does a higher amount of activation energy mean a reaction will be spontaneous?

What about a lower ?

also why does steel wool gain mass when oxidized?

Spontaneous processes are reactions which proceed without requiring an input of energy because the products are at a lower, more stable energy state than the reactants. Spontaneous processes often require activation energy, but do not require a prolonged input of energy. So the answer to your question is NO, and NO. In either case, activation energy is required.

Fe+O2 >>>>Fe2O3 you balance it. Now why is Fe2O3 have more mass than the original Fe?

4 Fe + 3 O2 = 2 Fe2O3 so it has gained oxygen atoms because it has rusted?

Also for the question above if it is not spontaneous is it endothermic for more activation energy and exothermic for less?

Since the reactants are lower than the products on endothermic and the reactants are higher on the exothermic than the products?

a. rust is heavier than the original iron because it has gained oxygen atoms.

b. Somehow you have been lead astray. Spontaneous has nothing to do with activation energy, and all to do with Gibbs Free Energy. Gibbs free energy (ignoring changes in entropy) is the difference between initial energy state and final energy state, which i mean by energy state the energy stored in chemical bonds. If the final state is higher, we call that endothermic (it absorbed energy). If the final state is lower, it is exothermic (it gave away energy).
Now spontaneous reactions 99.99 percent of the time are exothermic, they end up with less stored energy than they started. This ignores entropy changes, which can matter.
So what is activation energy? Activation energy is the energy required to start the reaction. If the reaction is exothermic, it then after starting may then give enough energy off to then keep the reactions combining over the activation energy "hump", and the reaction proceeds. Like striking a match. If one strikes it, the initial activation energy for a very small spot is overcome, the reaction starts, gives off heat, which then provides the activation energy for the next spot and so on. Do you call a burning math spontaneous? I dont. A spontaneous reaction often can require such little energy of activation, that you have to keep it in a cold area, or not let it be shaken (nitroglycerin). That is a very exothermic reaction,but it is not spontaneous. Now if you stored it in a metal shed, that got very hot, it might go off due to the temperature. At some temperature it could be spontaneous, and at a lower temp, stable. Again, required activation energy has to be supplied for the reaction to proceed.

No, a higher amount of activation energy does not necessarily mean that a reaction will be spontaneous. The concept of activation energy refers to the minimum energy required for a chemical reaction to occur. It represents the energy barrier that must be overcome for the reactants to transition into products. Whether a reaction is spontaneous or not depends on the difference in energy (enthalpy) between the reactants and products, rather than the activation energy itself.

In general, for a reaction to be spontaneous, the overall change in free energy (ΔG) must be negative. ΔG takes into account both the enthalpy (ΔH) and entropy (ΔS) changes in the system. Specifically, for a reaction to be spontaneous at a given temperature, ΔG must be negative.

If the activation energy is high, it means that there is a large energy barrier that must be overcome for the reaction to proceed. This might lead to a slower reaction rate, as it takes more energy for the reactants to reach the transition state. However, it does not directly determine if the reaction will be spontaneous or not.

On the other hand, a lower activation energy generally implies a lower energy barrier for the reaction, which can lead to a faster reaction rate. It does not necessarily guarantee spontaneity either.

To determine if a reaction will be spontaneous or not, you need to consider factors such as the overall change in free energy (ΔG) and the reaction conditions, including temperature and pressure.