If the pressure of the gas inside the flask were increased and the height of the column in the open-ended arm went up by 0.5mm, what would be the new pressure of the gas in the flask, in torr?

ANSWER IS 807.3 TORR

3 answers

I don't believe you have enough information.
This question [is a sample problem in Section 10.2 of the Beer, et. al. Chemistry text book and] is a follow up to the one asked and answered here:
tinyurl.com/sj4aaqt

Initial conditions needed to solve this question:
P_atmo = 764.7 torr
h_atmo = 136.4 mm (of Hg)
h_gas = 103.8 mm (of Hg)

Calculate the new heights:
h_atmo2 = h_atmo + 5.0 mm = 141.4 mm
h_gas2 = h_gas - 5.0 mm = 98.8 mm

Then plug and chug:
P_gas2 = P_atmo + (h_atmo2 - h_gas2)
= 764.7 + (141.4 - 98.8)
= 807.3 torr
Correction: Brown, et. al. text book.