Question

A solution containing 34.2 g of sugar dissolved in 1 litre of water has an osmotic pressure of 2.522 atmospheres at 20°C. Calculate the value of gas constant, R.

Answer 1

Given: Mass of sugar = 34.2 g

Volume of solution = 1 L = 1 dm³

Osmotic pressure (π) = 2.522 atm

Temperature (T) = 20°C = 293 K

Molar mass of sugar (sucrose, C₁₂H₂₂O₁₁) = 342 g/mol

Moles of sugar (n) = `"Mass"/"Molar mass"`

= `34.2/342`

= 0.1 mol

By using osmotic pressure formula,

`pi = (nRT)/V`

R = `(pi V)/(n T)`

R = `(2.522 xx 1)/(0.1 xx 293)`

R = `2.522/29.3`

R = 0.086 L atm mol⁻¹ K⁻¹