# Equalizing Pressure Question

I have a question about the gas collection over water lab:

We learned that when the water level inside the graduated cylinder is higher than the outside water level, the gases inside the graduated cylinder have a lower pressure than atmospheric pressure.

Then by adjusting water level of the graduated cylinder to match the water level outside would equalize pressure. However shouldn't the volume of the gas decrease if the pressure is increased? Shouldn't the water level go up as you push the cylinder down beneath water level or go down as you lift it through the water? Does Boyle´s law (PV = PV) not apply here? Why?

• Why don't you set up a model calculation to quantify exactly what happens? Treat the gas as ideal, and use the hydrostatic equation to quantify the pressure at the top of the water surface within the cylinder? – Chet Miller Oct 20 '18 at 1:07

The pressure exerted exerted by a column of liquid is $$P = \rho g h$$ where $$\rho$$ is the density of the liquid. But that means that for a small displacement on the order of a centimeter, $$P \approx 100\ \mathrm{Pa}$$. One atmosphere on the other hand is roughly 1000 times that magnitude, so you've managed to decrease the pressure of the gas bubble by about 0.1%. Boyle's law does apply and implies that you've increased the volume by the same amount.