What volume of hydrogen at STP can be produced by reacting \(8.30 \mathrm{~mol}\) of \(\mathrm{Al}\) with sulfuric acid? The equation is $$ 2 \mathrm{Al}(s)+3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+3 \mathrm{H}_{2}(g) $$

Understanding the mole ratio in a chemical reaction is pivotal in solving stoichiometry problems, as it acts as a bridge between reactants and products. When looking at a balanced chemical equation, in this case, \(2 \mathrm{Al}(s) + 3 \mathrm{H}_{2} \mathrm{SO}_{4}(aq) \rightarrow \mathrm{Al}_{2}(\mathrm{SO}_{4})_{3}(aq) + 3 \mathrm{H}_{2}(g)\), the mole ratio tells us how many moles of one substance will react or form when a certain number of moles of another substance are used.

The coefficients in the balanced chemical equation directly provide the mole ratio. For each 2 moles of aluminum (Al) that react, 3 moles of hydrogen gas (H2) are produced. If we have 8.30 moles of Al, the mole ratio allows us to determine the moles of H2 formed by setting up a proportion. This concept lays the foundation for predictive calculations in chemistry, allowing us to move onto the next step where we apply Avogadro's Law to decipher the volume of gas produced.

Avogadro's Law is key to understanding how gases behave under standard conditions. It states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. Consequently, the volume of a gas is directly proportional to the number of moles of gas present, as long as the temperature and pressure are constant.

At standard temperature and pressure (STP), which is 0 degrees Celsius (273.15 K) and 1 atmosphere of pressure, one mole of any gas occupies 22.4 liters. This uniform volume per mole of different gases at STP is crucial because it provides a common basis for comparing volumes. In the example problem, once we know the amount of H2 in moles, Avogadro's Law allows us to easily convert this to volume, reflecting the direct relationship between these two quantities.

Calculating the volume of a gas at STP can be done efficiently using the moles obtained from stoichiometry problems and applying Avogadro's Law. Once you've determined the number of moles of a gas produced or consumed in a reaction, simply multiply this value by the volume that one mole of gas occupies at STP, which is 22.4 liters.

In the exercise provided, the moles of H2 produced from the reaction of aluminum with sulfuric acid are first calculated using the mole ratio. Now, to find the volume of hydrogen gas at STP, we multiply the number of moles of hydrogen gas by 22.4 L/mol.

Example Calculation:

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For 8.30 moles of Al, we use the mole ratio (2 moles Al:3 moles H2) to calculate the moles of H2: \(\frac{3}{2} \times 8.30\) moles of H2. Then, we multiply the moles of H2 by 22.4 L/mol to get the final volume at STP. This approach offers a straightforward method to find out the volume of gas produced or required in a chemical reaction at standard conditions.