How much mass do the volcanoes of Io erupt past escape velocity? While trying to do some calculations to answer this quesion, I got stuck missing a crucial piece of data: I have no clue how much mass the volcanoes of Io manage to throw out of the gravity well of the Jupiter moon.

It is clear that most of the erupted material falls back to the surface, and the various velocity estimates I have found are quite a bit lower than the escape velocity (~2.56 km/s). For instance "up to 1 km/s".

One number that is possible to find is how much mass the magnetosphere of Jupiter strips of Io. Most are listing that as 1000kg/s (example). That is about as much as the wheat production of Canada.

Are the volcanoes directly throwing away a lot more than that? A lot less? Not at all?
The velocity required to escape the gravitational attraction of a massive body is given by the following equation:

$$ v_{\mathrm{escape}} = \sqrt{\frac{2GM}{R}}$$

where $G$ is the gravitational constant ($G = 6.67 \times 10^{-11} \; \mathrm{Nm^{2} {kg}^{-2}}$), $M$ is the mass of the body from which you are escaping, and $R$ is its radius. 

Inputting the values for Io's mass and mean radius, $M = 0.015 \, M_{\oplus}$ and $R = 0.286 \, R_{\oplus}$,1 we get an escape velocity of

$$ v_{\mathrm{escape}} = 2560 \; \mathrm{m/s}$$

However, the explosive ejecta are ejected from the top of volcanoes, so we should strictly add this to our radius. The tallest volcano on Io is approximately $2.5 \;\mathrm{km}$ above the surface; including this we get a marginally lower velocity

$$ v_{\mathrm{escape}} = 2559 \; \mathrm{m/s} $$ 

which is higher than the $\sim 1000 \; \mathrm{m/s}$ maximum velocity of ejecta calculated in McEwen &amp; Soderblom (1983). Therefore, no mass is ejected from the surface of Io through volcanic eruptions.

For comparison, the earth's escape velocity is much higher, $11.2 \; \mathrm{km/s}$.  As discussed in the linked paper, the most extreme ejecta can reach heights of $500 \; \mathrm{km}$ before falling back to the surface.



1where $M_{\oplus} = 5.972 \times 10^{24} \; \mathrm{kg}$ and $R_{\oplus} = 6371 \;\mathrm{km}$