# Question 5.13: Aqueous lithium hydroxide solution is used to purify air in ...

Aqueous lithium hydroxide solution is used to purify air in spacecraft and submarines because it absorbs carbon dioxide, which is an end product of metabolism, according to the equation

$2LiOH(aq) + CO_{2}(g) → Li_{2}CO_{3}(aq) + H_{2}O(l)$

The pressure of carbon dioxide inside the cabin of a submarine having a volume of $2.4 \times 10^{5} L is 7.9 \times 10^{-3}$  atm at 312 K. A solution of lithium hydroxide (LiOH) of negligible volume is introduced into the cabin. Eventually the pressure of $CO_{2}$ falls to$1.2 \times 10^{-4}$  atm. How many grams of lithium carbonate are formed by this process?

Strategy How do we calculate the number of moles of $CO_{2}$ reacted from the drop in $CO_{2}$ pressure? From the ideal gas equation, we write

$n=P\times (\frac{V}{RT} )$

At constant T and V, the change in pressure of $CO_{2}, \Delta P$, corresponds to the change in the number of moles of $CO_{2}, \Delta n$. Thus,

$\Delta n=\Delta n\times (\frac{V}{RT} )$

What is the conversion factor between $CO_{2}$ and $Li_{2}CO_{3}$?

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