Question

Some commercial drain cleaners contain two components: sodium hydroxide and aluminum powder. When the mixture is poured down a clogged drain, the following reaction occurs: $$2 \mathrm{NaOH}(a q)+2 \mathrm{Al}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow_{2 \mathrm{NaAl}(\mathrm{OH})_{4}(a q)+3 \mathrm{H}_{2}(g)}$$ The heat generated in this reaction helps melt away obstructions such as grease, and the hydrogen gas released stirs up the solids clogging the drain. Calculate the volume of \(\mathrm{H}_{2}\) formed at STP if \(3.12 \mathrm{~g}\) of \(\mathrm{Al}\) is treated with an excess of \(\mathrm{NaOH}\).

Short answer

The volume of \(H_{2}\) formed at STP when 3.12 g of \(Al\) is treated with an excess of \(NaOH\) is approximately 3.89 L.

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation is already provided: \[2 \mathrm{NaOH}(a q)+2 \mathrm{Al}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow_{2} \mathrm{NaAl}(\mathrm{OH})_{4}(a q)+3 \mathrm{H}_{2}(g)\] This equation tells us that 2 moles of Al produce 3 moles of H2.

Convert mass of Al to moles

Using the molar mass of Al which is \(26.98 \, \mathrm{g/mol} \), the given mass of Al (3.12 g) can be converted to moles: \[\frac{3.12 \, \mathrm{g}}{26.98 \, \mathrm{g/mol}} \approx 0.116 \, \mathrm{mol} \, \mathrm{Al}\]

Use stoichiometric ratios to find moles of H2

From the balanced equation, 2 moles of Al produce 3 moles of H2. Therefore, the moles of H2 produced from 0.116 mol Al are: \(0.116 \, \mathrm{mol} \, \mathrm{Al} \times \frac{3 \, \mathrm{mol} \, \mathrm{H2}}{2 \, \mathrm{mol} \, \mathrm{Al}} \approx 0.174 \, \mathrm{mol} \, \mathrm{H2}\]

Convert moles of H2 to volume at STP

At standard temperature and pressure (STP), 1 mole of any gas occupies a volume of 22.4 L. Therefore, the volume of 0.174 mol H2 is: \(0.174 \, \mathrm{mol}\times 22.4 \, \mathrm{L/mol} \approx 3.89 \, \mathrm{L}\)

Key concepts

Understanding a Balanced Chemical Equation

In chemistry, a balanced chemical equation shows the relationship between the reactants and products in a reaction. It's like a recipe that provides the exact proportions needed. Each side of the equation must have the same number of each type of atom. This is crucial because matter cannot be created or destroyed in a chemical reaction.

In the given equation: \(2 \ \text{NaOH}(aq) + 2 \ \text{Al}(s) + 6 \ \text{H}_2\text{O}(l) \rightarrow 2 \ \text{NaAl(OH)}_4(aq) + 3 \ \text{H}_2(g) \), it's clear how each reactant contributes to the formation of products. It specifies that 2 moles of sodium hydroxide react with 2 moles of aluminum to produce hydrogen gas, ensuring the atoms on both sides are balanced.

This balance allows us to predict how much product can be formed from a given amount of reactant.

Molar Mass Calculation Simplified

The concept of molar mass is essential in converting between grams and moles—a key step in stoichiometry. Molar mass is the mass of one mole of any substance, usually expressed in grams per mole (g/mol).

For the exercise at hand, we were tasked to convert 3.12 g of aluminum to moles, using its molar mass of 26.98 g/mol. Calculating this involves a simple division:

• \(\frac{3.12 \, \text{g}}{26.98 \, \text{g/mol}} \approx 0.116 \, \text{mol}\)

Understanding molar mass and its role helps predict and understand the quantities involved in chemical reactions.

What is Standard Temperature and Pressure (STP)?

STP, or Standard Temperature and Pressure, are standard conditions used to measure gases. It’s defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm (101.3 kPa). These conditions provide a reference that simplifies calculations for gases.

At STP, 1 mole of any ideal gas occupies 22.4 liters. This detail is incredibly handy for many calculations and was used in our exercise to find the volume of hydrogen gas produced. Given a stoichiometric conversion to moles of gas, you can quickly determine volume using the formula:

• \(\text{Volume} = \text{moles} \times 22.4 \, \text{L/mol}\)

In our example, this led to a calculation of \(0.174 \, \text{mol} \times 22.4 \, \text{L/mol} \approx 3.89 \, \text{L}\).

STP is a cornerstone concept in gas stoichiometry.

Chemical Reactions Made Easy

Chemical reactions are processes where reactants transform into products. They are illustrated in balanced equations that show how substances convert. This covers everything from simple to complex transformations.

In every chemical reaction, bonds in the reactants break, and new bonds form to create products. The ability to understand and balance these equations is crucial.

The reaction in this exercise shows aluminum reacting with sodium hydroxide and water to form sodium aluminate and hydrogen gas. This showcases how chemicals interact under certain conditions and can be harnessed for practical applications, like unclogging drains.

Understanding these interactions helps in predicting the outcomes of reactions in different environments and harnessing chemical processes effectively.