What mass of sucrose (C12H22O11) should be combined with 520 g of water to make a solution with an osmotic pressure of 8.15 atm at 275 K ? (Assume the density of the solution to be equal to the density of the solvent.)

We need 64.2 grams of sucrose

Explanation:

Step 1: Data given

Mass of water = 520 grams = 0.520 kg

Osmotic pressure = 8.15 atm

Temperature = 275 K

Step 2: Calculate molar concentration

Osmotic pressure can be defined as followed:

π = i*M*R*T

⇒π = the osmotic pressure = 8.15 atm

⇒i = the van't Hoff factor of sucrose = 1

⇒M = the molar concentration

⇒ R = the gas constant = 0.08206 L*atm/mol*K

⇒ T = the temperature = 275 K

M = 0.361 M

Step 3: Calculate volume of water

Volume = mass / density

Volume = 520 grams / 1g/mL

Volume = 520 mL

Step 4: Calculate moles of sucrose

Moles sucrose = molar concentration * volume

Moles sucrose = 0.361 M * 0.520 L

Moles sucrose = 0.1877 moles

Step 5: Calculate mass of sucrose

Mass of sucrose = moles sucrose * molar mass sucrose

Mass sucrose = 0.1877 moles * 342.3 g/mol

Mass sucrose = 64.2 grams

We need 64.2 grams of sucrose