Problem 90 - A Complete Resource Book in Chemistry for JEE Main

Question

The equivalent weight of phosphoric acid \(\left(\mathrm{H}_{3} \mathrm{PO}_{4}\right)\) in the reaction: \(\mathrm{NaOH}+\mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow \mathrm{NaH}_{2} \mathrm{PO}_{4}+\mathrm{H}_{2} \mathrm{O}\) is (a) 89 (b) 98 (c) 59 (d) 29

Step-by-Step Solution

Answer

The equivalent weight of \( \mathrm{H}_{3} \mathrm{PO}_{4} \) in this reaction is 98 g/eq (option b).

Step 1: Determine the Molar Mass of Phosphoric Acid

First, calculate the molar mass of phosphoric acid, \( \mathrm{H}_{3} \mathrm{PO}_{4} \). The molar masses of hydrogen (H), phosphorus (P), and oxygen (O) are approximately 1 g/mol, 31 g/mol, and 16 g/mol, respectively. This leads to the following calculation: \[(3 \times 1) + 31 + (4 \times 16) = 3 + 31 + 64 = 98 \, \text{g/mol} \]

Step 2: Identify Equivalent Weight Concept

The equivalent weight is determined by the formula: \[ \text{Equivalent weight} = \frac{\text{Molar mass}}{n} \] where \( n \) is the number of hydrogen ions (\( \text{H}^+ \)) furnished by the acid in the reaction.

Step 3: Determine Number of Replaceable Hydrogen Atoms

Analyze the reaction: \( \mathrm{NaOH} + \mathrm{H}_{3} \mathrm{PO}_{4} \rightarrow \mathrm{NaH}_{2} \mathrm{PO}_{4} + \mathrm{H}_{2} \mathrm{O} \). \( \mathrm{H}_{3} \mathrm{PO}_{4} \) loses one hydrogen ion to form \( \mathrm{NaH}_{2} \mathrm{PO}_{4} \) and water. Therefore, \( n = 1 \).

Step 4: Calculate Equivalent Weight

Using the relationship from Step 2 and the value of \( n = 1 \) from Step 3, we calculate the equivalent weight of \( \mathrm{H}_{3} \mathrm{PO}_{4} \): \[ \text{Equivalent weight} = \frac{98}{1} = 98 \, \text{g/eq} \]

Key Concepts

Phosphoric Acid

Phosphoric acid, chemically known as \( \text{H}_3\text{PO}_4 \), is a common inorganic acid. It's widely used in the food industry and in the manufacture of fertilizers. In terms of structure, phosphoric acid consists of three hydrogen atoms, a phosphorus atom, and four oxygen atoms. These atoms are arranged such that the phosphorus atom is centrally bonded to the four oxygen atoms, forming the core tetrahedral arrangement of the molecule. Each hydrogen is bonded to an oxygen, making these hydrogens acidic, allowing \( \text{H}_3\text{PO}_4 \) to donate protons during reactions.
Phosphoric acid is classified as a triprotic acid, which means it can lose up to three protons through ionization. This characteristic makes it versatile in acid-base reactions, as it can donate one, two, or all three of its hydrogens depending on the reaction conditions. Understanding the ionizable nature of phosphoric acid is crucial when calculating its equivalent weight, as it directly impacts the determination of the number of protons it donates in a chemical reaction.

Acid-Base Reaction

An acid-base reaction is a chemical process involving the reaction of an acid and a base. Through these reactions, acids donate protons (hydrogen ions), and bases accept them. The resulting products are usually a salt and water.
In the specific reaction given, \( \text{NaOH} + \text{H}_3\text{PO}_4 \rightarrow \text{NaH}_2\text{PO}_4 + \text{H}_2\text{O} \), sodium hydroxide (\( \text{NaOH} \)) acts as a base, accepting a hydrogen ion from phosphoric acid. In this case, \( \text{H}_3\text{PO}_4 \) donates only one of its three available protons to \( \text{NaOH} \). This exchange leads to the formation of sodium dihydrogen phosphate (\( \text{NaH}_2\text{PO}_4 \)) and water. Understanding the specific reaction path is crucial because it dictates the number of hydrogen ions participating in the reaction. This detail is key when determining the equivalent weight of phosphoric acid in this scenario, as only one hydrogen is involved in the exchange process.

Molar Mass Calculation

The molar mass of a compound is the sum of the atomic masses of its constituent elements. Calculating the molar mass is essential because it is used to convert between grams and moles, a fundamental concept in chemistry for quantifying substances.
To calculate the molar mass of phosphoric acid (\( \text{H}_3\text{PO}_4 \)), you tally the atomic masses of hydrogen, phosphorus, and oxygen:

• Hydrogen (H): 1 g/mol; for 3 atoms, multiply by 3.
• Phosphorus (P): 31 g/mol; for 1 atom.
• Oxygen (O): 16 g/mol; for 4 atoms, multiply by 4.

The formula is as follows: \[(3 \times 1) + 31 + (4 \times 16) = 3 + 31 + 64 = 98 \, \text{g/mol}\]This calculation yields a molar mass of 98 g/mol for \( \text{H}_3\text{PO}_4 \). Knowing the molar mass allows us to determine equivalent weight by factoring in the number of ionizable protons involved in the acid-base reaction.