Step-by-Step Solution to Find Molarity

Step 1: Understand what molarity is.

Molarity (M) is defined as the number of moles of solute per liter of solution. The formula is:

$Molarity \left(M\right)=\frac{number of moles of solute}{Volume of solution in Liters}$

Step 2: Calculate the number of moles of urea (the solute).

Given mass of urea = 120 g

Molar mass of urea = 60 g/mol

Number of moles (n) = Mass / Molar Mass

$n=\frac{120}{60}=2 moles$

Step 3: Find the total mass of the solution.

Mass of solute (urea) = 120 g

Mass of solvent (water) = 1000 g

Total mass of solution = Mass of solute + Mass of solvent

$Mass{solution}_{}=120g+1000g=1120g$

Step 4: Calculate the volume of the solution using its density.

Density (ρ) = 1.15 g/mL

Density = Mass / Volume, so Volume = Mass / Density

$Volume \left(V\right)=\frac{Mass}{Density}=\frac{1120}{1.15} mL$

Let's compute that value:

$V=\frac{1120}{1.15}\approx 973.913 mL$

We need the volume in Liters for the molarity formula (1 L = 1000 mL).

$V=\frac{973.913 mL}{1000}=0.973913 L$

Step 5: Calculate the Molarity.

Now we plug our values into the molarity formula:

Moles of solute (n) = 2 moles

Volume of solution (V) ≈ 0.9739 L

$Molarity \left(M\right)=\frac{n}{V}=\frac{2}{0.9739}\approx 2.053 M$

Final Answer: The molarity of the solution is approximately $2.05 M$.

Related Topics & Formulae

1. Molarity (M): The most common unit of concentration.

Formula: $M=\frac{moles of solute}{Liters of solution}$

2. Molality (m): Moles of solute per kilogram of solvent. It is temperature-independent because it uses mass, not volume.

Formula: $m=\frac{moles of solute}{kilograms of solvent}$

3. Mole Fraction (X): The ratio of the number of moles of a component to the total number of moles in the solution.

Formula (for solute A): $X_A=\frac{n_A}{n_A+n_B}$

4. Mass Percentage (w/w%): The mass of the solute divided by the total mass of the solution, multiplied by 100%.

Formula: $\% w/w=\left(\frac{mass of solute}{mass of solution}\right)\times 100$

Key Theory: The main difference between these concentration terms is what quantity is in the denominator. Molarity uses volume of solution, which can change with temperature. Molality and mass percentage use mass, which does not change with temperature, making them more robust for certain scientific calculations like colligative properties.