You have to both put the entirety of the tax towards it and ensure that the fact that you're funding it through the tax doesn't decrease the amount of additional funding you put towards it or else that decrease effectively decreases the tax rate (at least as far as carbon capture is concerned). The second part is harder than the first.
This is what happened when lotteries started spreading across the US. The proceeds were earmarked for schools, so naturally, the property tax rates (which pays for most school funding) was held in check, resulting in no actual increase in school spending.
