In an ideal gas, if only one molecule in a thousand has enough energy to react, how can all molecules in a reactor be consumed?

My answer: when the one molecule reacts, it causes the other molecules to gain energy.

Is this right? I'm still confused on the question

I wouldn't bet on it.

When only one molecule in a thousand has enough energy to react the odds are against much of a reaction at all. I think the question is asking what can you do to make more molecules react and I believe the answer is to raise the temperature. That gives more molecules enough energy to get over the activation energy. Remember that rule of thumb that says raising the temperature by 10 C just about doubles the rate of reaction. So raising T from 20 to 80 C should raise the rate 2^8 or 256 times.

With regard to your answer, if the reaction is exothermic you answer might be on the right track. But what if the reaction is endothermic?