Question

Consider separate solutions of 0.500M ${{C}_{2}}{{H}_{5}}O{{H}_{(aq)}}$, 0.250M $KB{{r}_{(aq)}}$, 0.125M $N{{a}_{3}}P{{O}_{4}}_{(aq)}$ and 0.100M $M{{g}_{3}}{{(P{{O}_{4}})}_{2\left( aq \right)}}$ at $25{}^\circ C$.
(A) 0.125M $N{{a}_{3}}P{{O}_{4}}_{(aq)}$ has highest osmotic pressure
(B) 0.500M ${{C}_{2}}{{H}_{5}}O{{H}_{(aq)}}$ has the highest osmotic pressure
(C) They all have same osmotic pressure
(D) 0.100M $M{{g}_{3}}{{(P{{O}_{4}})}_{2\left( aq \right)}}$ has the highest osmotic pressure

Answer 1

Hint: To answer this question we will have to calculate the osmotic pressure of the given aqueous compounds. The osmotic pressure of a solution is affected if any of the compound present in it dissociates like in case of ionic compounds. We will use the formula for calculating osmotic pressure as:
     \[\pi \,=\,iMRT\]
Where, $\pi $is the osmotic pressure.
‘i’ is the Van't Hoff factor.
‘M’ is the given molar concentration.
R is the gas constant
T is the temperature.
Osmotic pressure is a very useful colligative property. It is used to determine the molar masses of heavy molecules of proteins and polymers. This is because osmotic pressure is dependent on molarity and molarity can be easily calculated.

Complete answer:
Let’s look at the solution of the given question:
Colligative properties are those properties which are dependent on the amount of substance present or the number of particles present in a solution. For example: elevation in boiling point is a colligative property.
We will calculate the osmotic pressure in each case.
In case of 0.500M ${{C}_{2}}{{H}_{5}}O{{H}_{(aq)}}$, there is no dissociation in ethanol. So, the value of ‘i’ is 1.
So, i=1
\[\begin{align}
  & \pi \,=\,1\times 0.500RT \\
 & \pi \,=\,0.5RT \\
\end{align}\]
Now, in case of 0.250M $KB{{r}_{(aq)}}$, dissociation will occur and $KBr$ will dissociate into 2 ions. So, i = 2
\[\begin{align}
  & \pi \,=\,2\times 0.250RT \\
 & \pi \,=\,0.5RT \\
\end{align}\]
Now, in case of 0.125M $N{{a}_{3}}P{{O}_{4}}_{(aq)}$, dissociation will occur and $N{{a}_{3}}P{{O}_{4}}$ will dissociate into 4 ions.
So, i= 4
\[\begin{align}
  & \pi \,=\,4\times 0.125RT \\
 & \pi \,=\,0.5RT \\
\end{align}\].
Now, in case of 0.100M $M{{g}_{3}}{{(P{{O}_{4}})}_{2\left( aq \right)}}$, dissociation will occur and $M{{g}_{3}}{{(P{{O}_{4}})}_{2}}$ will dissociate into 5 ions.
So, i= 5
\[\begin{align}
  & \pi \,=\,5\times 0.100RT \\
 & \pi \,=\,0.5RT \\
\end{align}\]
So, we have seen that the osmotic pressure is the same for all the given solutions.
Hence, the answer for the given question is option (C).

Note:
Osmotic pressure is a colligative property. Its value depends on the number of the particles present in the solution. For ionic solutions the value of ‘i’ is used which is equal to the total number of ions but for non-ionic solutions the value of ‘i’ is taken as 1.