Problem 16 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Addition of sodium hydroxide solution to a weak acid (HA) results in a buffer of \(\mathrm{pH} 6\). If ionisation constant of \(\mathrm{HA}\) is \(10^{-5}\), the ratio of salt to acid concentration in the buffer solution will be : (a) \(4: 5\) (b) \(1: 10\) (c) \(10: 1\) (d) \(5: 4\)

Step-by-Step Solution

Answer

The ratio of salt to acid concentration is 10:1.

Step 1: Identify the Henderson-Hasselbalch Equation

To solve for the ratio of the concentrations of salt to acid in a buffer solution, we use the Henderson-Hasselbalch equation: \[ \mathrm{pH} = \mathrm{pK_a} + \log \left( \frac{[A^-]}{[HA]} \right) \] where \([A^-]\) is the concentration of the salt (conjugate base) and \([HA]\) is the concentration of the acid.

Step 2: Calculate pKa from the Ionization Constant

The ionization constant \(K_a\) of the weak acid \(\mathrm{HA}\) was given as \(10^{-5}\). Calculate \(\mathrm{pK_a}\) using the formula: \[ \mathrm{pK_a} = -\log(10^{-5}) = 5 \]

Step 3: Set Up the Henderson-Hasselbalch Equation

Substitute \(\mathrm{pH} = 6\) and \(\mathrm{pK_a} = 5\) into the Henderson-Hasselbalch equation: \[ 6 = 5 + \log \left( \frac{[A^-]}{[HA]} \right) \]

Step 4: Solve for the Logarithmic Term

Subtract \(5\) from both sides to isolate the logarithmic term: \[ 1 = \log \left( \frac{[A^-]}{[HA]} \right) \] This implies: \[ \log \left( \frac{[A^-]}{[HA]} \right) = 1 \]

Step 5: Evaluate the Exponential to Find the Ratio

Since \(\log(x) = 1\) means \(x = 10\), we have: \[ \frac{[A^-]}{[HA]} = 10 \] Therefore, the ratio of the concentration of salt to acid is \(10:1\).

Step 6: Verify Against the Given Options

Compare your calculated ratio \(10:1\) with the provided options. The correct answer from the options given is (c) \(10: 1\).

Key Concepts

Henderson-Hasselbalch equation

To understand buffer solutions and how they resist changes in pH, we use the Henderson-Hasselbalch equation. This equation is a simple and effective tool in chemistry, especially when it comes to buffer solutions. The equation is given by:\[ \mathrm{pH} = \mathrm{pK_a} + \log \left( \frac{[A^-]}{[HA]} \right) \]This formula helps us calculate the pH of a buffer by measuring the ratio of the concentrations of its components:

• \([A^-]\) is the concentration of the salt or conjugate base.
• \([HA]\) is the concentration of the weak acid.

The term \(\mathrm{pK_a}\) is crucial here. It's a measure of how easily the acid can lose a proton and covers the acid's strength in solution.By adjusting the ratio of the base to acid, we can control the pH of the solution, making this equation essential for maintaining the desired pH in many practical applications, like biological systems and chemical reactions.

pH calculation

Calculating the pH of a buffer solution isn't as complex as it might seem, thanks to the simplicity of the Henderson-Hasselbalch equation. In buffer systems, pH quantifies how acidic or basic a solution is by using a logarithmic scale. Let's break down the pH calculation process:Given the pH of the buffer solution, which is 6 in this case, Professor Hasselbalch's equation helps find the relationship between the acid and its conjugate base. Entering known values into the equation allows us to isolate and solve for unknowns. For instance, in the example provided:

• We have \(\mathrm{pH} = 6\) and \(\mathrm{pK_a} = 5\).
• Substitute these values into the equation: \[ 6 = 5 + \log \left( \frac{[A^-]}{[HA]} \right) \]
• Solving the equation gives us \[ \log \left( \frac{[A^-]}{[HA]} \right) = 1 \]

This result means that the ratio \(\frac{[A^-]}{[HA]}\) is 10. Understanding how to effectively use this equation enables conditions to be set that stabilize pH, invaluable for reactions or experiments sensitive to changes in acidity.

ionization constant

The ionization constant \(K_a\) is a reflection of an acid's ability to dissociate in solution. It's essential for understanding acid strength and behavior in different environments. When working with buffer solutions, calculating the \(\mathrm{pK_a}\) from the ionization constant is key for precise pH control.The given ionization constant for the weak acid \(\mathrm{HA}\) is \(10^{-5}\). To convert this into the \(\mathrm{pK_a}\), which is compatible with the Henderson-Hasselbalch equation, we use:\[ \mathrm{pK_a} = -\log(K_a) \]In this scenario:

• The \(K_a\) value is \(10^{-5}\).
• So \(\mathrm{pK_a} = -\log(10^{-5}) = 5\).

Knowing \(\mathrm{pK_a}\) allows you to insert this value into the pH equation, aiding in accurate predictions and adjustments of a buffer solution's properties.Understanding the ionization constant is fundamental when evaluating and predicting how an acid will behave in different situations, which is particularly useful for many scientific and industrial processes.