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What will be the molality of a solution of glucose in water which is $10\%$w/w?A.$0.01m$B.$0.617m$C.$0.668m$D.$1.623m$

Last updated date: 13th Jun 2024
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Hint:$10\%$ by w/w solution of glucose means there is $10g$ of glucose and $90g$ of water in $100g$ of solution. And the Molality is calculated by no. of moles of solute/ mass of solvent in Kilograms. The concentrations which are expressed in molality are used while studying properties of solutions
Formula Used:Molality no. of moles of solute/ mass of solvent

Here, mass of glucose is $10g$ as given in the question:
Moles of glucose = $10/180 = 0.556mole$
Molality is the total number of moles of a solute present in $1$ kilogram of a solvent.
We can say that, molality= number of moles of solute/ mass of solvent in Kg. Molality is expressed by “m”.
Formula of glucose is ${C_6}{H_{12}}{O_6}$ hence,
Atomic mass of carbon= $12g$
Atomic mass of hydrogen = $1g$
Atomic mass of oxygen= $16g$
Molecular weight of glucose=$(12*6) + (1*12) + (16*6) = 180$
The solution of glucose in water which is $10\%$ w/w implies $10g$ of glucose in $100g$ of solution
Mass of solute= $10g$
Mass of solution=$100g$
Mass of solvent=$(100 - 10)g = 90g = 0.090Kg$
Molality = $0.556/0.090 = 0.617m$

Hence, option (B) is the correct option.

Molarity is expressed by “M” whereas molality is expressed by “m” and these both express the concentration of a chemical solution. And always remember that $10\%$By w/w solution of glucose means there is $10g$ of glucose and $90g$ of water in $100g$ of solution. It will help in solving the problem given.