# 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

## 1 Answer

Inside the graduated cylinder there is some water and the air bubble above it. The key point is that at a depth inside the graduated cylinder, at the same height as the water line outside, the pressure is the same. That means that the pressure on the outside, which is 1 atmosphere, is equal to the pressure inside, which is the pressure exerted by the column of water that is higher than the outside water level, plus the pressure of the air bubble.

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.

The takeaway here is that the change in pressure inside the graduated cylinder is quite small, enough to pull or push the liquid up and down as you move the graduated cylinder.

Also, you shouldn't be using a graduate cylinder. There's a special glass tube called a eudiometer that you're supposed to use for these types of measurements.