Problem 16 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

\(10 \mathrm{~mL}\) of \(2(\mathrm{M}) \mathrm{NaOH}\) solution is added to \(200 \mathrm{~mL}\) of \(0.5\) (M) of \(\mathrm{NaOH}\) solution. What is the final concentration? (a) \(0.57(\mathrm{M})\) (b) \(5.7(\mathrm{M})\) (c) \(11.4(\mathrm{M})\) (d) \(1.14(\mathrm{M})\)

Step-by-Step Solution

Answer

The final concentration is \(0.57(\mathrm{M})\), option (a).

Step 1: Calculate Moles of NaOH in Each Solution

First, calculate the number of moles of NaOH in the 10 mL of 2 M solution using the formula: \( ext{moles} = ext{concentration} \times ext{volume} \). Therefore, \( ext{moles of NaOH} = 2 \, \text{M} \times 0.01 \, \text{L} = 0.02 \, \text{moles} \).Next, calculate the number of moles of NaOH in the 200 mL of 0.5 M solution: \( ext{moles of NaOH} = 0.5 \, \text{M} \times 0.2 \, \text{L} = 0.1 \, \text{moles} \).

Step 2: Find Total Moles of NaOH

Add the moles of NaOH from the two solutions to find the total number of moles: \( ext{Total moles of NaOH} = 0.02 \, \text{moles} + 0.1 \, \text{moles} = 0.12 \, \text{moles} \).

Step 3: Calculate Total Volume of the Mixture

Calculate the total volume of the mixture by adding the volumes of the two solutions: \( ext{Total volume} = 10 \, \text{mL} + 200 \, \text{mL} = 210 \, \text{mL} \). Convert this volume to liters: \( 210 \, \text{mL} = 0.21 \, \text{L} \).

Step 4: Find Final Concentration

Find the final concentration of the NaOH solution using the formula for concentration: \( ext{Concentration} = \frac{\text{Total moles}}{\text{Total volume}} \). Therefore, \( ext{Final concentration} = \frac{0.12 \, \text{moles}}{0.21 \, \text{L}} \approx 0.57 \, \text{M} \).

Key Concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that allows us to count particles like atoms, molecules, or ions by weighing them. One mole of any substance contains exactly Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\). To understand the mole concept, think of it as a bridge between the atomic world and the macroscopic world. This enables chemists to use mass measurements to determine amounts of substances that participate in chemical reactions.

In the context of solution concentration, the mole is crucial because it helps us calculate how many molecules of a compound, such as sodium hydroxide (NaOH), are present in a given volume. For example, in our exercise, we used the formula \(\text{moles} = \text{concentration} \times \text{volume}\) to find out how many moles of NaOH are present in each solution. Understanding this connection makes it easier to grasp the concepts of solution mixing and concentration changes.

• One mole equals Avogadro's number of particles.
• The moles allow the discussion of amounts of substances in macroscopic reactions.

Chemical Solutions

A chemical solution is a homogeneous mixture composed of two or more substances. In a solution, the solute particles are uniformly distributed in the solvent, making it appear as a single phase. The solvent is typically present in greater quantity than the solute. Common examples include salt water, sugar in coffee, or the NaOH solutions in our exercise. Understanding solutions is vital, as they are prevalent in chemical processes.

Solutions can be described by their concentration, which tells us how much solute is present in a given volume of solvent. Concentration is often expressed in molarity, denoted by the symbol \(M\), which stands for moles per liter (\(\text{mol/L}\)). By knowing the volumes and molarities, chemists can manipulate solutions for various reactions and processes.

• A solution is a homogeneous mixture of solute and solvent.
• Molarity (M) measures how concentrated a solution is.
• Uniform distribution characterizes a true solution.

Molarity Calculation

Molarity calculation is a key technique in chemistry that helps determine the concentration of a solute in a solution. It's calculated by dividing the number of moles of solute by the volume of the solution in liters. This simple formula \(\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\) is crucial for preparing solutions with desired properties.

In our exercise, we needed to find out the final concentration of an NaOH solution when two different concentrations are mixed. By identifying the total moles of NaOH and the total volume of the new mixture, we arrived at the final molarity. This exercise highlighted the ease of using molarity for practical applications, ensuring that chemical reactions are carried out with the right proportions.

• Molarity gives the concentration of a solution in mol/L.
• The formula involves dividing total moles by total volume in liters.
• Mixing solutions require careful molarity calculations for accuracy.