As someone who's currently trying to construct a sprayer for a sort of performance art thing, my recommendation is -- don't bother.
There are plenty of pump sprayers available at kitchen stores that you can fill and use.
There are two basic styles -- the ones where you squeeze a trigger and stuff shoots out with each squeeze like some cleaning products, and the ones that you pump up first and then press the button to release like an aerosol can.
I like the trigger ones for water (for keeping near the grill to deal with flareups). I like the aerosol-like ones for oils, as I get a finer spray for popcorn, and I can still lay down a decent coating in a pan for cooking.
I do not like the stainless steel aerosol sprayers -- you want a clear one, so you can see how much oil there is in the container, and you don't overfill, as you need to leave quite a bit of space for the pressurized air.
You should also look for ones where the tube goes deep into the container -- if it stops 1" from the bottom, that means you can't use it when the oil or liquid is low, and you have to refill it more often.
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I should also note that Pam and other spray oils have an additive in them that makes it so they won't bead up after you spray it, which means it'll coat things better ... misting it with oil works pretty well, but it'll start beading up if you leave it after doing it.
If the recipe calls for oil, butter, or any other fat, then you can try to scale the other quantities to match it.
If not, there's still a chance you can salvage it. The oil doesn't actually chemically react with the mix at all, it just "coats" it; in fact, most cake recipes use some amount of fat in order to slow gluten formation (i.e. stop the cake from getting tough and chewy).
However, if the recipe called for 1 1/4 cups water and you used the same quantity of oil instead, then that is going to be way too much oil for a single serving.
What I would do is double or maybe even triple the cake mix, make sure it's very well mixed with the oil, then add however much water you needed in the first place.
If you realized your mistake early (i.e. if the original recipe called for a lot more than 1 1/4 cups of water) then you might be able to just proceed as normal and end up with a very moist cake, but more likely you'll still need to add some more cake mix (and the corresponding amount of water) to compensate. I'd still double it, because otherwise you'll be stuck trying to figure out how to use the leftover mix.
Don't just add flour; the amount of water that the recipe calls for is proportional to all of the other ingredients in the mix, and it's virtually impossible for you to know how much extra water you'll need to compensate for the added flour. Besides, you'd only end up with a bland, flavourless cake if you did that.
If none of these options appeal to you then I'm afraid it's destined for the trash, unless you want to prepare your own cake mix from scratch and combine the two recipes.
Best Answer
Some chemicals and flavours dissolve or bind to water differently from oil. For example, chili binds with oil much better than with water and the honey in your recipe will dissolve into the water which it would not do in oil.