Ack! I used the wrong temperature the first time, so here it is again using T = 298.15 K ! 
Something like that can work, but it may be easier to just use PV = nRT before and after mixing:
1. Before allowing the gases to mix,
moles of gas A, nA = PAVA / RT = 16.4500 moles
moles of gas B, nB = PBVB / RT = 0.388291 VB moles
2. After allowing the gases to mix, PTVT = nTRT
where PT = 8.71 atm, VT = 48.2 L + VB, and nT = 16.4500 moles + 0.388291 VB moles.
Or, plugging in the numbers and leaving off the units for simplicity, we'll have
(8.71) (48.2 + VB) = (16.4500 + 0.388291 VB) (0.08206) (298.15)
From which we can get VB.
Steve
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