Problem 51 - Chemistry and Chemical Reactivity

Question

If you dilute \(25.0 \mathrm{mL}\) of \(1.50 \mathrm{M}\) hydrochloric acid to 500 . 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 the Relationship

To find the molar concentration of the dilute solution, we use the dilution formula, which is \[ C_1V_1 = C_2V_2 \]where \(C_1\) and \(V_1\) are the initial concentration and volume of the solution, and \(C_2\) and \(V_2\) are the final concentration and volume after dilution.

Step 2: Substitute Known Values

We know from the problem statement that \(C_1 = 1.50 \, \text{M}\), \(V_1 = 25.0 \, \text{mL}\), and \(V_2 = 500.0 \, \text{mL}\). Substitute these values into the dilution equation:\[ 1.50 imes 25.0 = C_2 imes 500.0 \]

Step 3: Solve for \(C_2\)

To find \(C_2\), solve the equation \[ 37.5 = C_2 imes 500.0 \]by dividing both sides by 500.0:\[ C_2 = \frac{37.5}{500.0} \]

Step 4: Calculate the New Concentration

Perform the division to find \(C_2\):\[ C_2 = 0.075 \, \text{M} \]This is the molar concentration of the dilute hydrochloric acid.

Key Concepts

Dilution Formula

When dealing with solutions, the dilution formula is a critical tool that helps in calculating changes in concentration. The formula, expressed as \( C_1V_1 = C_2V_2 \), succinctly represents the relationship between concentrations and volumes before and after the dilution process.
This formula works because, in a dilution, the amount of solute remains constant even though the total volume changes.

• \( C_1 \) and \( V_1 \) refer to the initial concentration and volume of the solution, respectively.
• \( C_2 \) and \( V_2 \) stand for the new concentration and volume after dilution.

Using this formula, we can calculate how diluting a concentrated solution affects its molarity, which is the concentration of the solution in moles per liter.

Molar Concentration

Molar concentration, or molarity, is an essential aspect of chemistry that defines the number of moles of solute per liter of solution. It is typically expressed in moles per liter (M).
Understanding molarity helps in predicting how a solution will behave in chemical reactions.
**Calculating Molarity** involves the formula:

• \( \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \)

When diluting a solution, the molarity changes as shown in the dilution example, but the total amount of solute stays the same.
Therefore, it is crucial to comprehend how to calculate and adjust molarity in various chemical processes.

Hydrochloric Acid

Hydrochloric acid (HCl) is a highly important mineral acid commonly used in laboratory and industrial settings.
It is a colorless solution and has a pungent smell.
**Properties of Hydrochloric Acid** include:

• **Corrosive Nature:** It can cause damage to living tissues and materials, which makes handling it with caution important.
• **Common Uses:** Used in cleaning, digesting foods in stomach, and chemical industry.
• **Reactivity:** Highly reactive, used in processes like pickling of steel and production of organic compounds.

In the context of preparing dilute solutions from concentrated HCl, understanding the potency and handling precautions of hydrochloric acid is crucial, as it can significantly influence the outcome and safety of experiments and processes.