With no change amount material in flask, the volume container question increased to 5.000 times original. Assuming constant temperature,calculate (new) total pressure, at equilibrium.

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It
makes no difference whether you increase 5times the volume after at the
equlibrium established in (1) of you start start the reaction from
initial pure nitrogen dioxide in a 5times bigger volume flask.

increasing the volume 5 times original means halving the initial pressure to
p₀/592 inHg

so normal atmosphere pressure= 29.92 in Hg

so initial pressure becomes = 29.92/5 =5.984

The partial fulfill equilibrium condition:
Kp = (p(NO2))² / p(N2O4)

Kp = (p₀ - 5·Δp)² / Δp

now we have Kp=0.26 and p0=5.984

now find out Δp

0.26 = p0^2 +25 Δp^2 -1op0 Δp

25 Δp^2 - 10.26 p0 Δp + p0^2=0

25 Δp^2 - 61.4 Δp +35.81 =0

find the value of Δp

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