What mass of sucrose (C12H22O11) would you combine with 5.00 * 10...

Question

What mass of sucrose (C12H22O11) would you combine with 5.00 * 10^2 g of water to make a solution with an osmotic pressure of 8.55 atm at 298 K? (Assume a density of 1.0 g/mL for the solution.)

Accepted Answer

Identify the formula for osmotic pressure: $$ \Pi = iMRT $$, where $$ \Pi  is $$the osmotic pressure, $$ i  is $$the van't Hoff factor, $$ M  is $$the molarity, $$ R  is $$the ideal gas constant, and $$ T  is $$the temperature in Kelvin.. Since sucrose is a non-electrolyte, the van't Hoff factor $$ i = 1 . $$Rearrange the formula to solve for molarity $$ M $$: $$ M = \frac{\Pi}{iRT} .. $$Substitute the given values into the rearranged formula: $$ \Pi = 8.55 	ext{ atm} $$, $$ R = 0.0821 	ext{ L atm/mol K} $$, and $$ T = 298 	ext{ K} . $$Calculate $$ M .. $$Use the definition of molarity $$ M = \frac{	ext{moles of solute}}{	ext{liters of solution}}  to $$find the moles of sucrose. Assume the volume of the solution is approximately the volume of water, which is $$ 500 	ext{ mL} = 0.500 	ext{ L} .. $$Calculate the mass of sucrose using its molar mass $$ C_{12}H_{22}O_{11} \approx 342.3 	ext{ g/mol} $$ and the moles of sucrose found in the previous step.

What mass of sucrose (C12H22O11) would you combine with 5.00 * 10^2 g of water to make a solution with an osmotic pressure of 8.55 atm at 298 K? (Assume a density of 1.0 g/mL for the solution.)

Concetti chiave

Osmotic Pressure

Molarity

Van 't Hoff Factor