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Question

Consider separate solution of 0.500 M C2H5OH(aq), 0.100 M Mg3(PO4)2 (aq), 0250 M KBr (aq) and 0.125 M Na3PO4(aq) at 25C. Which statement is true about these solutions, assuming all salts to be strong electrolytes?

A
They all have the same osmotic pressure
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B
0.100 M Mg3 (PO4)2(aq) has the highest osmotic pressure
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C
0.125 M Na3 PO4(aq) has the highest osmotic pressure
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D
0.500 M C2H5 OH(aq) has the highest osmotic pressure
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Solution

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 C2H5OH, 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×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×i=0.5moles

For Mg3(PO4)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×i=0.5moles

For Na3PO4, 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×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 Mg3(PO4)2 to be completely soluble. However, in reality, it is insoluble (sparingly soluble).

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