Q: how do i determine the model of my air to purchase a new drive if my oem drive failed?

I suppose you could always turn it upside down and read the model number that's printed on the bottom...

Click on the Apple symbol in the upper left hand corner of the task bar. Then click on "About This Mac". From there click on overview in the top left of the window that pops up. Finally, click on system report and you'll see the serial number printed. Hope this helps you out! It'll definitely work for you.

Try this: How to identify your MacBook Air - Apple Support