Question

What is the molality of $ 5.0g $ mass of toluene dissolved in 255g of benzene?

Answer 1

Hint: We know that molality is defined as the ratio of moles of solute to the mass of solvent in kilograms. So, to solve this question, first determine the number of moles corresponding to $ 5.0g $ mass of toluene and then substitute the given values in the formula of molality to get the final answer.
Molality $ m = \dfrac{{{\text{moles of solute}}}}{{{\text{mass of solvent (kg)}}}} $

Complete answer:
Toluene is an aromatic hydrocarbon which is composed of a benzene ring linked to one methyl group. It is represented by the chemical formula $ {C_6}{H_5}C{H_3} $ . The atomic mass of carbon and hydrogen is $ 12gmo{l^{ - 1}} $ and $ 1gmo{l^{ - 1}} $ respectively. So, the molar mass of toluene is as follows:
 $ {M_{toluene}} = 12 \times 6 + 5 \times 1 + 12 \times 1 + 3 \times 1 $
 $ \Rightarrow {M_{toluene}} = 92.14gmo{l^{ - 1}} $
Thus, the molar mass of toluene is $ 92.14gmo{l^{ - 1}} $ .
The number of moles of a substance is equal to the ratio of given mass of the substance to its molar mass and as per given question, the mass of toluene is $ 5.0g $ . Therefore, the number of moles of toluene are as follows:
 $ n = \dfrac{{{\text{given mass}}}}{{{\text{molar mass}}}} $
Substituting values:
 $ \Rightarrow n = \dfrac{5}{{92.14}} $
 $ \Rightarrow n = 0.054{\text{ moles}} $
Now, the molality of the solution can be calculated as follows:
 $ m = \dfrac{{{\text{moles of solute}}}}{{{\text{mass of solvent (kg)}}}} $
As per our calculations and given values, the number of moles of solute i.e., toluene is $ 0.054 $ moles and the mass of solvent i.e., benzene is $ 255g $ . Substituting values in the given formula for molality:
 $ \Rightarrow m = \dfrac{{0.054}}{{255 \times {{10}^{ - 3}}}}\;\;\;\;\;\;\;\;\;\;\left[ {\because 1g = {{10}^{ - 3}}kg} \right] $
 $ \Rightarrow m = 0.212\;{\text{molk}}{{\text{g}}^{ - 1}} $
Hence, the molality of the given solution is $ 0.212\;{\text{molk}}{{\text{g}}^{ - 1}} $ .

Note:
Remember to check the unit of mass of solvent before substituting it in the formula as the mass of solvent is always to be taken in kg. Also, it is important to note that the molality is always preferred over molarity because it is independent of volume and thus, it is independent of the value of temperature as well.