From what I have seen in old cars equipped with a carburetor is that pressing the gas pedal opens a flap on top of the carburetor.
Presumably that allows for more air (and consequently, more air/fuel mixture?) to flow down through the carburetor.
But does this by itself cause the engine to rotate faster? What is that happens that leads to the engine rotating faster when the gas pedal is pressed?
more air / fuel > more power developed which leads to more engine revs if there is no load, with load speed can stay constant but more torque is developed.
Not totally unrelated to Netwon's law of action and re-action, the engine when running constantly at a certain speed is in equilibrium, that is, the energy released by combustion is exactly what is needed to keep that exact speed.
As you figured, opening the throttle allows more air to be sucked into the combustion chamber per revolution and with it more fuel. Burning more fuel per revolution causes higher pressure in the chamber which exerts more force to the piston which results in higher torque. Now you have more force (torque) than needed for the previous speed and this makes the engine accelerate.
As the rpms increase, the amount of air/fuel passing to the engine does not increase (much), because it's limited by the position of the throttle. This means that, while more fuel is burned than before per time unit, the amount per revolution does not increase as much, potentially even decrease. Up to the point where equilibrium is reached again between the force from the combustion and the resistance from the engine and whatever it's driving.
