Unmute specific app when iPhone is in silent mode

I recently downloaded an app that tells me when someone in my direct area is in need of CPR (as I am an first aid worker). This app will sound an alarm to alert me, but this alarm is muted when I put my iPhone 4s in silent mode.

Is there a way I can specifically unmute this app and keep the rest muted?

Short answer:

No, that's not possible with third party apps.

Long answer:

Third party apps can not override the mute switch. It only works for Apple's own "Find my iPhone" app. The only possibility I know of is to jailbreak your phone and to use a tweak that lets you put some apps on a white list. Jailbreaking, however, is not recommended.

You may try to use "Do not disturb". It lets you add specific contacts to a favorites list. Only these contacts will ring with DND enabled.