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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 MB. 2.00 MC. 2.05 MD. 2.22 M

Last updated date: 23rd May 2024
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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).