Date: 201809
Local time of day: 1201-1800
Location: ROA.TRACON, VA
Flight conditions: Marginal
Aircraft: Medium Large Transport; Low Wing; 2 Turbojet Eng
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Final Approach
Airspace: Class C ROA
ATC / advisory: TRACON ROA
Second aircraft: Small Transport; Low Wing; 2 Turbojet Eng
Reporter organization: Government
Reporter qualification: Air Traffic Control Fully Certified
Human factors: Situational Awareness; Physiological - Other; Distraction; Time Pressure; Workload
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural FAR; Inflight Event / Encounter VFR In IMC; Inflight Event / Encounter CFTT / CFIT
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Human Factors; Procedure; Weather
Primary problem: Weather

Narrative: Normal East Radar position; weather was reported 10SM OVC012. Aircraft Z departed Runway 34; VFR; to the North East Practice Area. Aircraft X was on final for ILS 34 from the south. Aircraft Y was in the departure list for Runway 34 with a west turnout. Aircraft Z got around 2 miles northeast of the field and encountered clouds and lost site of the surrounding mountains. I informed him he was around 100 feet above the mountain in question and asked his intentions; followed by asking him if he wanted [additional services] and he did. He seemed very spooked and said his passenger was as well. I saw him starting to turn towards the field and thought he could possibly descend rapidly back to the field. I told tower of the [situation] and as a precaution I told them to break him off the approach on a 270; thinking Aircraft Z was going to head straight at the airport that wasn't insight.The loss of separation comes from the 270 turn off final for Aircraft X and the departure of Aircraft Y on a 250 heading off of Runway 34. I initially thought I had enough lateral separation; then realized it was going to be closer than I assumed and when I saw it; not long after; turned both away from each other. I believe the lateral separation was 2.6 NM. After Aircraft Z [notified us]; I asked him what he wanted to do. I suggested a possible IFR pickup for radar vectors back to ROA for the ILS 34. He said an IFR pickup sounds like the best. I followed it by clearing him; since he was still climbing and was above the MVA in the area. It was when I tried to turn him final to join the approach he informed me that he wasn't IFR rated. We followed by giving him a vector to maintain until we found an airport with suitable VMC. I was unaware of specific phraseology in an IFR pickup; and thought suggesting IFR for an approach--with his agreement; meant he was qualified. I'm unaware that you can't suggest IFR like a SVFR to an aircraft.No recommendations; just reviewed 7110 Chapter 10 on VFR aircraft encountering bad weather.




Synopsis: ROA TRACON Controller reported airborne conflict between two aircraft; after being distracted by a third aircraft that was VFR in IMC.