Switching the Polarity of the DC Power Source

At the slower intervals a double pole relay may work.

How much current are you driving through your reaction? What voltage is across your electrodes?

The voltage across the electrodes varies from 3V to 15V and the amount of current flows in the system is from 5mA to 300mA.

If you have a square wave generator that can sustain the wattage and voltage then OK for the 10ms and up to 1s. 15V at 300mA is 4.5Watt.

Above that, a relay with change over contact will do.

10ms for a mechanical relay will wear it quickly...

Guru,please read properly: I said Square wave Generator up to 1s........ not relay!

The voltage across the electrodes varies from 3V to 15V and the amount of current flows in the system is from 5mA to 300mA.

Look up "H-Bridge", drive it with your function generator.

Many hobbyist electronics shops sell "H-bridge" kits for driving stepper motors.

Agreed, H Bridge is the way to go, standard integrated ones intended to drive motors will work at your voltage level.

I built a H Bridge using DC output solid state relays early in my career. 175VDC, couple amps needed to be inverted.

One learns these turn on much faster than they turn off, shorting the power supply...

Motor drivers may have the compensating circuitry to prevent that. A PWM driver may not be what you want.

Also remember to use a good True-RMS meter to measure your real output. Standard AC measurement or cheap True-Rms are made to measure sinus or close to sinus waveforms and will give extensive error in your situation, square waves need Fluke True-RMS or equivalent...