Question

In \(1200 \mathrm{~g}\) solution, \(12 \mathrm{~g}\) urea is present. If density of the solution is \(1.2 \mathrm{~g} / \mathrm{ml}\), then the molarity of the solution is (a) \(0.2 \mathrm{M}\) (b) \(10 \mathrm{M}\) (c) \(0.167 \mathrm{M}\) (d) \(12 \mathrm{M}\)

Short answer

(a) 0.2 M (b) 0.25 M (c) 0.3 M (d) 0.4 M Answer: (a) 0.2 M

Step-by-step solution

Find the moles of urea

To find the moles of urea in the solution, we'll use the mass of urea given and the molar mass of urea, which is 60 g/mol. The formula for finding moles is: Moles of urea = (mass of urea) / (molar mass of urea) Moles of urea = (12 g) / (60 g/mol) = 0.2 moles

Find the volume of the solution

We are given the density of the solution, which is 1.2 g/ml and its mass of 1200 g. To find the volume, we need to divide the mass of the solution by its density using the formula: Volume of the solution = (mass of the solution) / (density of the solution) Volume of the solution = (1200 g) / (1.2 g/ml) = 1000 ml Since the volume is given in ml, we need to convert it to L (liter): Volume of the solution = 1000 ml * (1 L / 1000 ml) = 1 L

Calculate the molarity of the solution

We can now find the molarity of the solution by dividing moles of urea by the volume of the solution in liters: Molarity = (moles of urea) / (volume of the solution) Molarity = (0.2 moles) / (1 L) = 0.2 M The molarity of the solution is 0.2 M, which corresponds to option (a).

Key concepts

Moles of Solute

Understanding the concept of moles is fundamental in chemistry and is especially crucial when performing molarity calculations. A mole is a unit that represents a set number of particles, typically atoms or molecules, and this number is Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities per mole.

The number of moles of a solute in a solution is calculated by taking the mass of the solute (in grams) and dividing by its molar mass (the mass of one mole of that substance, measured in grams per mole). This relationship is expressed by the following formula:
\[ \text{Moles of solute} = \frac{\text{Mass of solute (g)}}{\text{Molar mass (g/mol)}} \]
As seen in the exercise, identifying the moles of urea involves dividing the given mass of urea by its molar mass. With the given steps showing how to calculate moles, this concept becomes clearer and a foundational skill for students to master.

Molar Mass

The molar mass, often measured in grams per mole (g/mol), is the mass of one mole of any substance. To calculate molarity, one must first understand the molar mass of the solute involved.

The molar mass is typically derived from the periodic table by adding the average atomic mass of all the atoms present in a molecule. For instance, for urea (\(NH_2CONH_2\)), the molar mass is calculated by adding the atomic masses of nitrogen, hydrogen, carbon, and oxygen accordingly:
\[ \text{Molar Mass of Urea} = (2 \times \text{N}) + (4 \times \text{H}) + (1 \times \text{C}) + (1 \times \text{O}) \]
With a correct understanding of molar mass, as highlighted in the solution, students can easily determine the moles of any solute in their calculations.

Solution Density

Solution density is another key parameter that often comes into play when working out solution concentrations. The density of a solution is its mass per unit volume and is expressed as grams per milliliter (g/ml) or kilograms per liter (kg/L).

The formula for calculating the volume of a solution based on its density is:
\[ \text{Volume of the solution (ml or L)} = \frac{\text{Mass of the solution (g or kg)}}{\text{Density of the solution (g/ml or kg/L)}} \]

Practical Application in Molarity Calculation

Using the exercise as an example, after knowing the mass of the solution and its density, you can compute the volume. This step is crucial for determining the molarity, which is a measure of the concentration of solute per unit volume of solution.

Volume Conversion

Once the volume of a solution is calculated, it may be necessary to convert that volume into liters (L) as the standard unit for molarity calculations is moles per liter (M). There are 1000 milliliters (ml) in one liter.

The conversion formula is:
\[ \text{Volume in liters} = \text{Volume in milliliters} \times \frac{1 \text{ L}}{1000 \text{ ml}} \]
Converting volume to liters, as explained in the example solution, helps simplify the final step of calculating the molarity. This step is essential since molarity is defined per liter of solution, making it critical that students remember to perform this conversion when required.