Question

How would you prepare \(1600 \mathrm{~mL}\) of a \(\mathrm{pH}=1.50\) solution using concentrated \((12 M) \mathrm{HCl} ?\)

Short answer

To prepare $1600 \mathrm{~mL}$ of a $\mathrm{pH} = 1.50$ solution using concentrated $(12 M) \mathrm{HCl}$, first calculate the molarity of the resulting solution using the pH equation, which gives $[H^+] = 0.0316M$. Next, determine the volume of concentrated HCl required using the dilution equation, which gives $V1 = 4.21 \mathrm{~mL}$. Finally, prepare the solution by measuring 4.21 mL of concentrated $12 M \mathrm{HCl}$, carefully adding it to $1600 \mathrm{~mL}$ of distilled water, and mixing gently until homogeneous.

Step-by-step solution

Calculate the molarity of the resulting solution

To find the molarity of the resulting solution, we use the pH equation: \( pH = -\log_{10} [H^+] \) Rearrange the equation to find [H+]: \( [H^+] = 10^{-pH} \) Plug in the given pH value: \[ [H^+] = 10^{-1.50} \] Calculate the molarity: \[ [H^+] =0.0316M \]

Determine the volume of concentrated HCl required

To find the volume of concentrated HCl needed, we use the dilution equation (M1V1 = M2V2): M1 = Concentration of the stock solution (12 M) V1 = ? (this is the volume of stock solution we need to determine) M2 = concentration of the diluted solution (0.0316 M) V2 = volume of the diluted solution (1600 mL) Plugging the numbers into the equation M1V1 = M2V2: \( 12V1 = 0.0316 \times 1600 \) Solve for V1: \( V1 = \frac{0.0316 \times 1600}{12} \) Calculate the volume, V1: \( V1 = 4.21 \mathrm{~mL} \)

Prepare the 1600 mL pH 1.50 solution

To prepare the solution, follow these steps: 1. Measure 4.21 mL of the concentrated 12 M HCl using a graduated cylinder or a pipette. 2. Pour the 4.21 mL of HCl into a 1600 mL volumetric flask. 3. Fill the volumetric flask with distilled water about ¾ of the way and gentle mix the solution. 4. Add more distilled water until the solution reaches the 1600 mL mark on the volumetric flask. 5. Mix the solution gently until homogeneous. Now, you have prepared 1600 mL of a pH 1.50 solution using concentrated 12 M HCl.

Key concepts

Molarity Calculation

Molarity, often denoted as \( M \), is an important concept in solution chemistry. It is defined as the number of moles of a solute dissolved in one liter of solution. For example, a 1 M solution of hydrochloric acid (HCl) contains one mole of HCl per liter of solution. Molarity helps chemists understand the concentration of a solution, making it easier to react the solution with other substances.
To calculate molarity, the equation \( M = \frac{n}{V} \) can be used, where \( n \) represents the moles of solute, and \( V \) represents the volume of solution in liters. In this case, we first determined the molarity of the resulting solution using the pH value. The formula to go from pH to hydrogen ion concentration is \( [H^+] = 10^{-pH} \).
This simple formula provides the molarity of hydrogen ions in the solution based on the pH scale, which is logarithmic. Therefore, a small change in pH reflects a significant change in hydrogen ion concentration.

Dilution Equation

The dilution equation, given as \( M_1V_1 = M_2V_2 \), is vital in chemistry for preparing solutions of desired concentrations. It allows us to calculate how much of a concentrated solution is needed to make a specific volume of a more diluted solution. Here, \( M_1 \) and \( V_1 \) refer to the molarity and volume of the concentrated solution, while \( M_2 \) and \( V_2 \) refer to the diluted solution.
In our exercise, a 12 M hydrochloric acid (HCl) solution is diluted to obtain a solution with a particular pH. By rearranging the dilution equation, we solve for the unknown volume \( V_1 \) using the known values: \( 12 M \) for \( M_1 \), \( 0.0316 M \) for \( M_2 \), and \( 1600 \mathrm{~mL} \) for \( V_2 \).
Understanding the dilution equation is crucial for laboratory work as it ensures accurate concentration control without wasting chemicals.

Volumetric Flask

A volumetric flask is a type of laboratory glassware used to prepare solutions to an exact volume. It is essential for making precise measurements in quantitative chemistry. These flasks are characterized by their narrow neck and a mark (known as a calibration mark) that indicates the specific volume the flask can hold, usually at the neck's narrowest point.
In our solution preparation task, the volumetric flask aids in ensuring the final solution is exactly 1600 mL as required. By filling the flask to the calibration mark with distilled water after adding the concentrated HCl, one can ensure that the dilution is accurate to the last milliliter.
Volumetric flasks come in various sizes, and using them correctly involves knowledge of their limitations, such as not overfilling and being aware of the meniscus level during measurements.

Hydrochloric Acid

Hydrochloric acid, often abbreviated as HCl, is a strong monoprotic acid, meaning it can donate one proton per molecule in an aqueous solution. It is widely used in industrial and lab settings because of its corrosiveness and ability to react with a wide range of compounds.
In this exercise, we are using a concentrated solution of HCl with a molarity of 12 M. When diluting concentrated HCl, care is taken due to its high reactivity and potential to release hydrogen chloride gas, which is corrosive.
Safety measures include using appropriate glassware like volumetric flasks for dilution, performing procedures in a well-ventilated area, and wearing protective gear. Understanding the properties of hydrochloric acid and its behavior in solutions is fundamental for safely and effectively preparing solutions in chemistry.