Final answer:
The volume of CO₂ gas that can be absorbed by 326 g of LiOH at 23°C and 783 mmHg is calculated by first determining the amount of LiOH in moles, then using the stoichiometry of the reaction to find the moles of CO₂, and finally applying the ideal gas law to find the volume.
Step-by-step explanation:
The volume of carbon dioxide gas at 23°C and 783 mmHg that could be absorbed by 326 g of lithium hydroxide (LiOH) can be calculated using the ideal gas equation and stoichiometry from the chemical reaction between LiOH and CO₂.
First, we calculate the moles of LiOH using its molar mass (23.95 g/mol):
326 g LiOH x (1 mol LiOH / 23.95 g LiOH) = 13.61 mol LiOH.
From the chemical reaction 2LiOH(s) + CO₂(g) → Li₂CO₃(s) + H₂O(l), 2 mol of LiOH absorb 1 mol of CO₂. Thus, the moles of CO₂ absorbed are half the moles of LiOH:
13.61 mol LiOH / 2 = 6.805 mol CO₂.
Using the ideal gas law PV=nRT, and converting the pressure from mmHg to atm (1 atm = 760 mmHg), the volume (V) can be found:
V = (nRT) / P
V = (6.805 mol x 0.0821 L·atm/K·mol x 296 K) / (783 mmHg / 760 mmHg/atm)
The volume of CO₂ absorbed is approximately.