Final answer:
The mole ratio of hydrogen to ammonia in the synthesis of ammonia from nitrogen and hydrogen is 3:2, based on the balanced equation N₂ + 3H₂ → 2NH₃. This means that for every 3 moles of hydrogen used, 2 moles of ammonia are produced.
Step-by-step explanation:
The student's question involves the mole ratio of hydrogen to ammonia in the balanced chemical equation for the synthesis of ammonia (NH₃) from nitrogen (N₂) and hydrogen (H₂). The balanced equation is: N₂ + 3H₂ → 2NH₃. The coefficients in a balanced chemical equation represent the mole ratios of the reactants and products involved in the reaction. The mole ratio for hydrogen to ammonia can be read directly from the equation: for every 3 moles of hydrogen, 2 moles of ammonia are produced. Therefore, the mole ratio of hydrogen to ammonia is 3:2.
Using this ratio, it's possible to solve stoichiometry problems. For example, if you start with 5.0 moles of nitrogen and 10.0 moles of hydrogen, it is the hydrogen which limits the reaction as it is in stoichiometric excess, and it will yield 6.67 moles of ammonia (using the 3:2 ratio and dividing 10.0 moles of H₂ by 1.5 to find the moles of NH₃ produced). This approach confirms that the correct answer to the student's initial question is Option C: a 3:2 mole ratio of hydrogen to ammonia.