MacBook Air 13 (mid 2012) shuts down at 50% battery without warning, SMC chip broken?
Verify your Battery information in Applications > Utility > System Information > Power and report the result in your post.

Example:

Charge Information:
  Charge Remaining (mAh):   6206
  Fully Charged:    No
  Charging: Yes
  Full Charge Capacity (mAh):   6451
  Health Information:
  Cycle Count:  208
  Condition:    Normal
  Battery Installed:    Yes
  Amperage (mA):    879
  Voltage (mV): 8548


The Charge Remaining (mAh) is the actual % you see.
The Full Charge Capacity (mAh) is the health and age indicator, that number goes down over the life. 
The cycle count is specified up to 1000 cycles.
The Amperage (mA) reports the current consumption.

Run pmset -g in Terminal to get System-wide power settings and report the result in your post.

These additional steps may help identify or resolve the issue: 

Reset the SMC

Reset NVRAM

Start up in Safe Mode to see if the issue is related to non-Apple startup items, login items, or kernel extensions. 

Try to isolate the issue by using another user account.