Problem 176 - A Complete Resource Book in Chemistry for JEE Main

Question

The density of a solution prepared by dissolving \(120 \mathrm{~g}\) of urea (mol. Mass \(=60 \mathrm{u}\) ) in \(1000 \mathrm{~g}\) of water is \(1.15 \mathrm{~g} / \mathrm{mL}\). The molarity of this solutions is: [2012] (a) \(1.02 \mathrm{M}\) (b) \(0.50 \mathrm{M}\) (c) \(2.05 \mathrm{M}\) (d) \(1.78 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of the solution is approximately \(2.05 \text{ M}\).

Step 1: Calculate Moles of Urea

First, determine the number of moles of urea. The molecular mass of urea is given as \(60\, u\). Given \(120\, \text{g}\) of urea, use the formula: \[ \text{moles of urea} = \frac{\text{mass of urea}}{\text{molar mass of urea}} = \frac{120\, \text{g}}{60\, \text{g/mol}} = 2\, \text{moles} \]

Step 2: Determine Total Volume of the Solution

Now, calculate the volume of the solution. Given the density of the solution is \(1.15\, \text{g/mL}\), and the total mass is \(1120\, \text{g}\) (\(120\, \text{g}\) of urea + \(1000\, \text{g}\) of water), the volume is: \[ \text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{1120\, \text{g}}{1.15\, \text{g/mL}} \approx 973.91\, \text{mL} \]

Step 3: Convert Volume to Liters

Since molarity is moles per liter, convert the volume from milliliters to liters: \[ 973.91\, \text{mL} = 0.97391\, \text{L} \]

Step 4: Calculate the Molarity of the Solution

Finally, calculate the molarity using the formula: \(\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\). Thus: \[ \text{Molarity} = \frac{2\, \text{moles}}{0.97391\, \text{L}} \approx 2.05\, \text{M} \]

Key Concepts

Molarity

Molarity is a measure of concentration that expresses the amount of a solute (in moles) dissolved in a liter of solution. It is expressed in units of moles per liter (mol/L), often represented as "M."

To calculate the molarity of a solution, you use the formula:

• Molarity (M) = \( \frac{\text{moles of solute}}{\text{volume of solution in liters}} \).

This formula highlights that molarity directly depends on both the number of moles of the solute and the total volume of the solution.

By understanding molarity, you can determine how concentrated a substance is in a mixture, which is crucial in chemical reactions and processes.

Density

Density is a physical property of matter that describes how much mass is contained in a given volume. It is calculated using the formula:

• Density = \( \frac{\text{mass}}{\text{volume}} \).

When you know the density of a solution, you can find the volume of the solution if you also know its mass.

In chemistry, density can help determine other properties of a substance. For example, in the exercise, figuring out the volume of the solution required knowing its density. Density is typically reported in units like grams per milliliter (g/mL) or kilograms per liter (kg/L). Understanding density helps assess how substances will settle or mix when combined, which is often essential during the preparation of chemical solutions.

Moles of Urea

The concept of "moles" in chemistry refers to a specific number of particles, typically atoms, molecules, or ions. One mole is equivalent to Avogadro's number, approximately \(6.022 \times 10^{23}\) particles.

To find out the number of moles of a substance, use the formula:

• Moles = \( \frac{\text{mass of substance}}{\text{molar mass}} \).

In our scenario with urea, the mass was given as \(120 \text{ g}\) and the molar mass of urea was \(60 \text{ g/mol}\).

By calculation:

• Moles of urea = \( \frac{120 \text{ g}}{60 \text{ g/mol}} = 2 \text{ moles} \).

Understanding moles allows you to quantify chemical reactions and the amount of reactants needed or products formed.

Volume Conversion

In many chemical calculations, converting volume into the appropriate units is vital, especially converting from milliliters (mL) to liters (L) when dealing with molarity.

The conversion is straightforward:

• 1 liter = 1000 milliliters.

Thus, to convert milliliters to liters:

• Volume in liters = \( \frac{\text{Volume in mL}}{1000} \).

In our solution, this conversion was essential in determining the molarity because molarity requires the volume in liters.

For example, if the volume is \(973.91 \text{ mL}\), then:

• Volume in liters = \( \frac{973.91}{1000} \approx 0.97391 \text{ L} \).

Quickly converting between units keeps calculations accurate and helps ensure precision in labs and real-world applications.