Problem 117 - Chemistry The Central Science In Si Units

Question

How many milliliters of concentrated hydrochloric acid solution \((36.0 \% \mathrm{HCl}\) by mass, density \(=1.18 \mathrm{~g} / \mathrm{mL}\) ) are required to produce \(10.0 \mathrm{~L}\) of a solution that has a pH of \(2.05 ?\)

Step-by-Step Solution

Answer

You need approximately 7.65 mL of concentrated HCl solution.

Step 1: Understand the pH

pH is a measure of the hydrogen ion concentration in a solution. A pH of 2.05 indicates a hydrogen ion concentration of \[ [H^+] = 10^{-2.05} \approx 8.91 \times 10^{-3} \text{ M} \]

Step 2: Calculate moles of HCl

To determine how many moles of HCl are needed, multiply the desired molarity by the volume of the solution:\[ \text{Moles of HCl} = 8.91 \times 10^{-3} \text{ mol/L} \times 10.0 \text{ L} = 8.91 \times 10^{-2} \text{ moles} \]

Step 3: Determine mass of HCl required

Next, calculate the mass of HCl needed using its molar mass (36.46 g/mol):\[ \text{Mass HCl} = 8.91 \times 10^{-2} \text{ moles} \times 36.46 \text{ g/mol} \approx 3.25 \text{ g} \]

Step 4: Calculate volume of concentrated HCl solution needed

Find how much of the 36.0% HCl solution is needed to provide this mass:\[ \text{Mass of solution} = \frac{3.25 \text{ g HCl} }{0.36} \approx 9.03 \text{ g} \]Then, convert the mass of the solution to volume using its density (1.18 g/mL):\[ \text{Volume} = \frac{9.03 \text{ g}}{1.18 \text{ g/mL}} \approx 7.65 \text{ mL} \]

Step 5: Review and verify calculations

Ensure all steps logically follow each other and the calculations have been double-checked to ensure accuracy.

Key Concepts

Hydrogen Ion Concentration

In the world of chemistry, understanding the concept of hydrogen ion concentration is crucial when discussing pH. The "pH" of a solution signifies how acidic or basic it is and is intricately linked to the concentration of hydrogen ions \([H^+]\). When a solution has a pH of 2.05, this corresponds to a hydrogen ion concentration equal to \(10^{-2.05}\).
This equates roughly to approximately \(8.91 \times 10^{-3}\) moles per liter (M), which means there are nearly 0.00891 moles of hydrogen ions in every litre of this solution.
Understanding this value helps you realize just how acidic the solution is, as lower pH values indicate higher concentrations of hydrogen ions. When dealing with such acidic solutions, precise calculations and understanding these numbers are fundamental.

Molarity

Molarity is an essential concept in chemistry, representing the concentration of a solute in a solution. It's defined as the number of moles of a solute per liter of solution. In our case, we have a hydrogen ion concentration that directly reflects the necessary molarity of the solution.
To produce a solution with a pH of 2.05, we aim for a molarity of about \(8.91 \times 10^{-3}\) M. This means we need 8.91 millimoles of hydrogen ions, or equivalently, HCl, in each liter of solution.

• Calculate total moles needed: Since we want to make 10.0 L of such a solution, the total moles required would be \(8.91 \times 10^{-2}\) moles.

Once this molarity is understood, it serves as a guiding anchor for preparing and adjusting any solution to a desired concentration.

Solution Density

When working with solutions, solution density is a key parameter, especially when converting between mass and volume. Density refers to how much mass of a substance is contained in a given volume. For hydrochloric acid (HCl) solutions, knowing the density allows us to calculate the volume of solution needed from its mass.
In our calculation, the concentrated HCl solution has a density of 1.18 g/mL. This means that every milliliter of this acid solution weighs 1.18 grams. It becomes essential when we want to convert from grams (mass of HCl we need) to milliliters (volume of concentrated solution necessary).

• Mass to volume conversion: For instance, if we require \(9.03\) grams of the solution, dividing this by the density gives us the volume needed, approximately \(7.65\) mL.

Understanding solution density helps ensure precise laboratory measurements and optimizes solution preparation.

Moles of HCl

Moles are a unit that measures quantity in chemistry, similar to how we measure items like "dozen" for eggs. One mole denotes Avogadro's number, \(6.022 \times 10^{23}\) entities, enabling a manageable way to count atoms or molecules involved in chemical reactions. Calculating the moles of HCl required helps in preparing a specified concentration of a solution.
From an HCl solution with a desired hydrogen ion concentration, the moles of HCl needed are obtained by: \(8.91 \times 10^{-3} \,\text{mol/L} \times 10.0 \,\text{L} = 8.91 \times 10^{-2} \,\text{moles}\).

• Application: Using this mole calculation, we then compute how much HCl solution is required in terms of mass, helping in deriving how much concentrated acid needs dilution.

Understanding this concept helps you link the microscopic chemical world to practical measurements and adjustments in the lab.