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