Hey guys. Fairly new to the old car community, and I have a 1970 cougar convertible, 351 W 4V.
I see a hose going into the top behind the carb that has a crack and is not tight, wondering what the function here is? See picture and thanks.
Trace it back, but looks like the vacuum source for power brakes.
If it’s cracked, it may be causing a vacuum leak impacting the engine and power brakes.
Thanks! The car sometimes stalls without warning as well, could this also be the cause og that?
Hard to say, could be unrelated…vacuum leaks can cause a variety of issues. I’d replace the hose (or cut cracked portion if possible and hose is still pliable) and see how that goes.
You also have a vacuum cap under the secondary diaphragm that is cracked. I would check all your vacuum hoses and caps. It’s amazing how much better they run when the vacuum leaks are fixed.
So I just replaced the cracked hose, and looked over the rest of the hoses, they all seemed fine. Didnt really have an impact on the random stalling but I think it runs a bit better? 
May want to check / replace the rubber fuel lines as well.