Disposition was partially deliberate, partially result of circumstances
Main objective of Fall Blau was oil, i.e. capture of oilfields (Maykop-Grozny-Baku) . In late July 1942, after the Battle of Voronezh, Army Group South was split into two Army Groups : A and B. Army Group A was going for aforementioned main objective, had to cover lot of distance, therefore it was envisaged that it should contain mostly motorized units. Army Group B had to cover northern (left) flank of Army Group A. Its goal was to capture Stalingrad (preferably on the march) , disrupt riverine traffic on Volga, and if possible move to capture Astrakhan .
Overall mood in OKW and OKH was fairly optimistic in July of 1942. Winter crisis of 1941 has passed, German Army was again smashing Soviets in the South like they did last year. Position in the North and Center seemed secure, in fact Soviets bleed themselves dry in futile Rzhev meat grinder. German attack toward Voronezh secured right bank of Don (fairly good defensive position) and possibly tricked Soviets that main objective of the offensive could be Moscow (north-eastern direction of attack). Considering losses in 1941, and early 1942, Germans hoped that Soviets exhausted their manpower reserves, and food shortage (with the loss of Ukraine) was also real possibility. Therefore, plan with two Army Groups (splitting of the forces) seemed possible in face of seemingly inevitable Soviet collapse.
However situation at the front was not that rosy. First, Soviets counter-attacked at Kalach. Counter-attack was poorly planned, Soviets again squandered lots of tanks in futile attacks without artillery and infantry support. However, they did disrupt advance on Stalingrad, caused some losses, held on small bridgehead across Don (latter used for Operation Uranus) , and forced OKW to reinforce Army Group B (mostly XIV Panzer Corps). Overall, this battle is relatively unknown in historiography - both sides had their reasons to gloss over it. However, it did stall Army Group B enough that they could not take Stalingrad on the march as they previously planned.
Army Group A had problems on their own. In the south, near Black Sea coast, advance was slow. They did manage to capture Novorossiysk, but not much beyond that, do to the presence of still powerful Black Sea Fleet and Soviet coastal forces. As a consequence, Army Group A had not only northern (left) flank open do to the stall at Stalingrad, their southern (right) flank was now at northern base of Caucasus mountains. Soviets had retreated into the mountains , and Germans unsuccessfully tried to cut them off by penetrating south. This was forced move - Army Group A was never intended for mountain warfare, but driving eastwards for oilfields with both flanks hanging in the air would be suicidal.
Finally, number of tanks is a fluid matter. OKH did shift units and reinforcements between Army Groups A and B (mostly First and Fourth Panzer Army) as situation demanded. Exact numbers are hard to get, research would have to over daily reports in panzer divisions . Also, some panzer divisions like for example 14th Panzer were initially slated for Army Group A, but ended fighting in area of Army Group B, because of the demands of the front. 23rd Panzer division had similar fate, but they were taken from Army Group A somewhat latter.