Fuel tank hose

[Alistair]

Can anyone please tell me where the hose on top of the fuel tank goes to And what it is there for? This is not the fuel line hose but it look like some so of breather.
Can this hose affect the running of the engine?
Thanks

 

[ILENGINE]

Depending on year without knowing model of JD it could be the vapor recovery slash rollover valve that is required for EPA standards. If they clog they can cause the same issues as a clogged fuel cap vent . Since mowers after 2012 don't have vented fuel caps only vapor recover systems that either connect to a charcoal canister, or straight into the air cleaner intake system.