Final answer:
To produce 405 moles of hydrogen gas (H2) in the reaction of NaOH with Al, 810 moles of NaOH are required based on the balanced chemical equation. However, the provided answer options do not include this correct answer, indicating a possible typo or mistake in the question or answer choices.
Step-by-step explanation:
The question concerns a chemical reaction in which sodium hydroxide (NaOH) reacts with aluminum (Al) to produce sodium aluminate (Na3AlO3) and hydrogen gas (H2). The equation given in the question appears to be unbalanced, but assuming it implies a balanced reaction, we can determine the amount of NaOH needed to produce a certain number of moles of hydrogen.
To answer the question correctly, we need to first write a balanced chemical equation for the reaction. The balanced equation for this reaction is:
- 6 NaOH + 2 Al → 2 Na3AlO3 + 3 H2
This shows us that 6 moles of NaOH react with 2 moles of Al to produce 2 moles of Na3AlO3 and 3 moles of H2. From this balanced equation, we can see that for every 3 moles of H2 produced, 6 moles of NaOH are required, which gives us a 2:1 ratio of NaOH to H2.
To produce 405 moles of hydrogen, we would need:
405 moles H2 × (6 moles NaOH / 3 moles H2) = 810 moles NaOH
However, none of the answer choices correspond to this calculation. This could be a typo in the question or a mistake in the answer options. The correct answer based on the stoichiometry of the balanced chemical equation should be 810 moles of NaOH, which is not listed.