Can someone tell me why this method is wrong even though it seems logical?

[lLovePhysics]

1. The problem statement, all variables and given/known data
Solid lithium hydroxide is used in space vehicles to remove exhaled carbon dioxide from the living environment by forming solid lithium carbonate and liquid water. What mass of gaseous carbon dioxide can be absorbed by 1.00kg of lithium hydroxide?



3. The attempt at a solution

First, I balanced out the equation with the reactants and products:

2LiOH+CO_2 \right arrow Li_{2}CO_{3}+H_{2}O

Then I found the molar mass of LiHO to be: 23.949g/ mol LiHO

So then I did this:

\frac{23.949g}{mol \\LiHO} \times \frac{2mol LiHO}{1molCO_{2}}=\frac{47.898g}{1molCO_2} \times \frac{1molCO_2}{44.01g}

Other than that the units cancel out.. can someone tell me why it is wrong and how to avoid these problems? As of now, I just try to cancel the units out to get grams but I don't really have a "systematic" way of doing things. Is there a a systematic way? How do avoid not knowing what you are doing and how to arrive at the right answer? Thanks.

[rocomath]

1000g LiOH \frac{(12.01+32.0)g CO_2}{2(6.941+16.0+1.01)g LiOH} = 919g CO_2

???

[lLovePhysics]

1000g LiOH \frac{(12.01+32.0)g CO_2}{2(6.941+16.0+1.01)g LiOH} = 14.8g CO_2

???

My book says the answer is 920g.

[rocomath]

My book says the answer is 920g.lol damn i'm way off, ok let me check

EDIT: ok i obviously shouldn't calculate in the dark, lol

i got 919g CO2

since you have a 2:1 stoichiometric ratio between LiOH and CO_2. i assume bc like to avoid writing too much, so i skip out on the moles and assume they cancel out nicely and just stick to the units that i am required in my answer.