Final answer:
In the chemical reaction 2NO(g) + O₂(g) → 2NO₂(g), 3.25 L of gaseous oxygen is needed to produce 6.50 L of gaseous nitrogen dioxide at STP, according to the stoichiometric relationship and Avogadro's law.
Step-by-step explanation:
The question involves stoichiometry, which is a section of chemistry that deals with the quantitative relationships between the amounts of reactants and products in a chemical reaction. Specifically, we are looking at the reaction 2NO(g) + O₂(g) → 2NO₂(g), which tells us that 1 mole of O₂ will react with 2 moles of NO to create 2 moles of NO₂.
According to Avogadro's law, equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. So, since the volumes are directly proportional to the number of moles, we can use this relationship to determine the amount of O₂ needed to produce a given volume of NO₂.
Given that we are producing 6.50 L of NO₂, and the stoichiometry of O₂ consumption is 1 volume of O₂ for 2 volumes of NO₂, we would need half of the volume of NO₂ in O₂, which is 6.50 L / 2 = 3.25 L of O₂.
Therefore, option B. 3.25 L is the correct answer.