Animated Solution for Chemistry - Basic Concepts in Chemistry: The density of a solution prepared by dissolving $120\text{ g}$ of urea (mol. mass $=60\text{ u}$) in $1000\text{ g}$ of water is $1.15\text{ g/mL}$. The molarity of this solution is

You take a beaker and pour exactly $1000\text{ g}$ of pure water into it. This water is your solvent. Next, you carefully weigh out $120\text{ g}$ of urea and dissolve it completely into the water. Urea here acts as your solute.

The question asks us to find the molarity of this newly formed solution. To do this, we need two critical pieces of information: the number of moles of the solute (urea) and the total volume of the solution in liters.

Finding the Volume One of the most common traps students fall into is assuming the volume of the solution is just the volume of the water. But remember, adding $120\text{ g}$ of solid urea changes the total mass and the volume of the system!

First, let's find the total mass of our solution. It's simply the sum of the masses of the solvent and the solute:

Now, how do we get the volume? The problem provides a crucial bridge: the density of the solution, which is $1.15\text{ g/mL}$. Density relates mass to volume via the formula $\rho =\frac{m}{V}$. Rearranging this to solve for volume gives us:

Substituting our values:

Since molarity requires the volume to be in liters, we divide by $1000$:

Moles and Molarity Next, we need the moles of our solute. The molar mass of urea is given as $60\text{ g/mol}$. Using the mole formula:

We now have everything we need! The definition of molarity ($M$) is the number of moles of solute per liter of solution:

Plugging in our calculated values:

And there we have it! The molarity of the solution is $2.05\text{ M}$, which perfectly matches option (d). Always remember to account for the mass of the solute when calculating the total volume of a solution from its density!