# Collecting gas over water -- is the textbook explanation wrong?

I was revising my chemistry and while doing a problem on collecting a gas over water, I felt like I disagreed with a part of their explanation.

Firstly, an illustration to show how I think about pressure, I could be wrong about this but from what I researched it seems correct:

A barometer, it's pretty self explanatory. At the bottom level the atmospheric pressure and the pressure in the mercury are equalized. Everywhere at this level the pressure is the same.

In the vacuum tube this pressure causes the mercury to push against the vacuum, being able to hold a column of mercury 760mm high. At the top of the mercury in the vacuum tube the pressure is 0; if it wasn't 0, it would be able to push some more mercury higher.

Now the collecting gas over water part, I will first explain how they do it in the textbook:

They explain that the gas collected in the inverted bottle, is equalized with atmospheric pressure. Then they also say that this gas collected over the water, contains some water vapor. So the pressure of the gas is actually equal to: "atmospheric pressure" - "pressure due to water vapor".

I posit that the pressure of the gas mixture in the bottle is not exactly equal to atmospheric pressure:

If my diagram is correct, the pressure at the bottom of the bottle is equal to atmospheric pressure but the pressure at the water surface in the bottle is equal to "atmospheric pressure" - "pressure due to the column of water".

I calculated how much this "pressure due to the column of water" would be for a bottle 300mm high, and it would come down to around 2900 Pa. Which is quite small, about 3% of atmospheric pressure. So maybe they don't mention this small distinction because the error is quite small anyway? The lower the column of water gets the lower the error becomes.

I would appreciate someone telling me if I'm thinking about it correctly or if I'm totally wandering into the fog. Thanks.

$$P_{gas} = P_{atm} - P_{column} - P_{w.vap}$$