Answer
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Hint: Molarity is defined as the number moles of a solute present in one liter of a solution and it is denoted with a symbol ‘M’.
Molality is defined as the number of moles of solute present in 1 kg of a solvent and it is denoted with a symbol ‘m’.
The relationship between molality and molarity is as follows.
\[M=\dfrac{1000md}{1000+m{{M}_{o}}}\]
Here \[{{M}_{o}}\]= Molar mass
d = density
m = molality of the solution
M = molarity of the solution
Complete answer:
In the question it is given that the density of NaOH solution d = 1.110 g/mL
The molality of the NaOH solution = 3 molal
We know the molecular weight of NaOH, \[{{M}_{o}}\] = 40 g
Substitute all the values in the following formula
$M=\dfrac{1000md}{1000+m{{M}_{o}}}$
$M=\dfrac{1000\times 3\times 1.110}{1000+3\times 40}$
$M=\dfrac{3330}{1120}=2.973$
Therefore the molarity of the solution is 2.973 mol/L.
So, the correct option is B.
Note: In case of an infinite dilute aqueous solution, molality (m) of the solution is equal to molarity (M) of the solution. Their volume will be equal to its mass.
Therefore, 1 kg of solution will weigh 1 L.
The number of moles of solute present in per liter of the solvent is equal to the number of moles of solute present in per kg of solvent.
Molality is defined as the number of moles of solute present in 1 kg of a solvent and it is denoted with a symbol ‘m’.
The relationship between molality and molarity is as follows.
\[M=\dfrac{1000md}{1000+m{{M}_{o}}}\]
Here \[{{M}_{o}}\]= Molar mass
d = density
m = molality of the solution
M = molarity of the solution
Complete answer:
In the question it is given that the density of NaOH solution d = 1.110 g/mL
The molality of the NaOH solution = 3 molal
We know the molecular weight of NaOH, \[{{M}_{o}}\] = 40 g
Substitute all the values in the following formula
$M=\dfrac{1000md}{1000+m{{M}_{o}}}$
$M=\dfrac{1000\times 3\times 1.110}{1000+3\times 40}$
$M=\dfrac{3330}{1120}=2.973$
Therefore the molarity of the solution is 2.973 mol/L.
So, the correct option is B.
Note: In case of an infinite dilute aqueous solution, molality (m) of the solution is equal to molarity (M) of the solution. Their volume will be equal to its mass.
Therefore, 1 kg of solution will weigh 1 L.
The number of moles of solute present in per liter of the solvent is equal to the number of moles of solute present in per kg of solvent.
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