Final answer:
The most important factor that allows the decomposition of magnesium oxide into magnesium and oxygen is temperature, because it provides the energy necessary to drive the endothermic reaction.
Step-by-step explanation:
The reaction that decomposes magnesium oxide (MgO) into magnesium (Mg) and oxygen (O2) is endothermic, requiring an input of 601.7 kJ of energy. Among the options provided, temperature is the most important factor that can allow this reaction to occur. This is because increasing the temperature can provide the necessary energy to overcome the reaction's activation energy barrier, driving the decomposition process. Neither concentration nor pressure is particularly relevant in the case of the decomposition of a solid compound like MgO. While surface area can affect the rate of a reaction involving solids, it does not play as significant a role in the energy requirements for a decomposition reaction such as this.
In general, for a combination reaction involving the oxidation of a metal like magnesium, factors such as temperature, molarity, and surface area can influence the rate of the reaction. When magnesium burns in the air to form MgO, the process is exothermic and releases heat. However, when MgO decomposes, it absorbs heat, which is why an increase in temperature is essential for the decomposition of magnesium oxide into magnesium and oxygen.