Question

The mass of glucose to be dissolved in $50g$ of water to get $0.3$ $Molal$ solution is :
A.$27g$
B.$0.27g$
C.$2.7g$
D.$5.4g$

Answer 1

To solve this question we must remember the formula of molality . Molality is a quantity to measure concentration of a solution and it is calculated by number of moles of solute present in $1kg$ of solvent and its unit is $mol/kg$ and $1mol/kg$ is also termed as $1Molal$ solution .

Complete step by step answer:
If $n$ is the number of moles of solute and $w$is the mass of solvent in kilograms present in the solution then molality $= \dfrac{n}{w}$.
In the given question water is solvent and glucose is solute and mass of water present in solution is $50g = \dfrac{{50}}{{1000}}kg = 0.05kg$ and molality of the solution is $0.3Molal$ .
Now with the given data we can easily calculate the required number of moles of glucose.
$n = 0.3 \times 0.05$ $=$ $0.015$
So $0.015$ moles of glucose is required to make the solution of $0.3Molal$ . But in the given question we have to calculate mass of glucose so we need to convert it into grams .
We know that the number of moles is calculated by dividing the mass of the compound in grams divided by its molar mass .
The molar mass of glucose $= 180g$
Therefore required mass of glucose $=$molar mass of glucose $\times$ number of moles of glucose
Required mass of glucose $= \left( {0.015 \times 180} \right)g$ $= 2.7g$
Hence option (C) is the correct answer .

Note:
While calculating concentration terms like molarity or molality we should take care of units like in when we calculate molality we should put the value of mass of solvent in kilograms . Molarity is defined as the number of moles of solute present per litre of the solution so in the case of molarity we have to divide the number of moles to the volume of the whole solution .