What is the exact definition of isotonic solutions?

Question

Background of the Question I am a high school student so maybe my understanding of this topic is quite less, so apologies in case I have asked an elementary question.

My chemistry sir taught that :-

The flow of solvent in osmosis is dependent upon the difference in vapour pressures of two solutions.

For Example , if we have a dilute solution and concentrated solution separated by a selectively permeable membrane , then apart from deciding the flow of the solvent on the basis of concentrations , we can also define it as :- The dilute solution has lesser concentration of solute , as a result of which the vapour pressure will be more ( we are considering that the solution contains non volatile solute, as a result of which its addition into the solution causes a decrease in the vapour pressure) and hence the difference in vapour pressure causes the movement of solvent particles from dilute to concentrated

And then he defined osmotic pressure on these terms and said that it will be the minimum pressure required to stop the movement of the solvent due to osmosis (to be applied on the side with less vapour pressure).

So on that basis , if we have a pure solvent on one side of SPM , and we have a solution (of the same solvent with some non volatile solute) on the other side of the SPM , and if the vapour pressure of the pure solvent is $p^0$ and that of solution is $P$ , then we can define osmotic pressure ($\pi$) as

P + $\pi$ = $p^0$

He also told me that

If two solutions have same osmotic pressure at the same temperatures , then they are isotonic solutions (by using the formula $\pi$ = $iCRT$ where i = Vant Hoff factor , C = concentration of solution , R = universal gas constant and T is the absolute temperature.) Also , there will be no movement of solvent if they are kept side by side separated by a selectively permeable membrane.

Doubt:-

Now , we define the isotonic solutions as two solutions which have the same osmotic pressures, and also , there will be no movement of solvent if they are kept side by side separated by a selectively permeable membrane

Now if we have two solutions, each of two different solvent , say A and B , but have the same osmotic pressures, i.e.

$i_1C_1RT = i_2 C_2RT$ ($i_1$ and $i_2$ are the Vant Hoff factors for both the solutes , but let us say we have the same solute)

$C_1$ = $C_2$

So we have the same concentrations of both the solutions. However,we know that the pressure of the solution can be determined by the above listed formula ,

P + π = $p^0$

$\therefore$ if $P_a$ is the pressure of the first solution(A) and $P_b$ is the pressure of the second solution(B), and the pressure of the solvents A and B (in pure states) are given by $p_a^0$ and $p_b^0$ , then :-

$P_a$ = $p_a^0$ - $\pi$

$P_b$ = $p_b^0$ - $\pi$

Now , $p_a^0$ is not equal to $p_b^0$ as we have different solvents. Therefore the pressure on the both sides of the solution will be different , and that would mean that the solvent should flow from one side to another

So Basically my question is, How do we exactly define isotonic solutions? Can any two solutions even be isotonic by definition if they consist of differen solvents?

Answer 1

Note that the value of the osmotic pressure is NOT equal to the difference of the solvent vapor pressures between the solution and the pure solvent. It is MUCH bigger than that. Water vapor pressure at $\pu{25^{\circ}C}$ is about $\pu{3.2 kPa}$, so the difference is less than $\pu{3.2 kPa}$. Osmotic pressure of $\pu{1 M}$ solutions is about $\pu{2.5 MPa}$.

$\pi = icRT = 1 \times (\pu{1000 mol m-3}) \cdot (\pu{8.314 J K-1 mol-1}) \cdot (\pu{298 K}) \\ \approx \pu{2.5E6 J m-3}=\pu{2.5E6 N m-2}=\pu{2.5 MPa}$

In context of osmosis, there is implied the same solvent on both membrane sides, for most cases water.

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Osmolality (or Osmotic concentration) is the total molarity of solutes, counting solute particles considering eventual disociation, using the unit osmol instead of mol.

E.g. Osmolality of $\pu{0.1 M } \ce{CaCl2}$ is $\pu{0.3 osmol/L}$, osmolality of $\pu{0.1 M } \ce{NaCl}$ is $\pu{0.2 osmol/L}$.

There is frequent confusion with tonicity, resp. of isotonic and isoosmotic solutions.

Tonicity is the partial osmolality, considering just solutes, for which is the membrane not permeable. In our case below, urea is not considered for the tonicity evaluation.

Isotonic solutions need not be isoosmotic, isoosmotic solutions need not to be isotonic. Isoosmotic solutions have the same osmolality. Isotonic solutions have the same tonicity.

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Human body cells have a semi-permeable membrane, permeable for urea ($\ce{CO(NH2)2}$), but not for $\ce{Na+}$ and $\ce{Cl-}$ ions. In this context,

these solutions are mutually isoosmotic, but not isotonic:

$\pu{0.05 M }\ce{NaCl} + \pu{0.1 M } \ce{urea}$
$\pu{0.025 M } \ce{NaCl} + \pu{0.15 M } \ce{urea}$

while these solutions are mutually isotonic, but not isoosmotic:

$\pu{0.05 M }\ce{NaCl} + \pu{0.1 M } \ce{urea}$
$\pu{0.05 M } \ce{NaCl} + \pu{0.15 M } \ce{urea}$

In context of medicine, as isotonic solutions are considered solution isotonic with $0.9\%$ aqueous solution of $\ce{NaCl}$.