Yes, an exothermic reaction can have a positive value of ΔH, and an endothermic reaction can have a negative value of ΔH. The sign of ΔH (the change in enthalpy) is determined by the direction of heat flow during the reaction.
In an exothermic reaction, heat is released to the surroundings, resulting in a decrease in the internal energy of the system. The value of ΔH for an exothermic reaction is usually negative because the system loses heat. However, there can be situations where the magnitude of the heat absorbed from the surroundings is greater than the heat released, resulting in a positive value for ΔH. This can happen, for example, if the reactants have a lower enthalpy than the products, and the overall reaction is still exothermic despite the positive value of ΔH.
On the other hand, in an endothermic reaction, heat is absorbed from the surroundings, leading to an increase in the internal energy of the system. The value of ΔH for an endothermic reaction is usually positive because the system gains heat. However, there can be cases where the magnitude of the heat released by the system is greater than the heat absorbed, resulting in a negative value for ΔH. This can occur if the reactants have a higher enthalpy than the products, and the overall reaction is still endothermic despite the negative value of ΔH.
It's important to note that the sign of ΔH alone does not determine whether a reaction is exothermic or endothermic. The sign of ΔH only indicates the direction of heat flow, while the classification of a reaction as exothermic or endothermic depends on the net energy change of the system.