Switching on a battery powered air pump using arduino

I am working on a project where I need to set up an automated inflation system for an air mattress using arduino. The mattress is supposed to inflate when it comes in contact with water. I have a water sensor for this. I need to set up a way where the arduino will signal the battery powered air pump to start inflating the mattress when shown a particular value by the water sensor.

Also, the pressure inside the mattress has to be maintained at all times, so I was thinking of using a digital air pressure sensor (the kind used for a tyre). Arduino could read if the pressure is below a certain number and then have the pump inflate the mattress again to the desired pressure (PSI).

You can open up the negative battery lead and use a low side switch, either a logic level N-MOSFET or an NPN transistor with appropriate current carrying capacity. See the circuits associated with Q1 and Q3 on the diagram below. You will have to add a diode across the motor terminals to prevent voltage spikes from destroying the transistor, as shown at Q3.

Break that lead, measure the current with your multimeter and if you need help with component selection, let us know what you find.

An NPN transistor would have to be a darlington for high currents, note. MOSFET would
run cooler if appropriate one is chosen.

You need to find the stall current and normal running current for the motor - whatever device
you choose has to survive stall current for short periods, and not overheat at the running current.

And when switching any inductive load such as a motor, relay, solenoid, electromagnet it is
completely essential to use a free-wheel diode or snubber circuit to prevent high voltage kick-back.

Note in the diagram above the diode across the motor (bottom, middle) - omit that and you'll
risk blowing up your circuit. Such a diode just has to handle normal current levels of the motor for
short periods everytime the motor is switched off.