Animated Solution for Chemistry - Basic Concepts in Chemistry: In the reaction, $2\text{Al}(s)+6\text{HCl}(aq)⟶2{\text{Al}}^{3+}(aq)+6{\text{Cl}}^{-}(aq)+3{\text{H}}_2(g)$

Let's dive into the fascinating world of stoichiometry! We are given a classic single-displacement reaction where solid aluminum reacts with aqueous hydrochloric acid to produce aluminum chloride and hydrogen gas. The balanced chemical equation is our ultimate guide here:

This equation isn't just a string of symbols; it's a precise recipe. It tells us exactly how many moles of each reactant are needed to produce a specific number of moles of products.

Stoichiometric Ratios

If we look closely at the coefficients of the reactants and products, we can establish a direct relationship between the hydrochloric acid consumed and the hydrogen gas produced.

According to the balanced equation, $6$ moles of $\text{HCl}$ react to produce exactly $3$ moles of ${\text{H}}_2$ gas.

We can use the unitary method to find out how much hydrogen is produced per mole of $\text{HCl}$ consumed. If $6$ moles of $\text{HCl}$ give $3$ moles of ${\text{H}}_2$, then $1$ mole of $\text{HCl}$ will produce:

So, for every single mole of $\text{HCl}$ that reacts, half a mole of hydrogen gas bubbles out of the solution.

Molar Volume at STP

Now, the options are given in terms of volume (liters) at Standard Temperature and Pressure (STP). Recall the fundamental principle of ideal gases: $1$ mole of any ideal gas at STP occupies a volume of $22.4\text{ L}$.

Since we have $0.5$ moles of ${\text{H}}_2$ gas produced per mole of $\text{HCl}$, we can easily calculate its volume:

Therefore, $11.2\text{ L}$ of ${\text{H}}_2(g)$ at STP is produced for every mole of $\text{HCl}(aq)$ consumed. This perfectly matches option (d).

It is always a good practice to understand why the wrong options are wrong.

- Option (a) suggests $6\text{L}$ of $\text{HCl}(aq)$ is consumed. This is a trap! The coefficient '$6$' represents moles, not liters. $\text{HCl}$ is in an aqueous solution, so its volume depends on its molarity, not the ideal gas law. - Option (b) claims the volume is produced regardless of temperature and pressure. This violates the ideal gas law ($PV=nRT$). Gas volume is highly dependent on both $T$ and $P$. - Option (c) states $67.2\text{ L}$ of ${\text{H}}_2$ is produced per mole of $\text{Al}$. Let's check: $2$ moles of $\text{Al}$ give $3$ moles of ${\text{H}}_2$. So, $1$ mole of $\text{Al}$ gives $1.5$ moles of ${\text{H}}_2$. At STP, $1.5\text{ moles}\times 22.4\text{ L/mol}=33.6\text{ L}$, not $67.2\text{ L}$.