Aluminum dissolves readily in hot aqueous NaOH to give the...

Aluminum dissolves readily in hot aqueous NaOH to give the aluminate ion, $\left[\mathrm{Al}(\mathrm{OH})_{4}\right]^{-},$ and $\mathrm{H}_{2} .$ Write a balanced equation for this reaction. If you begin with $13.2 \mathrm{g}$ of $\mathrm{Al}$, what volume (in liters) of $\mathrm{H}_{2}$ gas is produced when the gas is measured at $22.5^{\circ} \mathrm{C}$ and a pressure of $735 \mathrm{mm} \mathrm{Hg} ?$

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Key Concepts

Balanced Chemical Equation

A balanced chemical equation accurately represents a chemical reaction by showing the correct proportions of reactants and products so that the number of atoms for each element is the same on both sides of the equation. This is essential to ensure the conservation of mass and to establish the stoichiometric ratios needed for further calculations.

Stoichiometry

Stoichiometry involves using the balanced chemical equation to quantitatively relate the moles of reactants and products. It allows one to determine how much product is formed given a certain amount of reactant by applying the mole ratios derived from the balanced equation.

Molar Mass Calculations

Molar mass calculations are used to convert between the mass of a substance and the number of moles, which is a key step in stoichiometry. This conversion is necessary when the given quantities of substances are in grams, and you need to relate them to the mole ratios in the balanced equation.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. This principle is crucial when determining the volume of a gas produced or consumed under specified conditions, by calculating the number of moles and then using the law to find the corresponding volume.

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