Question

Calculate the molality of a 1 M solution of sodium nitrate. The density of the solution is 1.25\[gc{{m}^{-3}}\].
a.) 0.66 \[molk{{g}^{-1}}\]
b.) 0.86 \[molk{{g}^{-1}}\]
c.) 0.46 \[molk{{g}^{-1}}\]
d.) None of these

Answer 1

Hint: We should know that molality is a property of a solution and is defined as the number of moles of solute per kilogram of solvent. The SI unit for molality is mole per kilogram.

Complete step-by-step answer:
In this question, we have to calculate the molality 1M solution of \[NaN{{O}_{3}}\].
In this question, there is also given molarity. Molarity is most commonly expressed in units of moles of solute per litre of solution.
So, 1M solution of sodium nitrate means that 1M molar solution has 1 mole of \[NaN{{O}_{3}}\] for 1000ml of solution.
Therefore, mass of solute is a mass of 1 mole of \[NaN{{O}_{3}}\]​= 23+14+48 = 85 gm.
 Volume of solution = 1000 ml as per definition.
Now, given that density is 1.25 gram per centimetre cube.
Therefore, mass = 1.25×1000 (m = density $\times $volume)
So, solution of mass will be mass = 1250 gram
Mass of solvent = mass of solution - mass of solute
                          = 1250 - 85= 1165 gram
So, as per definition, molality of a solution is defined as the amount of substance of solute divided by the mass (in kg) of the solvent.
$Molality(m)=\dfrac{~amount\text{ }of\text{ }substance~(in~moles)\text{ }of\text{ }solute}{~mass~(in~kg)\text{ }of\text{ }the~solvent}$
So, no moles of sodium nitrate = 1
Mass of solvent in kilogram= $\dfrac{1165}{1000}$kg
$Molality(m)=\dfrac{1}{~\dfrac{1165}{1000}}=\dfrac{1}{1165}\times 1000=\dfrac{1000}{1165}=0.85m$
So, our correct answer is option D, which is none of these.
No option matches with our calculated value.

Note: We should understand the difference between molarity and molality. We should know that both molarity and molality are measures of a chemical solution’s concentration. The primary difference between the two comes down to mass versus volume. The molality describes the moles of a solute in relation to the mass of a solvent, while the molarity is concerned with the moles of a solute in relation to the volume of a solution.