Question

Hydrogen gas is prepared in a lab experiment. In this experiment, \(18.00 \mathrm{~g}\) of aluminum metal are mixed with \(25 \mathrm{~mL}\) of \(\mathrm{HCl}\left(d=1.025 \mathrm{~g} / \mathrm{cm}^{3}\right) .\) After the experiment, there are \(12.00 \mathrm{~g}\) of aluminum and \(30.95 \mathrm{~g}\) of a solution made up of water, aluminum ions, and chloride ions. Assuming no loss of products, how many liters of \(\mathrm{H}_{2}\) gas are obtained? The density of hydrogen gas at the temperature and pressure of the experiment is \(0.0824 \mathrm{~g} / \mathrm{L}\)

Short answer

Based on the information given, we can determine that the amount of hydrogen gas obtained in the experiment is approximately 8.16 liters.

Step-by-step solution

Calculate the amount of aluminum reacted

First, we need to find out how much aluminum reacted in the experiment. We can find this by subtracting the final mass of aluminum from the initial mass of aluminum: Aluminum reacted = Initial mass of aluminum - Final mass of aluminum Aluminum reacted = \(18.00 \mathrm{~g} - 12.00 \mathrm{~g} = 6.00 \mathrm{~g}\)

Determine the balanced chemical equation for the reaction

The balanced chemical equation for the reaction between aluminum and hydrochloric acid (HCl) is: $$2 \mathrm{Al} + 6 \mathrm{HCl} \rightarrow 2 \mathrm{AlCl}_{3} + 3 \mathrm{H}_{2}$$

Calculate the moles of hydrogen gas produced

Next, we need to find the moles of hydrogen gas produced. To do this, we can use stoichiometry with the balanced chemical equation. The molar mass of aluminum (Al) is approximately \(26.98 \mathrm{~g/mol}\), and the molar ratio of aluminum to hydrogen in the balanced equation is 2 Al to 3 H2. Moles of aluminum reacted = \(\frac{6.00 \mathrm{~g}}{26.98 \mathrm{~g/mol}} = 0.222 \mathrm{~mol}\) Moles of H2 produced = \(\frac{3 \mathrm{H2}}{2 \mathrm{Al}} \times 0.222 \mathrm{~mol} = 0.333 \mathrm{~mol}\)

Convert moles of hydrogen gas to liters

Finally, we need to convert the moles of hydrogen gas into liters using the given density of hydrogen gas: Density = \(\frac{mass}{volume}\) We can rearrange this to find the volume using the density and mass: Volume = \(\frac{mass}{density}\) First, convert moles of H2 to mass using molar mass (Molar mass of H2 is approximately \(2.02 \mathrm{~g/mol}\)): Mass of H2 = \(0.333 \mathrm{~mol} \times 2.02 \mathrm{~g/mol} = 0.6726 \mathrm{~g}\) Now, convert the mass of H2 to liters using the given density: Volume of H2 in liters = \(\frac{0.6726 \mathrm{~g}}{0.0824 \mathrm{~g/L}} = 8.16 \mathrm{~L}\) So, the volume of hydrogen gas obtained is approximately \(8.16 \mathrm{~L}\).