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Dissolving 120g of urea (mol.wt.60) in 1000g of water gave a solution of density 1.15 g/mL. The molarity of the solution is:
A. 1.78 M
B. 2.00 M
C. 2.05 M
D. 2.22 M

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Last updated date: 23rd May 2024
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Answer
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Hint: To proceed in answering the question, we must recall the basic definition of molarity and we must also keep in mind the correlation of volume and density of a solution. Molarity is the number of moles of solute per liter of solution, which can be calculated using the following equation:
\[Molarity=\dfrac{Moles\,of\,solute}{Litres\,of\,solution}\]

Complete step by step solution:
To calculate the molarity of the solution, we first need to know the number of moles of solute (urea) in the solution.
\[No.\,of\,moles\,=\,\dfrac{Mass\,of\,urea\,in\,solution}{Molecular\,mass\,of\,urea}=\dfrac{120}{60}=\,2\,moles\]
We know,
 The total mass of the solution = mass of solute + mass of solvent
= mass of urea + mass of water
= 120g + 1000g = 1120g
Given: Density of solution = 1.15 g/mL; which means every 1mL of the solution has mass of 1.15g.
We can calculate the volume of the solution from the mass and density of the solution.

We know,
\[Volume\,=\dfrac{Mass}{Density}\,=\dfrac{1120\,g}{1.15\,g/mL}\,=\,973.9\,mL\]
Now we see,
In 973.9 mL of solution we have = 2 moles of Urea
Or, in 1 mL of solution we have = \[\dfrac{2}{973.9}\] moles of Urea
Or, in 1000 mL or 1L of solution, we have =\[\dfrac{2}{973.9}\times 1000\,=\,2.0535\]moles of urea.
The Molarity of the solution is 2.05M (Option C).

Additional Information:
Molarity, molality, and normality are all units of concentration. Molarity is defined as the number of moles of solute per liter of solution. Molality is defined as the number of moles of solute per kilogram of solvent and Normality is defined as the number of equivalents per liter of solution. We should use Molality instead of Molarity in experiments involving significant temperature changes. This is because as the volume of a solution increases with temperature, heating causes molarity to decrease; however, since molality is based on mass rather than volume, molality remains unchanged.

Note: Molar concentration can be used to convert between the mass or moles of solute and the volume of the solution.
Molarity is a measurement of the moles in the total volume of the solution, whereas Molality is a measurement of the moles in relationship to the mass of the solvent. Hence, the two should never be confused.