Question

\(1 \mathrm{~mL}\) of \(0.1 \mathrm{~N} \mathrm{HCl}\) is added to \(999 \mathrm{~mL}\) solution of \(\mathrm{NaCl}\). The \(\mathrm{pH}\) of the resulting solution will be : (a) 7 (b) 4 (c) 2 (d) 1

Short answer

The pH of the resulting solution will be 4.

Step-by-step solution

- Determine the total volume of the solution

After adding 1 mL of 0.1 N HCl to 999 mL of NaCl solution, the total volume of the solution becomes the sum of both volumes: 1 mL + 999 mL = 1000 mL or 1 L.

- Calculate the number of moles of HCl

0.1 N HCl means that there are 0.1 moles of H+ ions in 1 L of solution. Since we only have 1 mL of HCl, the moles of H+ ions we have is 0.1 moles/L * 0.001 L = 0.0001 moles.

- Calculate the concentration of H+ ions in the new solution

The concentration of H+ ions after dilution can be calculated by using the formula concentration = moles/volume. The volume of the new solution is 1 L. Hence, the concentration of H+ = 0.0001 moles / 1 L = 0.0001 M.

- Calculate the pH of the solution

The pH is given by the negative logarithm (base 10) of the hydrogen ion concentration. Thus, pH = -log(0.0001).

- Solve for pH

To find the pH, compute the logarithm of 0.0001, which is -log(0.0001) = 4. The pH of the resulting solution is therefore 4.

Key concepts

Dilution of Solutions

Understanding the process of diluting a solution is crucial for various laboratory and industrial applications. Dilution refers to the addition of solvent, which is typically water, to a solution in order to decrease the concentration of solutes. In other words, when you dilute a solution, you are spreading the solute's particles over a larger volume, thus reducing its concentration. A key point to remember is that while the volume of the solution increases through dilution, the amount of solute remains unchanged. This principle is used in our example where adding 1 mL of hydrochloric acid (HCl) to a larger volume decreases the acid's concentration.
To elaborate, when the 0.1 N HCl is added to 999 mL of NaCl solution, the resulting solution's volume increases to 1000 mL, or 1 L. However, the moles of HCl remain the same; they are simply less concentrated over the new volume. When performing dilutions, it is essential to keep track of both the volume and the concentration changes to understand the resulting solution's properties.

Molarity and Normality

Molarity and normality are two critical concepts when dealing with chemical solutions in chemistry. Molarity, denoted as M, is the number of moles of solute per liter of solution, making it a measure of the concentration of a solute in a solution. On the other hand, normality, symbolized by N, is a measure of the concentration of reactive units in a solution, and it is particularly useful for acid-base reactions since it accounts for the number of protons (hydrogen ions) or hydroxide ions that one mole of the acid or base can donate or accept, respectively.
In our textbook problem, we deal with a normality of 0.1 N HCl. This means that the 0.1 N HCl solution has 0.1 equivalent of H+ ions per liter. An important thing to note is that for HCl, which is a monoprotic acid (donates one proton per molecule), the molarity is equal to its normality. Hence, in the exercise, the molarity of HCl before dilution is also 0.1 M. After dilution, though, the molarity changes as the volume increases, altering the acid's concentration in the resulting solution.

Logarithms in Chemistry

Logarithms play a significant role in chemistry, particularly in the study of acid-base chemistry. A logarithm is a way to express the power to which a number, called the base, must be raised to produce a given number. In chemistry, the most common logarithms are those with a base of 10, also known as common logarithms, denoted as 'log'.
The pH scale, which is a measure of the acidity or basicity of an aqueous solution, is logarithmic. This means that each whole number change in pH represents a tenfold increase or decrease in hydrogen ion concentration. The formula for pH is given by \( pH = -\text{log}([H^+]) \),where \([H^+]\)is the hydrogen ion concentration. Because the pH scale is logarithmic, it compresses the wide range of hydrogen ion concentrations into a more manageable scale of 0 to 14. In our exercise, we use the logarithmic relationship to calculate that a hydrogen ion concentration of 0.0001 M corresponds to a pH of 4.

Acid and Base Concentration

The concentration of acids and bases in a solution is a critical factor in understanding their chemical behavior, especially in reactions. The concentration determines the strength of the acid or base in a solution, which is essential for predicting the outcomes of chemical reactions. High concentrations of hydrogen ions (H+) indicate acidic solutions, while high concentrations of hydroxide ions (OH-) imply basic solutions. In our exercise case, the solution's acidity is influenced by the HCl's concentration after dilution.
To determine the acid concentration after dilution, we use the formula \( [H^+] = \frac{\text{moles of acid}}{\text{volume of solution}} \).This means that the lower the volume of solvent added, the less diluted the acid will be, and therefore, the higher the concentration of H+ ions. After the HCl is diluted with NaCl solution, the H+ concentration decreases, leading to a lower acidity level of the resulting solution, as shown by the calculated pH of 4.