Would air pressure be greater at the South pole or the equator? why?

The air pressure would be greater at the South Pole than the equator.

The reason why is because:

The equator is warmer than the South Pole, because the sun's rays are hitting it more directly. Warmer particles move faster, and since the equator's air is warmer than the South Pole's, the particles at the equator must be moving faster.

Then that means that the particles at the equator must be more spread out than the particles at the South Pole. This means that the air particles at the equator would have less air pressure, because there's less of them, than the particles at the South Pole, which has more air pressure because there are more air particles.

It would be great at south pole because cold air weighs more due to particle of air being closer to each other.