Problem 162 - A Complete Resource Book in Chemistry for JEE Main

Question

\(1 \mathrm{~g}\) of an acid \(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{O}_{4}\) required \(0.768 \mathrm{~g}\) of \(\mathrm{KOH}\) for complete neutralization. Determine the basicity of acid.

Step-by-Step Solution

Answer

The basicity of the acid is 2.

Step 1: Understanding Basicity

Basicity of an acid refers to the number of hydrogen ions ( H^+ ) that can be replaced by a base during a reaction. This means we need to find how many moles of KOH (a base) are required to completely neutralize one mole of the acid, C_6H_{10}O_4 .

Step 2: Calculate Moles of KOH

First, calculate the number of moles of KOH used. Using the molar mass of KOH, which is approximately 56 g/mol, we calculate the moles:\[moles \ of \ KOH = \frac{0.768 \ g}{56 \ g/mol} = 0.0137 \ mol\]

Step 3: Calculate Moles of Acid

We need the molar mass of the acid C_6H_{10}O_4 to find its moles. The molar mass is calculated by adding the atomic masses:\(C: 12 \times 6; \ H: 1 \times 10; \ O: 16 \times 4\).Thus,\[molar \ mass \ of \ acid = 146 \ g/mol\]Using this, the moles of acid is:\[moles \ of \ acid = \frac{1 \ g}{146 \ g/mol} = 0.00685 \ mol\]

Step 4: Determine the Basicity

The basicity is determined by the ratio of the moles of KOH to the moles of the acid, since each mole of KOH replaces one hydrogen ion. Calculate this ratio:\[basicity = \frac{0.0137 \ mol \ KOH}{0.00685 \ mol \ acid} = 2\]So, the basicity of the acid C_6H_{10}O_4 is 2. Each molecule can donate 2 hydrogen ions to KOH.

Key Concepts

Basicity of Acids

Understanding the concept of basicity in acids is important. Basicity refers to the number of hydrogen ions (H\(^+\)) that an acid can donate to a base in a neutralization reaction. In simpler terms, it tells us how many hydrogen ions in an acid can be replaced by other ions during the reaction.

In the given exercise, the acid in question is C\(_6\)H\(_{10}\)O\(_4\). Basicity helps us determine how many moles of a base, like KOH, are needed to completely neutralize one mole of this acid. Since basicity is basically the count of replaceable hydrogen ions, an acid with a basicity of 1 can donate only one hydrogen ion, whereas an acid with a basicity of 2 can donate two. The key here is to look at the ratio of the moles of base (KOH) to the moles of acid to determine basicity.

Calculating Moles

Mole calculation is an essential part of chemistry that allows us to relate mass to the amount of substance. A mole is simply a way to count atoms or molecules, just like a dozen counts twelve items.

To calculate moles, you use the formula:

• moles = \( \frac{\text{mass of the substance}}{\text{molar mass}} \)

Using this formula helps us convert between mass and moles. In the exercise, we calculated the moles of KOH first by dividing its given mass (0.768 g) by its molar mass (56 g/mol). This gave us 0.0137 moles of KOH.

Similarly, calculating the moles of C\(_6\)H\(_{10}\)O\(_4\) involves dividing its mass (1 g) by its molar mass (146 g/mol), resulting in 0.00685 moles. These calculations are crucial for further determination of chemical properties like basicity.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, measured in grams per mole. It's an important calculation that allows us to determine the moles of a substance from its mass. You find molar mass by adding up the atomic masses of all atoms in a given molecule.

Consider the molecule C\(_6\)H\(_{10}\)O\(_4\). To find its molar mass:

• Carbon (C) has an atomic mass of about 12 g/mol and there are 6 C atoms, so it's 6 \( \times 12= 72 \) g/mol.
• Hydrogen (H) has an atomic mass of about 1 g/mol and there are 10 H atoms, totaling 10 g/mol.
• Oxygen (O) has an atomic mass of about 16 g/mol and there are 4 O atoms, hence 64 g/mol.

Adding these together, the molar mass of C\(_6\)H\(_{10}\)O\(_4\) is 146 g/mol. This calculation is straightforward once you know the individual atomic masses and how many of each kind of atom are in the molecule.