PNP transistors don't require a 'negative' voltage to switch. Rather, the current which flows from the Emitter (+) through the Base (-) is amplified to produce a current (up to ~100x, dependent on the demand) flowing from the Emitter (with the arrow on it) to the Collector. The Base-Emitter junction is generally modeled as a diode, so in order to get any current to flow through it, you have to at least create a voltage difference that exceeds its diode-voltage drop, but more is better.
Waving my hands a lot here, but if you set up a condition whereby you sink 2mA into your Arduino pin, you'll be able to drive about 200mA into the motor in this way. To set up that condition, given that your PNP transistor has a 0.7V base-emitter junction voltage drop, and your VCC is 5V, you want to size your base resistor at (5 - 0.7) / 0.002 = ~2kOhms. Then drive the PNP transistor low to open the valve and let current flow, and high to choke the current off.
Note, you actually might be able to sink as much as 40mA into the Arduino pin, under several caveats, and get a commensurately larger emitter-collector current. Just keep in mind that BJTs are current-controlled devices, voltages are (mostly) incidental (within limits).