Problem 42 - Chemistry and Chemical Reactivity

Question

"Aerated" concrete bricks are widely used building materials. They are obtained by mixing gas-forming additives with a moist mixture of lime, sand, and possibly cement. Industrially, the following reaction is important: $$ \begin{aligned} 2 \mathrm{Al}(\mathrm{s})+3 \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})+6 \mathrm{H}_{2} \mathrm{O}(\ell) & \longrightarrow \\ \left[3 \mathrm{CaO} \cdot \mathrm{Al}_{2} \mathrm{O}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\right](\mathrm{s})+3 \mathrm{H}_{2}(\mathrm{g}) \end{aligned} $$ Assume that the mixture of reactants contains \(0.56 \mathrm{g}\) of \(\mathrm{Al}\) for each brick. What volume of hydrogen gas do you expect at \(26^{\circ} \mathrm{C}\) and atmospheric pressure \((745 \mathrm{mm} \mathrm{Hg}) ?\)

Step-by-Step Solution

Answer

Approximately 0.784 liters of hydrogen gas is produced.

Step 1: Calculate the moles of Al

First, we need to determine the moles of aluminum (Al) present in the mixture. We are given 0.56 g of Al. The molar mass of Al is approximately 26.98 g/mol.\[\text{moles of Al} = \frac{0.56 \text{ g}}{26.98 \text{ g/mol}} = 0.02075 \text{ moles}\]

Step 2: Determine moles of H₂ produced

According to the reaction, 2 moles of Al produce 3 moles of H₂. Thus, we use stoichiometry to find the moles of hydrogen gas.\[\text{moles of } \mathrm{H}_2 = \left(\frac{3}{2}\right) \times 0.02075 = 0.031125 \text{ moles}\]

Step 3: Convert pressure to atmospheres

To use the ideal gas law, the pressure must be in atmospheres. Convert 745 mmHg to atm (1 atm = 760 mmHg).\[P = \frac{745 \text{ mmHg}}{760 \text{ mmHg/atm}} = 0.9803 \text{ atm}\]

Step 4: Calculate volume of H₂ gas

Use the ideal gas law to find the volume of hydrogen gas. The ideal gas law is: \[PV = nRT\]Where:- \(P\) is the pressure (0.9803 atm),- \(n\) is the number of moles (0.031125 moles),- \(R\) is the ideal gas constant (0.0821 L·atm/mol·K),- \(T\) is the temperature in Kelvin (26°C = 299 K).\[V = \frac{nRT}{P} = \frac{0.031125 \times 0.0821 \times 299}{0.9803} \]Calculating yields: \[ V \approx 0.784 \text{ L}\]

Step 5: Conclude with the calculated volume

The calculated volume of hydrogen gas expected to be produced at the given conditions is approximately 0.784 liters.

Key Concepts

Aerated Concrete

Aerated concrete, also known as autoclaved aerated concrete (AAC), is a lightweight, precast building material ideal for producing concrete blocks that are easy to handle. What makes aerated concrete unique is its airy, porous structure achieved by introducing gas-forming agents during the concrete mixture preparation. This material is highly energy-efficient and provides superior insulation properties. The production process typically involves the addition of aluminum powder to a wet mixture of lime, sand, and cement.

• Aluminum powder reacts with calcium hydroxide and water to generate hydrogen gas, creating a porous, foamed structure.
• The gas bubbles are trapped within the mixture as it hardens, giving the material its light and insulating characteristics.
• Aerated concrete provides a balance between strength and lightness, making it suitable for various construction applications.

The reaction involved is carefully controlled to ensure consistent quality and performance of the aerated concrete blocks.

Ideal Gas Law

The ideal gas law is a crucial concept in understanding gas behavior under various conditions. It's often used to relate the pressure, volume, temperature, and number of moles of a given gas. The ideal gas law can be expressed in the formula: \[PV = nRT\]Where:

• \(P\) is the pressure of the gas,
• \(V\) is the volume of the gas,
• \(n\) is the number of moles of the gas,
• \(R\) is the gas constant (0.0821 L·atm/mol·K),
• \(T\) is the temperature in Kelvin.

The ideal gas law assumes that gases behave ideally, which means they obey the gas laws perfectly. While real gases might deviate from ideal behavior under certain conditions, the ideal gas law provides a good approximation for many practical purposes, especially under moderate conditions.

Stoichiometry

Stoichiometry is the calculation of reactant and product quantities in chemical reactions. It involves the use of balanced chemical equations to determine the relationships between the amounts of reactants and products. In the context of aerated concrete, stoichiometry allows us to predict the amount of hydrogen gas produced when aluminum reacts with calcium hydroxide and water.

• Stoichiometric coefficients in a balanced reaction equation guide us on the relative amounts of reactants and products involved.
• For example, in the production of hydrogen gas: 2 moles of aluminum produce 3 moles of hydrogen according to the balanced equation.
• Using stoichiometry, we can compute the expected yield of a product like hydrogen gas, knowing the initial amount of a reactant like aluminum.

By applying stoichiometric principles, we can optimize substance usage in industrial applications, reduce waste, and enhance efficiency.

Gas Volume Calculation

Gas volume calculation often involves manipulating the ideal gas law equation to find unknown quantities in a chemical reaction. When given specific pressure and temperature conditions, the ideal gas law can help determine the volume occupied by a certain amount of gas. In the problem regarding aerated concrete, we used the ideal gas law to calculate the volume of hydrogen gas produced.

• First, we determine the moles of hydrogen gas from the given Al amount using stoichiometry.
• Then we convert any non-standard pressure or temperature conditions into the appropriate units (e.g., converting pressure from mmHg to atm).
• Finally, by rearranging the ideal gas equation \(V = \frac{nRT}{P}\) , we can solve for the volume \(V\) of hydrogen gas.

These steps are essential for accurate gas volume calculations in chemical processes, ensuring precise predictions of system behavior.