Question

Can someone help me with this? Concentrated $HN{O_3}$ has a specific gravity of $1.42$ . It contains $69\% w/w$ (weight by weight) of $HN{O_3}$ . calculate the molarity and molality of the solution?

Answer 1

From specific gravity, the density will be calculated. Using the density and volume of solution as one litre, gives the mass of solution. From the given weight by weight of $HN{O_3}$ mass of nitric acid can be determined. It helps in determining the moles of $HN{O_3}$ . Thus, moles of $HN{O_3}$ and volume of solution given molarity. Later the mass of water in kilograms and moles of $HN{O_3}$ gives molality.

Complete answer:
Given specific gravity of concentrated $HN{O_3}$ is $1.42$
$S = \dfrac{{{\rho _{HN{O_3}}}}}{{{\rho _{{H_2}O}}at{4^0}C}}$
By substituting the given specific gravity and water density at ${4^0}C$ which is $1gm{l^{ - 1}}$
The density of nitric acid will be $1.42gm{l^{ - 1}}$
The mass of solution will be $1.42 \times 1000 = 1420gm$
Given $69\% w/w$ (weight by weight) of $HN{O_3}$ it means $100gm$ of solution consists of $69gmHN{O_3}$
Thus, the solution consists of $1420 \times \dfrac{{69}}{{100}} = 979.8gHN{O_3}$
Nitric acid has molar mass of $63.01gmo{l^{ - 1}}$
Thus, moles of $HN{O_3}$ will be $\dfrac{{979.8}}{{63.01}} = 15.55moles$
Molarity is the ratio of number of moles of $HN{O_3}$ which is solute divided by volume of solution in litres
$M = \dfrac{{15.55}}{1} = 15.6M$
Molarity of nitric acid is $15.6M$
Mass of solution is $1420gm$
Mass of nitric acid is $979.8g$
Thus, mass of water will be $1420 - 979.8 = 440.2g$
When the mass of water is converted into kilograms from mass,
Molality is the ratio of the moles of concentrated nitric acid to mass of water in kilograms
$m = \dfrac{{15.55}}{{440.2 \times {{10}^{ - 3}}}} = 35.3m$
The Molarity of nitric acid is $35.3m$ .

Note:
While calculating the molarity, the volume of solution must be in litres, if the volume of solution is in millilitres it should be multiplied by $1000$ . While calculating the molality, the mass of the solvent must be in kilograms, if it is in grams, it should be converted into kilograms.