Question

A solution of 6.85g of a carbohydrate in 100.0g of water has a density of 1.024 g/mL and an osmotic pressure of 4.61 atm at 200C. Calculate molar mass of the carbohydrate

Answer 1

Answer:

$M=233.62g/mol$

Explanation:

Hello,

In this case, since the solute is a carbohydrate the van't Hoff factor is 1, therefore, osmotic pressure, defined via:

$\Pi=MRT$

Allows us to compute the molarity of the carbohydrate in the solution:

$M=\frac{\Pi}{RT}=\frac{4.61atm}{0.082\frac{atm*L}{mol*K}*(200+273)K}=0.281\frac{mol}{L}$

Next, with the computed molarity, we can compute the volume in liters of the solution with the mass of the carbohydrate and water:

$V=(6.85+100.0)g*\frac{1mL}{1.024g}*\frac{1L}{1000mL} =0.104L$

After that, we compute the moles of the carbohydrate:

$n=0.281\frac{mol}{L}* 0.104L=0.0273mol$

Finally, we compute the molar mass with the obtained moles and the given mass of carbohydrate:

$M=\frac{6.85g}{0.0293mol}\\ \\M=233.62g/mol$

Regards.

Answer 2

The molar mass of the carbohydrate is 552.41 g/mol

We'll begin by calculating the volume of the solution.

• Mass of carbohydrate = 6.85 g

• Mass of water = 100 g

• Mass of solution = 6.85 + 100 = 106.85 g

• Density of solution = 1.024 g/mL

• Volume of solution =?

Volume = mass / density

Volume of solution = 106.85 / 1.024

Volume of solution = 104.35 mL

Next, we shall determine the molarity of the solution.

• Temperature (T) = 200 °C = 200 + 273 = 473 K

• Van't Hoff's factor (i) = 1 (non-electrolyte)

• Osmotic pressure (π) = 4.61 atm

• Gas constant (R) = 0.08206 atm.L/Kmol

• Molarity (M) =?

π = iMRT

4.61 = 1 × 0.0821 × M × 473

4.61 = 38.8333 × M

Divide both side by 38.8333

M = 4.61 / 38.8333

M = 0.119 M

Next, we shall determine the number of mole of the carbohydrate.

• Molarity = 0.119 M

• Volume = 104.35 mL = 104.35 / 1000 = 0.10435 L

Mole of carbohydrate =?

Mole = Molarity x Volume

Mole of carbohydrate = 0.119 × 0.10435

Mole of carbohydrate = 0.0124 mole

Finally, we shall determine the molar mass of the carbohydrate.

• Mole of carbohydrate = 0.0124 mole

• Mass of carbohydrate = 6.85 g

• Molar mass of carbohydrate =?

Molar mass = mass / mole

Molar mass of carbohydrate = 6.85 / 0.0124

Molar mass of carbohydrate = 552.41 g/mol

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