There is no mention of a timeframe in your post so I'm assuming that you are referring to the period during the Axis advance in Operation Blau II when the Stalingrad Front was formed in July 1942.
The Reserve Armies that were created to help form the Stalingrad Front were actually the 62nd, 63rd and 64th, together with the existing 21st Army. 61st Army was located on the Western Front and did not participate in the Stalingrad battles.
The armies of the Stalingrad Front were formed with a view of establishing a defensive line to counter any Axis breakthrough and drive eastward south of the Don River towards Stalingrad. They were therefore ideally placed to counter the Axis breakthrough that had developed between the Briansk and Southwestern Fronts in July 1942. The mission of the Stalingrad front as allocated to it in a Stavka directive of 12 July was "to occupy the Stalingrad line west of the Don River firmly......and under no circumstances permit an enemy penetration east of this line toward Stalingrad".
62nd Army (7th Reserve Army) - commanded by Major General V I Kolpakchi consisting of 33 Guards, 192, 147, 184, 196 & 181 Rifle Divisions formed in the Stalingrad area and was to be located on the Stalingrad axis. On 11 July 62nd Army was ordered to move from their existing positions, occupying the defences of Stalingrad, forward and occupy the Stalingrad line being prepared at Karazhenskii - Evstratovskii - Kalmykov - Slepukhin - Surovikino Station - Farm No.2 of State Farm 79 - Suvorovskii. HQ at Kamyshi. This defensive line formed a gentle arc extending from North to South across the western base of the Great Bend, roughly halfway between the Chir River in the west and the Great Bend itself in the east, beyond which Stalingrad was only 50 kilometres to the east. Forward deployment by rail started on 11 July and was completed by 14 July.
63rd Army (5th Reserve Army) - commanded by Lieutenant General V I Kuznetsov consisting of 14 Guards, 1, 153, 197 & 203 Rifle Divisions formed and located south of Novaia Kalitva on the Don Bend. By 12 July 63rd Army was defending a 90 kilometre sector along the northern bank of the Don River between Babka - Veshenskaia. HQ at Kruglovskii. Mission allocated was to defend the northern bank of the Don River in the sector it occupies and prevent the enemy from forcing the Don River under any circumstances.
64th Army (1st Reserve Army) - commanded by Lieutenant General V I Chuikov consisting of 131, 229, 29, 18, 214 & 112 Rifle Divisions formed at Tula but quickly transferred to the region south of Stalingrad. On 12 July 64th Army was ordered to deploy forward into the sector between Surovikino on the Chir River and Verkne-Kurmoiarskaia on the Don River. HQ at Averinskii.
21st Army's mission was to move up to the Serafimovich region and to the east along the northern bank of the Don River, joining it's right flank to 63rd Army's flank and its left flank to 62nd Army's flank, to prevent the enemy from forcing the Don River in this sector under any circumstance, and firmly protect the junction between 62nd and 63rd Armies. HQ at Frolovo.
Retreating Armies of the Briansk & Southwestern Fronts reached the Stalingrad Front's defensive lines on 15 - 16 July. German armoured columns engaged forward detachments of 62nd Army on 22 July.
Hope this helps
"Whoever wishes to master the art of war must study it continuously. I....am of the opinion that one lifetime is not enough to attain this goal." - Frederick II