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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.$1.623m$

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Last updated date: 13th Jun 2024
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Answer
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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

Complete step by step answer:
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.

Additional Information:
Some uses of molality is: The concentrations which are expressed in molality are used while studying properties of solutions linked to vapor pressure and temperature changes. Molality is also used because its value does not change with variations in temperature. The volume of a solution, on the other hand, is somewhat dependent upon temperature.

Note:
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.