Problem 24 - A Complete Resource Book in Chemistry for JEE Main

Question

The molarity of pure water is (a) \(55.56 \mathrm{M}\) (b) \(5.56 \mathrm{M}\) (c) \(1.0 \mathrm{M}\) (d) \(0.01 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of pure water is (a) 55.56 M.

Step 1: Understand Molarity

Molarity (M) is defined as the number of moles of solute divided by the volume of the solution in liters. For pure water, we need to calculate the number of moles of water in a given volume.

Step 2: Calculate the Moles of Water

First, determine the molar mass of water. The molecular formula for water is H₂O, with hydrogen having a molar mass of approximately 1 g/mol and oxygen about 16 g/mol. So, the molar mass of water is \[ 2 \times 1 + 16 = 18 ext{ g/mol} \]

Step 3: Determine the Density of Water

The density of pure water is approximately 1 g/mL, which is equivalent to 1000 g/L. This information allows us to calculate how many moles of water are in a liter.

Step 4: Calculate Moles in 1 L of Water

Using the density and molar mass, calculate the moles of water in 1 liter:\[ \text{Mass of 1 L of water} = 1000 \text{ g} \]\[ \text{Moles of water} = \frac{1000 \text{ g}}{18 \text{ g/mol}} = 55.56 \text{ moles} \]

Step 5: Determine the Molarity of Pure Water

Since molarity is the number of moles of solute per liter of solution and water in this case is both the solvent and 'solute', the molarity of pure water is the previously calculated moles per liter:\[ 55.56 \text{ M} \]

Step 6: Select the Correct Answer

The calculated molarity of pure water is 55.56 M, which corresponds to answer option (a).

Key Concepts

Moles of Water

To fully understand the concept of the molarity of water, it's essential to grasp the idea of moles first. A mole is a unit in chemistry that represents a specific number of particles, typically atoms or molecules. This number is Avogadro's number, which is approximately \(6.022 \times 10^{23}\). When you talk about moles of water, you're referring to a quantity of water molecules.

To find the number of moles in a substance, you need to know the mass of the substance and its molar mass. For water, which is often used as a universal solvent in chemistry, calculating the moles in a given volume is a helpful starting point for understanding solutions.

• Given 1 liter of water weighing 1000 grams, as its density is about 1 g/mL.
• Using the molar mass of water, you can convert this mass into moles to find out how many moles exist in a given volume.

Density of Water

The density of water is a fundamental property, which plays a crucial role in various physical and chemical calculations. In its most common liquid form, water has a density of approximately 1 g/mL or 1000 g/L. This property of water makes it easy to work with in laboratory settings, as 1 liter of water is roughly equivalent to 1000 grams.

Density is significant because it allows scientists and students to convert between the volume of water and its mass. This conversion is essential when calculating the number of moles for reactions or when measuring other properties of water. Remember:

• Density provides a simple way to relate the mass of a liquid to its volume.
• Knowing the density of water helps in determining its molarity by enabling mass to be converted to moles.

Molar Mass of Water

The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). For water (H₂O), the molar mass is calculated from its elemental components: hydrogen and oxygen. Water's molecular formula tells us that each molecule consists of two hydrogen atoms and one oxygen atom:

• Hydrogen has a molar mass of approximately 1 g/mol.
• Oxygen has a molar mass of approximately 16 g/mol.

Therefore, the molar mass of water is:\[ 2 \times 1 + 16 = 18 \text{ g/mol} \]Understanding the molar mass is key to many calculations in chemistry because it allows chemists to convert between the mass of a substance and the amount in moles. For water, this conversion is particularly useful when dealing with solutions and their concentrations.

With this knowledge, you can easily calculate other properties of water, such as molarity, which directly depends on knowing the molar mass.