An aqueous dextrose solution having a density of 1.04 g/cm³ freezes at -1.15^$\circ$C. Find the osmotic pressure of this solution at 25^$\circ$C. K_f of water is 1.86 ^$\circ$C/m; molecular mass of dextrose = 180.16 g/mol. A) 12.9 atm B) 13.8 atm C) 14.1 atm D) 15.1 atm E) 120 atm

Question

Quizplus · Accepted Answer

First, we need to calculate the molality of the solution:

ΔT = i*Kf*m
where ΔT = 1.15°C (we convert Fahrenheit to Celsius), Kf = 1.86°C/m, and i = 1 since dextrose does not dissociate in water. Solving for m, we get:

m = ΔT/(i*Kf) = 0.617 mol/kg

Next, we need to calculate the molar concentration of the solution:

density = mass/volume
1.04 g/cm^3 = (molar mass of dextrose * moles of dextrose)/volume of solution
Solving for moles of dextrose, we get:

moles of dextrose = density * volume of solution / molar mass of dextrose
Assuming 1 L of solution, we have:

moles of dextrose = 1.04 g/cm^3 * 1000 cm^3 / 180.16 g/mol = 5.77 mol

And the molar concentration is:

Molarity = moles of solute/volume of solution (in L)
Molarity = 5.77 mol/L

Finally, we can calculate the osmotic pressure using the van't Hoff equation:

π = i*MRT
where i = 1, M = 5.77 mol/L, R = 0.08206 L*atm/(mol*K), and T = 25°C + 273.15 = 298.15 K. Solving for π, we get:

π = i*MRT = 1*5.77 mol/L*0.08206 L*atm/(mol*K)*298.15 K = 14.1 atm

Therefore, the answer is choice C.

An Aqueous Dextrose Solution Having a Density of 1 ∘\circ∘ C Find the Osmotic Pressure of This Solution at 25

An Aqueous Dextrose Solution Having a Density of 1 $\circ$ C Find the Osmotic Pressure of This Solution at 25