Answer
The change in pressure of the gas is $392~Pa$
Work Step by Step
Initially, the two columns of water are even. This shows that initially, the pressure of the gas was equal to the atmospheric pressure.
The change in the gas pressure is equal to the gauge pressure. We can find the gauge pressure of the gas:
$P_g = \rho gh$
$P_g = (10^3~kg/m^3)(9.80~m/s^2)(0.040~m)$
$P_g = 392~N/m^2$
The change in pressure of the gas is $392~Pa$.
