Problem 177 - A Complete Resource Book in Chemistry for JEE Main

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 [2013] (a) \(1.75 \mathrm{M}\) (b) \(0.975 \mathrm{M}\) (c) \(0.875 \mathrm{M}\) (d) \(1.78 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of the solution is \(0.875\, \text{M}\), option (c).

Step 1: Understand the problem

We need to find the molarity of the solution when two different \( ext{HCl}\) solutions are mixed. We have 750 mL of a 0.5 M \( ext{HCl}\) solution and 250 mL of a 2 M \( ext{HCl}\) solution.

Step 2: Calculate moles of HCl in each solution

To find the moles of \( ext{HCl}\) in each solution, use the formula: \[\text{Moles} = \text{Molarity} \times \text{Volume in Liters}\]- For the 0.5 M solution: \[ \text{Moles} = 0.5 \, \text{M} \times 0.750 \, \text{L} = 0.375 \, \text{moles}\]- For the 2 M solution: \[ \text{Moles} = 2 \, \text{M} \times 0.250 \, \text{L} = 0.500 \, \text{moles}\]

Step 3: Add moles from both solutions

Add the moles from both solutions to find the total moles of \( ext{HCl}\): \[ \text{Total moles} = 0.375 \, \text{moles} + 0.500 \, \text{moles} = 0.875 \, \text{moles}\]

Step 4: Calculate total volume of mixed solution

The total volume of the mixed solution is the sum of the volumes of the two solutions: \[ \text{Total volume} = 750 \, \text{mL} + 250 \, \text{mL} = 1000 \, \text{mL} = 1 \, \text{L}\]

Step 5: Determine the molarity of the mixed solution

Use the formula for molarity: \[ \text{Molarity} = \frac{\text{Total moles}}{\text{Total volume in Liters}}\]Substitute the known values: \[ \text{Molarity} = \frac{0.875 \, \text{moles}}{1 \, \text{L}} = 0.875 \text{ M}\]This is the molarity of the mixed solution.

Key Concepts

Solution mixing

When dealing with mixtures in chemistry, especially solutions, a common task is combining different solutions to create one uniform solution. In our specific problem, this involves mixing two solutions of hydrochloric acid (HCl) with distinct concentrations and volumes: 750 mL of a 0.5 M solution and 250 mL of a 2 M solution.

Mixing solutions means physically combining them together, but it is essential to consider the resultant concentration after this process. The key here is that both solutions must be combined in such a way that they remain evenly distributed and the original properties of the solutions are altered only by their concentration per unit volume. Understanding this is crucial for the consistent production of solutions in labs based on specific needs or experiments.

• First, we add the volumes together to get a total volume.
• Afterwards, we calculate how the concentrations affect each other by combining their total moles of solute.
• The mixing results in dilution or concentration changes depending on the involved solutions.

By grasping this concept, students can replicate similar calculations in combining any chemical solutions, beyond just hydrochloric acid.

Moles calculation

In chemistry, moles represent a fundamental unit for quantifying chemical entities. Calculating moles accurately is key to solving many chemistry problems, especially those involving reactions and solutions. In the given problem, we understand moles through the relationship between molarity, volume, and moles.

The formula to find moles is: \[\text{Moles} = \text{Molarity} \times \text{Volume in Liters}\]

• For 0.5 M HCl in 750 mL (which is 0.750 L), the moles are calculated as 0.5 * 0.750 = 0.375 moles.
• For 2 M HCl in 250 mL (0.250 L), the moles are 2 * 0.250 = 0.500 moles.

By calculating the moles from different solutions separately, we can merge these values to find the total moles present after the solutions are mixed. It is this sum of moles from all components that crucially determines the resulting molarity of a combined solution.
Understanding the calculation of moles aids in accurately determining how concentrations change through reactions or mixing.

Chemical concentration

Chemical concentration is one of the critical concepts in chemistry that defines how much solute is present in a given volume of solvent. In our scenario, molarity is used as a measure of concentration, yet understanding it entails knowing that molarity (M) is defined as moles of solute per liter of solution.

To determine the concentration of a solution after mixing, it is necessary to consider:

• The total moles of solute, when solutions are mixed, which signifies the cumulative quantity of the solute in the final solution.
• The total final volume of the solution, which sets the scale over which the moles are distributed.

For our example problem, the mixed solutions end up with a net concentration of 0.875 M, achieved by dividing the total moles (0.875 moles) by the total volume (1 L). This calculation reflects the fundamental principle that dilution or concentration through mixing impacts the total distribution of the solute, yet doesn’t alter the total number of moles present. Mastery of chemical concentration concepts is fundamental for effective laboratory work and comprehension of chemical reactions in solutions.