Question

The drain cleaner, Drainex contains small bits of aluminium which react with caustic soda to produce hydrogen. What volume of hydrogen at \(27^{\circ} \mathrm{C}\) and \(0.831\) bar will be released when \(0.15 \mathrm{~g}\) of aluminium reacts? \((\mathrm{Al}=27)\) (a) \(250 \mathrm{ml}\) (b) \(150 \mathrm{~m} 1\) (c) \(500 \mathrm{ml}\) (d) \(125 \mathrm{ml}\)

Short answer

250 ml

Step-by-step solution

Write the balanced chemical equation

To solve this problem, you first need to write the balanced chemical equation for the reaction between aluminium and caustic soda (sodium hydroxide) to produce hydrogen. The reaction is: \[2\text{Al} + 2\text{NaOH} + 6\text{H}_2\text{O} \rightarrow 2\text{NaAl(OH)}_4 + 3\text{H}_2.\]

Calculate moles of aluminium

Use the molar mass of aluminium to convert grams into moles: \[\text{Moles of Al} = \frac{\text{mass of Al}}{\text{molar mass of Al}} = \frac{0.15\text{ g}}{27\text{ g/mol}} \approx 0.00556\text{ mol}.\]

Deduce moles of hydrogen gas produced

From the balanced equation, 2 moles of Al produce 3 moles of H2. So, 0.00556 moles of Al will produce: \[\text{Moles of H}_2 = \frac{3}{2} \times 0.00556\text{ mol} \approx 0.00834\text{ mol}.\]

Use the ideal gas law to find the volume of hydrogen gas

Using the ideal gas equation, PV = nRT, we can solve for the volume, V. Convert the temperature to Kelvin: T = 27 + 273.15 = 300.15 K. The pressure is given in bar and needs to be converted to Pa: P = 0.831 bar = 83100 Pa. The ideal gas constant R for the units of moles, Kelvin, and Pascals is 8.314 J/(mol K). Now, calculate the volume: \[V = \frac{nRT}{P} = \frac{0.00834 \text{ mol} \times 8.314 \text{ J/(mol K)} \times 300.15 \text{ K}}{83100 \text{ Pa}} \approx 0.025\text{ m}^3.\]

Convert the volume to milliliters

Since \(1 \text{ m}^3 = 10^6 \text{ ml}\), convert the volume from cubic meters to milliliters: \[V_{\text{H}_2} = 0.025 \text{ m}^3 \times 10^6 \text{ ml/m}^3 = 25000 \text{ ml} = 250 \text{ ml}.\]

Key concepts

Stoichiometry

Stoichiometry, the heart of chemical reactions, is the calculation involving the quantities of reactants and products in a chemical process. It leans heavily on the law of conservation of mass that states matter is neither created nor destroyed in a chemical reaction. Therefore, the amount of reactants consumed will dictate the volume or mass of the products formed.

Understanding stoichiometry requires a solid grasp of chemical equations, which represent how reactants transform into products. A balanced chemical equation follows the stoichiometric coefficients: the numbers leading each molecule that ensure the same number of each type of atom appears on both sides of the reaction.

One usually calculates the moles of a reactant, like aluminium in our drain cleaner example, which interacts with other chemicals - in this case, caustic soda, to form hydrogen. Using a balanced chemical equation, one can decipher the proportional relationships and thus predict the moles of hydrogen produced.

Ideal Gas Law

The ideal gas law is a crucial equation for understanding how gases behave under different conditions of pressure (P), volume (V), temperature (T), and number of moles (n). The equation is written as PV = nRT, where R is the gas constant. This law combines several simpler gas laws and provides a powerful tool for predicting the behavior of gases.

The application of the ideal gas law extends to numerous scientific exercises, including the prediction of a gas's volume after a chemical reaction, as we've seen with hydrogen gas production. To apply the ideal gas law, one must consider the proper units (P in Pascals, V in cubic meters, n in moles, R in J/(mol·K), and T in Kelvin) and make conversions when necessary, ensuring that the conditions specified in the exercise are met.

When you know the amount of gas in moles, the temperature, and pressure, you can easily compute the volume. Always remember to adjust the temperature to Kelvin and pressure to the suitable units if they are not initially provided in the standard units.

Molar Mass

Molar mass is the weight of one mole of a given substance and is typically expressed in grams per mole (g/mol). It is fundamental for converting between grams and moles, a common task in chemistry known as molar conversions. The molar mass of each element is found on the periodic table and is equal to the atomic weight of the element.

For compounds, the molar mass is the sum of the atomic weights of all atoms in the molecule. For example, as seen in the drain cleaner situation, aluminium (Al) has a molar mass of 27 g/mol. Having the molar mass allows chemists to count molecules by weighing them, enabling stoichiometric calculations that convey how many moles of each reactant are involved and what volume of gaseous product can be expected after the reaction proceeds.