Question

What is the molal concentration of 0.1 mol/L `"HCN"`?

Answer 1

The molality of 0.1 mol/L `"HCN"` is 0.1 mol/kg.

Explanation:

We have to convert moles of `"HCN"` per litre of solution to moles of `"HCN"` per kilogram of solvent.

A concentration of 0.1 mol/L is quite dilute, so I will take the density of the solution as that of water (1 g/mL).

Assume that we have 1 L of 0.1 mol/L `"HCN"`.

Then,

`"mass of solution" = 1000 color(red)(cancel(color(black)("mL solution"))) × "1 g solution"/(1 color(red)(cancel(color(black)("mL solution")))) = "1000 g solution"`

`"mass of HCN" = 0.1color(red)(cancel(color(black)("mol HCN"))) × "27.03g HCN"/(1 color(red)(cancel(color(black)("mol HCN")))) = "2.703 g HCN"`

`"mass of water" = "mass of solution – mass of HCN" = "1000 g – 2.703 g" = "997.3 g"`

Now, we are ready to calculate the molality of the solution.

`"Molality" = "moles of solute"/"kilograms of solvent" = "0.1 mol"/"0.9973 kg" = "0.1003 mol"//"kg"`

Thus, a 0.1000 mol/L solution of HCN has a molality of 0.1003 mol/kg .

Conclusion: If the solution is sufficiently dilute, the molality is almost the same as the molarity.