Question

A solution is prepared by dissolving $\,1.08gms\,$ of human serum albumin. A protein is obtained from blood plasma in $50cc$ of aqueous solution. The solution has an osmotic pressure of $\,5.85mm\,of\,Hg\,$ at $298K$. What is the molar mass of albumin?
A) $686.55g/mole$
B) $68655g/mole$
C) $34328g/mole$
D) $343.28g/mole$

Answer 1

Osmotic pressure is a colligative property that relies on the solute particle concentration in the solution. We can find the osmotic pressure using the respective formula with the given data. This calculation is only valid for those solutions that function as ideal solutions.
FORMULA USED: $\pi = CRT$
Where, $\,\pi \,$ is the osmotic pressure,
$\,C\,$is the concentration of the solute
$\,R\,$ is the gas constant,
And $\,T\,$ is the absolute temperature

Complete step by step answer:
Now, let us first discuss about osmosis;
Osmosis is the spontaneous and unidirectional flow of solvent molecules through a semipermeable membrane, into the solution or in other words flow of solvent from a solution of higher concentration to the solution of lower concentration. Now, let us talk about the osmotic pressure;
The excess of pressure on the side of solution that stops the net flow of solvent into the solution through semipermeable membrane is called osmotic pressure. The osmotic pressure is denoted by $\pi$.
Now let us consider the given data provided to us;
Here, $w = 1.08g$ , $\pi = 5.85mm$ , $V = 50c.c$
So now, according to the equation we know,
$\pi = CRT$
We know, $C = \dfrac{n}{V}$,
Thus, $\pi = \dfrac{{nRT}}{V}$
Also, $n = \dfrac{w}{{MW}}$ where, $\,w\,$is the given weight and $\,M\,W\,$is the molecular weight
$\Rightarrow \pi = \dfrac{{w.R.T}}{{MW.V}}$
$\Rightarrow \pi = \dfrac{{w.R.T}}{{MW}} \times \dfrac{{1000}}{{V(ml)}}$
Since, the value of $\,R\,$ is constant, we can put it into the equation, $R = 0.0821\,L.atm/mol.K\,$
Also, the value of osmotic pressure is in $mm$, hence we have to convert it into $atm$
$\, \Rightarrow 7.69 \times {10^{ - 3}} = \dfrac{{1.08}}{{MW}} \times \dfrac{{1000}}{{50}} \times 0.0821 \times 298\,$
$\, \Rightarrow MW = \dfrac{{1.08 \times 1000 \times 0.0821 \times 298}}{{50 \times 7.69 \times {{10}^{ - 3}}}}\,$
Therefore, $MW = 68654.79g/mol \approx 68655g/mol$
Thus, the molecular weight of albumin is $68655g/mol$. Therefore, option B is correct.

Additional Information:
Osmotic pressure of a solution can also be defined as the excess mechanical pressure which must be applied on the side of solution to stop the flow of solvent molecules through semipermeable membranes into the solution.
There are three types of solutions depending upon the osmotic pressure.
Isotonic solution: Two or more solutions exerting the same osmotic pressure are called isotonic solution.
Hypertonic solution: a solution having osmotic pressure higher than the other solution is said to be hypertonic with the solution.
Hypotonic solution: a solution having osmotic pressure lower than that of another solution with that solution.

Note:
In osmosis, the semi-permeable membrane only permits liquid molecules to pass through it and it is difficult for the solute particles to migrate through it. In fact, osmotic pressure is not a "desire" to transfer water, but rather an extension of the natural law that over time, all matter will be dispersed spontaneously.
In the calculation of osmotic pressure, the value of the universal gas constant which we used is $\,0.0821\,L.atm/mol.K\,$ as here our calculations involve gas equation. On the other hand if we are calculating other values, we have to use the value $\,8.314J/K/mol\,$.