Question

Suppose 2.37 gof a protein is dissolved in water and diluted to a total volume of 100.0 mL . The osmotic pressure of the resulting solution is 0.0319 atm at${\mathbf{20}}^{\mathbf{0}}\mathit{C}$ . What is the molar mass of the protein?

Short answer

The molar mass of the unknown compound is $1.78\times {10}^4{\text{gmol}}^{-1}$.

Step-by-step solution

Given data

2.37 g of a protein is dissolved in water and diluted to a total volume of 100.0 mL . The osmotic pressure of the resulting solution is 0.0319 atm at ${20}^{0}C$.

Concept of molar mass

The mass of one mole of a sample is its molar mass. The equation shown below can be used to determine the molar mass.

Molar mass (M) =Mass of the substance (g) /Solute concentration (mol) .. (1)

Calculate the solute concentration (C )

Solute concentration is calculated by the formula as follows;

$c=\frac{\pi }{RT}$ ......... (2)

$$\begin{gathered} \pi =0.0319\text{atm} \\ T=20.0+273.15=293.15\text{K} \\ R=0.08206{\text{atmLmol}}^{-1}{\text{K}}^{-1} \end{gathered}$$

Substitute these values in equation (2)

$$\begin{gathered} c=\frac{0.0319\text{atm}}{0.08206{\text{atmLmolm}}^{-1}{\text{K}}^{-1}\times 293.15\text{K}} \\ =0.001326{\text{molL}}^{-1} \end{gathered}$$

Calculate the molar mass

Mass of the substance = 23.7 g .

Solute concentration$=0.001326\text{mol}$.

Substitute these values in equation (1) to calculate molar mass

$$\begin{gathered} M=\frac{23.7\text{g}}{0.001326\text{mol}} \\ =1.78\times {10}^4{\text{gmol}}^{-1} \end{gathered}$$