Question

What will be the molality of the solution containing$18.25g$of $HCl$ gas in $500g$ of water?
A.$0.1m$
B.$1m$
C.$0.5m$
D.$1m$

Answer 1

We need to know that the molality is a chemical property which states that, the number of solutes dissolved in one kilogram of the solvent. And the SI unit of molality is equal to$mol/kg$ . If the molality of a solution is equal to $5mol/kg$ it is described as $'3m'$ or $'3molar'$ . Hence, if the concentration of solution is given in moles of solute which dissolved in one kilogram of solvent, the molality can be calculated by dividing the mass of solute with mass of solvent in kilograms.

Complete answer:
The molality of the solution will not be equal to $0.1m$ . Hence, option (A) is incorrect.
The molality of the solution can be calculated by dividing the number of moles of solute with the mass of the solvent present in kilograms. And the chemical formula can be written as,
$molality = \dfrac{{number\;of\;moles\;of\;solute}}{{mass of solvent(kg)}}$
And the equation can also be written as,
Molality $= \dfrac{W_B \times 1000}{M_B \times W_A}$
Here, ${W_B}$ is equal to the given weight of hydrochloric acid gas and it is equal to $18.25g$ . And $M _B$ is equal to the molar mass of hydrochloric acid, which is equal to $36.5$ . And ${W_A}$ is equal to the given weight of the solvent it is equal to $500g$ . Substituting the given values in the above equation, will get the value of molality.
$molality = \dfrac{{18.25 \times 1000}}{{36.5 \times 500}} = 1m$
Therefore, the molality of the solution is equal to $1m$ . Hence, option (B) is correct.
By substituting the given values in the equation of molality, then the molality will not be equal to$0.5m$. Hence, the option (C) is incorrect.
The molality of the solution is equal to $1m$ .

Hence, the option (D) is correct.

Note:
We have to know that the molality is the chemical property of a solution which is equal to the number of moles of solute present in one kilogram of the solvent. Which means, it is expressed on the base of kilogram of the solvent. The value of molality will not change with temperature. The molarity states that the number moles of solute dissolve in one liter of the solvent.