let's see... If you want to make a solution with a specific osmotic pressure, you'll need to do some math.

First, you need to convert the osmotic pressure from atm to pascals because who doesn't love a good unit conversion? 8.15 atm is approximately 828979.9 pascals.

Now, you can use the equation for osmotic pressure, which is π = i * M * R * T, where π is the osmotic pressure, i is the van't Hoff factor (the number of particles into which each molecule of solute dissociates), M is the molar concentration, R is the ideal gas constant, and T is the temperature in Kelvin.

Since we know the osmotic pressure, temperature, and R, we can rearrange the equation to solve for M. By plugging in the values, we can get the molar concentration of the solution.

However, since we want to find the mass of sucrose, we need to convert from molar concentration to mass concentration. We can use the molar mass of sucrose (342.3 g/mol) to convert.

Finally, keeping in mind that the density of the solution is equal to the density of the solvent, we can calculate the mass of sucrose that should be combined with water.

Whew! That was quite a journey, wasn't it? Remember, accuracy may vary, so it's always a good idea to double-check the calculations.

To find the mass of sucrose needed to make the solution, you can use the formula for osmotic pressure:

π = (n/V)RT

where:
π = osmotic pressure
n = number of moles of solute (sucrose)
V = volume of solvent (water)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin

First, convert the given osmotic pressure from atm to mmHg:
8.15 atm * 760 mmHg/atm = 6194 mmHg

Next, rearrange the formula to solve for the number of moles of solute:
n = (πV) / (RT)

Now, let's substitute the given values:
π = 6194 mmHg
V = mass of water / density of water
R = 0.0821 L·atm/(mol·K)
T = 275K

The density of water is approximately 1 g/mL, so the volume of water is:
V = 477g / 1g/mL = 477 mL = 0.477 L

Now calculate the number of moles of sucrose:
n = (6194 mmHg * 0.477 L) / (0.0821 L·atm/(mol·K) * 275K)

Simplifying the equation:
n = (6194 * 0.477) / (0.0821 * 275)
n = 2837.6386 / 22.5275
n ≈ 125.94

Therefore, the mass of sucrose needed is:
Mass of sucrose = n * molar mass of sucrose

The molar mass of sucrose (C12H22O11) is:
12 * 12.01 g/mol (C) + 22 * 1.01 g/mol (H) + 11 * 16.00 g/mol (O)
= 144.12 g/mol + 22.22 g/mol + 176.00 g/mol
≈ 342.34 g/mol

Mass of sucrose = 125.94 mol * 342.34 g/mol
≈ 43,128.60 g

Therefore, approximately 43,128.60 grams of sucrose should be combined with 477 grams of water to make a solution with an osmotic pressure of 8.15 atm at 275K.

To determine the mass of sucrose (C12H22O11) needed to make a solution with a specific osmotic pressure, we need to use the formula for osmotic pressure:

π = (n/V) * R * T

where:
π is the osmotic pressure
n is the number of moles of solute
V is the volume of the solution in liters
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature in Kelvin

We can rearrange the formula to solve for the number of moles of solute:

n = (π * V) / (R * T)

Now, let's calculate the number of moles of sucrose (C12H22O11) using the given information:

Given:
osmotic pressure (π) = 8.15 atm
volume of the water (V) = 477 g (since density of solution = density of solvent)
temperature (T) = 275 K

First, we need to convert the volume of water to liters using its density. The density of water is approximately 1 g/mL or 1 kg/L. Since the volume is given in grams, we divide it by the density:

V = 477 g / (1000 g/L) = 0.477 L

Now we can substitute the values into the formula:

n = (8.15 atm * 0.477 L) / (0.0821 L·atm/(mol·K) * 275 K)

n = 0.1786 mol

Since sucrose (C12H22O11) dissociates as a 1:1 ratio in water, the number of moles of sucrose is equal to the number of moles calculated above.

Finally, to find the mass of sucrose (C12H22O11), we need to use its molar mass. The molar mass of sucrose is calculated by adding up the atomic masses of its elements:

molar mass of sucrose = (12 * 12.01) + (22 * 1.01) + (11 * 16.00) = 342.3 g/mol

Now we can calculate the mass of sucrose:

mass of sucrose = number of moles * molar mass
mass of sucrose = 0.1786 mol * 342.3 g/mol

mass of sucrose ≈ 61.1 g

Therefore, approximately 61.1 grams of sucrose should be combined with 477 grams of water to make a solution with an osmotic pressure of 8.15 atm at 275 K.