Problem 49 - Chemistry and Chemical Reactivity

Question

If you dilute \(25.0 \mathrm{mL}\) of \(1.50 \mathrm{M}\) hydrochloric acid to \(500 . \mathrm{mL},\) what is the molar concentration of the dilute acid?

Step-by-Step Solution

Answer

The molar concentration of the dilute acid is 0.075 M.

Step 1: Identify Known Values

First, identify the known values given in the problem. You have the initial volume of the concentrated solution, \(V_1 = 25.0\,\text{mL}\), and the initial molarity, \(M_1 = 1.50\,\text{M}\). The final volume after dilution is \(V_2 = 500.0\,\text{mL}\).

Step 2: Use the Dilution Equation

The dilution equation is \(M_1 \times V_1 = M_2 \times V_2\), where \(M_2\) is the molarity of the dilute solution that we need to find. Plug in the known values: \(1.50\,\text{M} \times 25.0\,\text{mL} = M_2 \times 500.0\,\text{mL}\).

Step 3: Solve for the Unknown Molarity

Rearrange the equation from Step 2 to solve for \(M_2\). Divide both sides by \(500.0\,\text{mL}\): \[M_2 = \frac{1.50\,\text{M} \times 25.0\,\text{mL}}{500.0\,\text{mL}}\]

Step 4: Calculate the Final Molarity

Perform the calculation: \[M_2 = \frac{1.50 \times 25.0}{500.0} = 0.075\,\text{M}\]Thus, the molar concentration of the dilute acid is \(0.075\,\text{M}\).

Key Concepts

Molarity

Molarity is a way to express the concentration of a solution. It tells you how many moles of a solute are dissolved in a liter of solution. This is an important concept because it allows you to determine how strong or weak a solution is.

Molarity is expressed in moles per liter (mol/L) and is abbreviated with the letter "M". The formula to calculate molarity is given by:

• \( M = \frac{n}{V} \)

where \( n \) is the number of moles of the solute and \( V \) is the volume of the solution in liters. This formula helps to know precisely how much of a substance is present in a given amount of solution.

When dealing with chemical reactions, knowing the molarity helps in predicting how much product will be formed or how much reactant is needed. It is essential in stoichiometry calculations and plays a critical role in various scientific analyses.

Dilution Equation

The dilution equation is a simple and powerful tool you can use to calculate the concentration of a solution after it has been diluted. It is rooted in the principle that the amount of solute stays the same before and after the dilution; only the volume changes.

This is expressed mathematically as:

• \( M_1 \times V_1 = M_2 \times V_2 \)

In this equation:

• \( M_1 \) is the molarity of the concentrated solution.
• \( V_1 \) is the volume of the concentrated solution.
• \( M_2 \) is the molarity of the dilute solution.
• \( V_2 \) is the volume of the diluted solution.

By rearranging this equation, you can solve for any unknown quantity. In practice, you plug in three known values, and solve for the missing one. This helps in determining how much solvent to add to achieve a desired concentration.

The equation simplifies the process of finding the concentration of a solution after dilution, making it easy to handle a common task in chemistry with precision and confidence.

Solution Concentration

Solution concentration refers to the amount of solute that is dissolved in a given volume of solvent. It is expressed in various ways, but molarity (M) is one of the most common units used in chemistry. Understanding and calculating solution concentrations is crucial in preparing solutions for experiments and chemical reactions.

Concentration indicates the strength or intensity of a solution. A highly concentrated solution has more solute particles per unit volume than a diluted one, which affects how the solution behaves in chemical reactions or physical processes.
Methods to measure concentration can include:

• Molarity as we've discussed, which is moles of solute per liter of solution.
• Mass percent, which is the mass of solute divided by the total mass of the solution, multiplied by 100.
• Volume percent, involving the volume of solute compared to the total volume of the solution.

These measurements are critical for diverse applications such as dosing medications, mixing chemicals accurately in laboratories, or even in everyday tasks like preparing beverages. Having a firm grasp on solution concentration ensures precision and effectiveness in both scientific and practical contexts.