Problem 17 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of moles of sodium hydroxide present in \(2.5 \mathrm{~L}\) and \(0.5 \mathrm{M}\) aqueous solution will be (a) \(1.25\) (b) \(0.5\) (c) \(12.5\) (d) 5

Step-by-Step Solution

Answer

The number of moles of sodium hydroxide is 1.25; the correct answer is (a).

Step 1: Understand Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. The formula is \( M = \frac{n}{V} \), where \( n \) is the number of moles and \( V \) is the volume in liters.

Step 2: Identify Known Values

We are given that the molarity (\( M \)) is \(0.5 \, M\) and the volume (\( V \)) is \(2.5 \, L\).

Step 3: Rearrange the Formula

To find the number of moles (\( n \)), rearrange the molarity formula to \( n = M \times V \).

Step 4: Calculate the Number of Moles

Substitute the known values into the formula: \( n = 0.5 \, M \times 2.5 \, L = 1.25 \, ext{moles} \).

Step 5: Choose the Correct Option

From the calculation, we have \( 1.25 \) moles of sodium hydroxide, which matches option (a).

Key Concepts

Moles calculation

To calculate the number of moles, it's crucial to understand what moles are in the context of chemistry. A mole is a unit that scientists use to express amounts of a chemical substance. One mole equates to approximately 6.022 x 10^23 particles, like atoms or molecules, and this number is called Avogadro's number.

In our exercise, we want to calculate the moles of sodium hydroxide (NaOH) in a solution. The formula for moles () based on molarity is given by: \[ n = M \times V \]

• \( M \) is the molarity in moles per liter.
• \( V \) is the volume in liters.
• \( n \) is the number of moles.

Using the formula is straightforward. You multiply the molarity of the solution by its volume in liters. For example, a 0.5 M solution of NaOH with a volume of 2.5 L translates to this calculation: \[ n = 0.5 \text{ M} \times 2.5 \text{ L} = 1.25 \text{ moles} \]This tells us that there are 1.25 moles of NaOH in the solution.

Solution concentration

Solution concentration defines how much solute is present in a given quantity of solvent or solution. It plays a crucial role in chemistry as it affects reaction rates and equilibrium.

There are several methods to express concentration, but molarity is one of the most common. Molarity ( M ) is the number of moles of solute per liter of solution, expressed as \[ M = \frac{n}{V} \]

• Molar solutions are typically used in labs for various chemical experiments.
• Concentration can impact the properties of the solution, such as conductivity or boiling point.

Understanding how to manipulate and measure concentration is essential for conducting accurate chemical reactions and achieving desired outcomes in experimental settings. In practical scenarios, measuring accurate concentrations require precise calculation and careful preparation of solutions.

Chemical equations

Chemical equations represent the transformation of reactants into products. They contain molecules, compounds, and sometimes energy changes.

To interpret a chemical equation, it's important to understand the role of coefficients and subscripts:

• Coefficients indicate the quantity of molecules involved and ensure that the equation abides by the law of conservation of mass.
• Subscripts, part of chemical formulas, denote the number of atoms in a molecule.

For instance, in \( 2 \text{H}_2 + \text{O}_2 \to 2 \text{H}_2\text{O} \), coefficients show that two molecules of hydrogen react with one molecule of oxygen to form two molecules of water.
Balancing chemical equations is critical because it reflects how mass and energy are conserved in chemical reactions. It also helps in calculating reactant or product amounts, often through moles and molarity in solution phase reactions.