Answer: The pressure that must be applied to the apparatus is 0.239 atm
Explanation:
To calculate the osmotic pressure, we use the equation for osmotic pressure, which is:
[tex]\pi=iMRT[/tex]
or,
[tex]\pi=i\times \frac{m_{solute}}{M_{solute}\times V_{solution}\text{ (in L)}}}\times RT[/tex]
where,
[tex]\pi[/tex] = osmotic pressure of the solution
i = Van't hoff factor = 1 (for non-electrolytes)
[tex]m_{solute}[/tex] = mass of sucrose = 3.40 g
[tex]M_{solute}[/tex] = molar mass of sucrose = 342.3 g/mol
[tex]V_{solution}[/tex] = Volume of solution = 1 L
R = Gas constant = [tex]0.0821\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the solution = [tex]20^oC=[20+273]K=293K[/tex]
Putting values in above equation, we get:
[tex]\pi =1\times \frac{3.40g}{342.3g/mol\times 1}\times 0.0821\text{ L. atm }mol^{-1}K^{-1}\times 293K\\\\\pi =0.239atm[/tex]
Hence, the pressure that must be applied to the apparatus is 0.239 atm
