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 (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 final solution is 0.875 M, option (c).

Step 1: Calculate moles in 750 mL of 0.5 M HCl

First, determine the number of moles of HCl in 750 mL of 0.5 M solution using the formula: \( \text{Moles} = \text{Volume (L)} \times \text{Molarity} \). Thus, \( 0.750 \, \mathrm{L} \times 0.5 \, \mathrm{M} = 0.375 \, \text{moles} \).

Step 2: Calculate moles in 250 mL of 2 M HCl

Next, determine the number of moles of HCl in 250 mL of 2 M solution using the same formula. So, \( 0.250 \, \mathrm{L} \times 2 \, \mathrm{M} = 0.5 \, \text{moles} \).

Step 3: Find total moles of HCl

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

Step 4: Calculate total volume in liters

Add the volumes of both solutions in liters: \( 0.750 \, \mathrm{L} + 0.250 \, \mathrm{L} = 1.0 \, \mathrm{L} \).

Step 5: Calculate final molarity

Calculate the molarity of the final solution using the formula: \( \text{Molarity} = \frac{\text{Total moles}}{\text{Total volume (L)}} \). Thus, \( \frac{0.875 \, \text{moles}}{1.0 \, \mathrm{L}} = 0.875 \, \mathrm{M} \).

Key Concepts

Moles Calculation

Understanding how to calculate the number of moles in a solution is a fundamental skill in chemistry. The number of moles is essentially a count of how many molecules are present in a given volume of solution. To calculate moles, you'll need to know the molarity and the volume of your solution.

• Molarity (M): This is the concentration of your solution and is expressed in moles per liter (mol/L).
• Volume (L): This is the amount of solution you have, converted into liters.

Once you have these two key pieces of information, the formula for calculating moles is straightforward:
\[ \text{Moles} = \text{Volume (L)} \times \text{Molarity (M)} \]This formula allows you to determine how many moles of solute (in this case, HCl) are in your solution. It helps in understanding how concentrated your solution is and how it will react in chemical equations.

Volume Conversion

Often when working with solutions, volumes need to be converted for calculations. Chemistry problems, like the one given, typically require you to convert units to ensure consistency—especially converting milliliters (mL) to liters (L).

The conversion is simple:

• 1 L = 1000 mL

To convert from milliliters to liters, divide the number of milliliters by 1000:

\[ \text{Volume in liters} = \frac{\text{Volume in mL}}{1000} \]In most problems, make sure all volumes are in liters to use them in the molarity equation. For instance, in the problem, converting 750 mL of solution to liters gives you 0.750 L. This conversion is crucial when calculating the moles or molarity of a solution.

HCl Solution

The strength of a hydrochloric acid (HCl) solution is characterized by its molarity. This tells you how effective the solution will be in chemical reactions or when you mix it with other substances.

• Hydrochloric acid (HCl): A strong acid used in laboratories and industry, known for completely dissociating in water.

When working with HCl solutions, understanding the mixture's concentration after combining different solutions is important. The total moles of solute from each separate solution are combined, and then the overall molarity is calculated by dividing by the total volume:
\[ \text{Final Molarity} = \frac{\text{Total moles}}{\text{Total volume (L)}} \]This equation helps you find out how concentrated the newly mixed solution is. Knowing the molarity of your HCl solution can guide you in predicting how it will interact in various chemical scenarios, ensuring you get the desired outcome.