Problem 13 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The molarity of a solution obtained by mixing \(750 \mathrm{~mL}\) of \(0.5(\mathrm{M}) \mathrm{HCl}\) with \(250 \mathrm{~mL}\) of \(2(\mathrm{M}) \mathrm{HCl}\) will be : (a) \(0.875 \mathrm{M}\) (b) \(1.00 \mathrm{M}\) (c) \(1.75 \mathrm{M}\) (d) \(0.975 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of the mixed solution is \(0.875 \mathrm{M}\), option (a).

Step 1: Calculate moles of HCl from each solution

First, calculate the moles of HCl present in each solution using the formula \( ext{moles} = ext{Molarity} \times ext{Volume (L)} \). For the first solution \( (0.5 \, M, 750 \, mL) \): \( 0.5 \, ext{M} \times 0.750 \, ext{L} = 0.375 \, ext{moles} \). For the second solution \( (2.0 \, M, 250 \, mL) \): \( 2 \, ext{M} \times 0.250 \, ext{L} = 0.5 \, ext{moles} \).

Step 2: Calculate total moles of HCl

Add the moles from both solutions to get the total moles of HCl: \( 0.375 \, ext{moles} + 0.5 \, ext{moles} = 0.875 \, ext{moles} \).

Step 3: Calculate total volume of the mixed solution

Add the volumes of the two solutions to find the total volume: \( 750 \, ext{mL} + 250 \, ext{mL} = 1000 \, ext{mL} \). Convert this to liters: \( 1000 \, ext{mL} = 1.0 \, ext{L} \).

Step 4: Calculate the molarity of the mixed solution

The molarity of the mixed solution is given by \( \text{Molarity} = \frac{\text{Total moles}}{\text{Total volume (L)}} \). Substitute the values: \( \frac{0.875 \, ext{moles}}{1.0 \, ext{L}} = 0.875 \, M \).

Step 5: Match with given options

Compare the calculated molarity \( 0.875 \, M \) with the provided options. The answer is option (a): \( 0.875 \, ext{M} \).

Key Concepts

Solution Mixing

When it comes to mixing chemical solutions, it is important to understand how different concentrations of solutions will behave once combined. In this exercise, you are presented with two solutions of hydrochloric acid ( HCl ) that need to be mixed together.
The concentration of a solution is expressed in terms of molarity, which is defined as moles of solute per liter of solution. Each solution has a specific molarity and volume. This exercise involves mixing a 750 mL solution of HCl with a molarity of 0.5 M, and another 250 mL solution with a molarity of 2.0 M. When these two solutions are mixed, the resulting solution will have its own unique molarity that's determined by the combined volumes and moles from each of the original solutions. It is important to note that the chemical identity of the solutions remains unchanged; only the concentration and volume properties are combined.

Chemical Moles Calculation

Calculating moles is central to understanding the composition of a solution. A mole is a unit that quantifies the amount of substance. The key formula for calculating the moles in a solution is: \[ \text{moles} = \text{Molarity} \times \text{Volume (L)} \]
For the first solution in our problem, which has a volume of 750 mL (or 0.750 L) and a molarity of 0.5 M, the moles are calculated as: \[ 0.5 \, \text{M} \times 0.750 \, \text{L} = 0.375 \, \text{moles} \]For the second solution that has a volume of 250 mL (or 0.250 L) and a molarity of 2.0 M, the moles are:\[ 2 \, \text{M} \times 0.250 \, \text{L} = 0.5 \, \text{moles} \]Once the moles of each solution are determined, they are summed to find the total moles present in the final mixed solution. This total will then be used to find the new molarity of the mixture.

Volume Conversion

Volume conversion is a crucial step in calculations involving molarity. Typically, volumes given in milliliters (mL) need to be converted to liters (L) because molarity is expressed in moles per liter.

• 1,000 mL equals 1.0 L.
• To convert from mL to L, divide the volume in mL by 1,000.

In our exercise, the volumes of 750 mL and 250 mL need to be added to find the total volume of the mixed solution. Together they make: \[ 750 \, \text{mL} + 250 \, \text{mL} = 1,000 \, \text{mL} \]When converted to liters, this total volume becomes 1.0 L. Accurate volume conversion is important because it significantly impacts the calculation of molarity for the mixed solution. In the end, it's the total moles divided by this converted volume that gives the final molarity.