Q.Hydrogen gas is prepared in the laboratory by reacting dilute HCl with granulated zinc. Following reaction takes place. $Zn + 2HCl \rightarrow ZnCl_2 + H_2$ Calculate the volume of hydrogen gas liberated at STP when 32.65 g of zinc reacts with HCl. 1 mol of a gas occupies 22.7 L volume at STP; atomic mass of Zn = 65.3 u.

The key idea is Stoichiometry and Mole Concept.

First, calculate the moles of zinc reacting.

From the balanced chemical equation, $Zn + 2HCl \rightarrow ZnCl_2 + H_2$, 1 mole of Zn produces 1 mole of H$_2$.

Therefore, 0.5 mol of Zn will produce 0.5 mol of H$_2$.

Finally, use the given molar volume at STP to find the volume of hydrogen gas. …

When we talk about chemical reactions, the quantities involved are often expressed in grams or litres. However, chemical reactions fundamentally occur at the molecular level, where atoms and molecules combine in specific whole-number ratios. To bridge this gap between the macroscopic (grams, litres) and microscopic (atoms, molecules) world, we use the concept of the mole.

The balanced chemical equation, $Zn + 2HCl \rightarrow ZnCl_2 + H_2$, tells us the stoichiometric relationship between the reactants and products. The coefficients in front of each chemical species represent the relative number of moles involved in the reaction. In this case, 1 mole of zinc reacts to produce 1 mole of hydrogen gas. This mole ratio is the cornerstone of solving stoichiometry problems.

Furthermore, for gases, we have a convenient relationship between moles and volume at standard conditions. Standard Temperature and Pressure (STP) are defined conditions (usually $0^\circ C$ or $273.15 K$ and $1 \text{ bar}$ or $10^5 \text{ Pa}$), under which 1 mole of any ideal gas occupies a specific volume. The problem states that 1 mole of a gas occupies 22.7 L at STP. This is the molar volume at STP according to IUPAC recommendations (older definitions might use 22.4 L at $1 \text{ atm}$).

Here's how we can calculate the volume of hydrogen gas:

1. Determine the moles of zinc reacting.

   We are given the mass of zinc and its atomic mass. The atomic mass of an element, when expressed in grams, represents the mass of one mole of that element.

   $\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$

   Given mass of Zn = 32.65 g

   Molar mass of Zn = 65.3 g/mol (since atomic mass is 65.3 u)

   $n_{Zn} = \frac{32.65 \text{ g}}{65.3 \text{ g/mol}}$

   $n_{Zn} = 0.5 \text{ mol}$

   So, 0.5 moles of zinc are reacting.

2. Use the stoichiometry of the balanced equation to find the moles of hydrogen gas produced.

   The balanced equation is:

   $Zn + 2HCl \rightarrow ZnCl_2 + H_2$ …

Method: Mole Concept and Stoichiometric Calculation

This problem uses the mole concept to relate the mass of a reactant to the volume of a gaseous product at STP.

Steps

Step 1: Write the balanced chemical equation

The given equation is already balanced:

Step 2: Find the number of moles of zinc

Given: mass of Zn = 32.65 g, atomic mass of Zn = 65.3 u

Step 3: Use stoichiometric ratio to find moles of H₂

From the equation: 1 mol Zn produces 1 mol H₂

So, 0.5 mol Zn produces 0.5 mol H₂

Step 4: Convert moles of H₂ to volume at STP

Given: 1 mol of gas occupies 22.7 L at STP …

Here are the common mistakes students make on this classic stoichiometry problem, along with clear strategies to avoid each.

Mistake 1: Using the Wrong Molar Volume at STP

The error:

Many students automatically use 22.4 L/mol for STP, but the problem explicitly states 22.7 L/mol. This is because different definitions of STP exist (old IUPAC: 0°C, 1 atm → 22.4 L; new IUPAC: 0°C, 1 bar → 22.7 L). Using 22.4 L here would give a wrong final answer.

How to avoid:

• Read the problem carefully — always check the given molar volume.
• If the problem says “at STP” but does not give a value, use 22.4 L/mol (the older, still common exam standard).
• If a specific value like 22.7 L is given, use that value only.

Mistake 2: Incorrect Mole Calculation from Mass

The error:

Students sometimes divide the given mass by the wrong atomic mass or forget that the atomic mass of Zn is given as 65.3 u (not 65.4 or 65). They might also round too early.

Correct approach:

• Use the exact given atomic mass:

• Do not round intermediate steps — keep 0.5 exactly.

Mistake 3: Forgetting the 1:1 Mole Ratio

The error:

Some students think 2 moles of HCl produce 2 moles of H₂, so they multiply by 2 incorrectly. Others mistakenly use the ratio from HCl instead of Zn.

The key fact:

From the balanced equation:

The mole ratio of Zn : H₂ is 1 : 1.

So, moles of H₂ = moles of Zn = 0.5 mol.

How to avoid:

• Always write the balanced equation first.
• Identify the reactant you are given (here, Zn) and find its ratio to the product (H₂).
• Ignore HCl unless it is the limiting reagent — here, HCl is in excess.

Mistake 4: Using the Wrong Volume Formula

The error:

Students sometimes use the ideal gas equation $PV = nRT$ unnecessarily, or they multiply moles by 22.4 instead of 22.7.

Correct method:

Volume of gas = moles of gas × molar volume at given conditions.

$V = 0.5 \times 22.7 = 11.35 \text{ L}$ …