Question

Consider separate solution of $0.500M{C}_2{H}_{5}OH\left(aq\right),0.100MM{g}_3\left(P{O}_4{)}_2\right(aq),0250MKBr(aq\left)and0.125MN{a}_{3}P{O}_4\right(aq)at{25}^{\circ }C$. Which statement is true about these solutions, assuming all salts to be strong electrolytes?

• A. They all have the same osmotic pressure
• B. $0.100MM{g}_3\left(P{O}_4{)}_2\right(aq)$ has the highest osmotic pressure
• C. $0.125MN{a}_{3}P{O}_4\left(aq\right)$ has the highest osmotic pressure
• D. $0.500M{C}_2{H}_{5}OH\left(aq\right)$ has the highest osmotic pressure

Answer 1

The correct option is A They all have the same osmotic pressure

We need to figure out the colligative properties of each solution. But we don't need to do that directly. We can instead just calculate the number of particles after the ionic salts have been dissolved. And since colligative properties depend on the number of particles we can predict the relative values.

Number of particles in solution = number of moles of substance * Van't Hoff factor

Let's assume 1 litre of solution in each case.

For $C_2{H}_{5}OH$, Van't Hoff factor = i = 1 (covalent molecule doesn't dissociate)
0.5M ⇨ O.5 moles per litre ⇒ Number of particles in 1 litre = $0.5\times i=0.5moles$

For $KBr$, Van't Hoff factor = i = 2 (2 ions per molecule)
0.25M ⇨ O.25 moles per litre ⇒ Number of particles in 1 litre = $0.25\times i=0.5moles$

For $M{g}_3(P{O}_4{)}_2$*, Van't Hoff factor = i = 5 (5 ions per molecule)
0.1M ⇨ O.1 moles per litre ⇒ Number of particles in 1 litre = $0.1\times i=0.5moles$

For $N{a}_{3}P{O}_4$, Van't Hoff factor = i = 4 (4 ions per molecule)
0.125M ⇨ O.125 moles per litre ⇒ Number of particles in 1 litre = $0.125\times i=0.5moles$

So, we can see that the number of particles per litre is equal 0.5 moles in each case. So, the colligative properties of all the solutions will be exactly the same.irrespective of the chemical composition.


* - This question is solved by assuming that the examiner has taken $M{g}_3(P{O}_4{)}_2$ to be completely soluble. However, in reality, it is insoluble (sparingly soluble).