Problem 14 - Chemistry for Allied Health

Question

What volume of \(12 \mathrm{M} \mathrm{HCl}\) is required to prepare \(6.00 \mathrm{~L}\) of a \(0.300 \mathrm{M}\) solution?

Step-by-Step Solution

Answer

150 mL of 12 M HCl is needed to prepare the solution.

Step 1: Identify Given Information

We are provided with the initial concentration of the solution, which is \(12 \mathrm{M} \mathrm{HCl}\), and we need to prepare \(6.00\, \mathrm{L}\) of a \(0.300 \mathrm{M}\) solution.

Step 2: Identify Formula to Use

To solve dilution problems, we use the formula \(C_1V_1 = C_2V_2\), where \(C_1\) and \(V_1\) are the concentration and volume of the initial solution, and \(C_2\) and \(V_2\) are the concentration and volume of the final solution.

Step 3: Set Up the Equation

Using the formula \(C_1V_1 = C_2V_2\), substitute the given values: \(12 \mathrm{M} \cdot V_1 = 0.300 \mathrm{M} \cdot 6.00 \mathrm{L}\).

Step 4: Solve for \(V_1\)

Rearrange the equation to solve for \(V_1\): \(V_1 = \frac{0.300 \times 6.00}{12}\).

Step 5: Calculate \(V_1\)

Perform the calculation: \(V_1 = \frac{1.8}{12} = 0.150\, \mathrm{L}\).

Step 6: Convert to Desired Units

Since the volume is often required in milliliters, convert \(0.150\, \mathrm{L}\) into milliliters by multiplying by 1000. \(V_1 = 0.150 \times 1000 = 150\, \mathrm{mL}\).

Key Concepts

Concentration

Concentration is a measure of the amount of solute present in a given quantity of solvent or solution. Think of it like the strength of coffee—strong coffee has a high concentration of coffee beans, while weaker coffee has fewer beans. Concentration can be expressed in various ways, but in chemistry, one of the most common is molarity. Molarity ( M ) indicates the moles of a solute per liter of solution, which makes it particularly useful for stoichiometric calculations.

• Importance of Concentration: Understanding concentration is crucial when you want to predict how chemical reactions proceed or determine the dosage of chemicals needed in different conditions.
• Applications: High concentrations imply more solute, which is often used when you need a more reactive solution, such as in industrial processes or laboratory analyses.

To adjust the concentration of a solution, you can dilute it with more solvent, effectively decreasing the molarity without changing the number of moles of solute.

Volume calculations

Volume calculations are critical when preparing solutions with specific concentrations.
Calculating the volume involves understanding how much space the liquid occupies, which is essential in mixing solutions accurately. When calculating volumes in solutions, especially for chemical dilutions, it is vital to use a consistent unit of measure, such as liters or milliliters.

• Volume of Solution: To calculate the volume of a solution being prepared, you need to know how much of the stock solution you have to start with (initial volume) and how much final solution you need.
• Using the Formula: The formula \( C_1V_1 = C_2V_2 \) is used for fixing the volume of a solution to attain a desired concentration. Here, \(C_1\) is the initial concentration, \(V_1\) is the volume of the stock solution, \(C_2\) is the final concentration, and \(V_2\) is the final volume of the solution.

By breaking down the problem into manageable parts, you can accurately calculate the required volume of solutions for various experiments or lab activities.

Molarity

Molarity is a very focused term crucial in chemistry, representing the concentration of a solution. It is described by the number of moles of solute per liter of solution (mol/L). It's like the measure of how crowded the solute particles are in the solution.

• Importance of Molarity: Knowing the molarity of a solution helps understand its strength and reactivity. For example, a 12 M HCl solution is quite strong and must be handled with care.
• Calculating Molarity: You can calculate molarity using the formula \( M = \frac{n}{V} \) where \(n\) is the number of moles of the solute, and \(V\) is the volume of the solution in liters.
• Using Molarity in Dilution: In preparing a diluted solution, understanding molarity is crucial. The concentration of the solute changes, but the total moles of solute remain the same.
  By applying the concept of molarity to chemical problems, it becomes easier to predict and control the outcome of reactions and prepare solutions with accuracy.