Final answer:
Without specific data on enthalpy, volume, temperature, or pressure, it's not possible to determine if the change in internal energy (ΔU) for the reaction 2Na(s) + 2H₂O(l) → 2 NaOH(aq) + H₂(g) is positive, negative, or zero; thus the answer is 'Variable'.
Step-by-step explanation:
The question is asking for the change in internal energy (ΔU) for the reaction where sodium reacts with water to form sodium hydroxide and hydrogen gas: 2Na(s) + 2H₂O(l) → 2 NaOH(aq) + H₂(g). The change in internal energy for a chemical reaction such as this one can generally be determined from the enthalpy change (ΔH) and the change in the number of moles of gas (Δngas) during the reaction, which often correlates with the heat flow at constant pressure. However, since we are not provided with values of enthalpy or volume change, nor are we given conditions such as temperature or pressure, the change in internal energy (ΔU) cannot be conclusively determined from the information given. Without additional data, it is not possible to state whether ΔU is positive, negative, or zero. Therefore the best answer selection, given the options provided, would be (d) Variable, since it depends on the specific conditions of the reaction and cannot be determined with the given information.