Chapter 9, Problem 46A

Interpretation Introduction

Interpretation:

The percent amount of carbon dioxide absorbed by the lithium hydroxide canister needs to be deduced under the given conditions.

Concept Introduction:

• 'Yield refers to the amount of product obtained from a reaction.
• 'Theoretical yield' refers to the amount of product obtained from the molar ratio in the balanced equation, whereas the 'actual yield' represents the product recovered from an experimental procedure.
• 'Percent yield' is a ratio of the actual and theoretical yields.

  $\text{\% Yield = }\frac{\text{Actual yield (or experimental yield)}}{\text{Theoretical yield}}\text{×100 ------(1)}$

Answer to Problem 46A

% capacity of LiOH canister = 71.7%.

Explanation of Solution

Given:

Mass of LiOH = 155 g

Mass of CO₂ absorbed by the LiOH canister = 102 g

Calculations:

The given reaction is:

  ${\text{LiOH + CO}}_2\to {\text{Li}}_{\text{2}}{\text{CO}}_{\text{3}}{\text{+ H}}_{\text{2}}\text{O}$

The balanced equation is:

  ${\text{2LiOH + CO}}_2\to {\text{Li}}_{\text{2}}{\text{CO}}_{\text{3}}{\text{+ H}}_{\text{2}}\text{O}$

Step 1:Calculate the moles of LiOH as follows:

Mass of LiOH = 155 g

Molar mass of LiOH = 24 g/mol

  $\begin{array}{l}\text{Moles of LiOH}=\frac{\text{Mass of LiOH}}{\text{Molar mass LiOH}}\\ =\frac{155\text{ g}}{24\text{ g/mol}}=6.458\text{ moles}\end{array}$

Step 2: Calculate the moles of CO₂ reacted as follows:

Based on the reaction stoichiometry:

2 moles of LiOH reacts with 1 mole of CO2

Therefore, 6.458 moles of LiOH will combine with:

  $\frac{6.458\text{ moles LiOH}\times {\text{ 1 moles CO}}_{\text{2}}}{2\text{ mole LiOH}}=3.23{\text{ moles CO}}_{\text{2}}$

Step 3: Calculate the theoretical mass of CO₂ absorbed as follows:

Moles of CO2 =3.23

Molar mass CO2 = 44 g/mol

  $\begin{array}{l}{\text{Mass CO2}}_{}\text{= moles }\times \text{ molar mass}\\ \text{=3}\text{.23 }\times \text{44 = 142}\text{.12 g}\end{array}$

Step 4: Calculate the % capacity reached as follows:

Based on equation (1):

  $\begin{array}{l}\text{\% Yield/Capacity = }\frac{\text{Actual yield (or experimental yield)}}{\text{Theoretical yield}}\text{×100}\\ \text{=}\frac{102}{142.12}\times 100=71.7\%\end{array}$

Conclusion

Therefore, the LiOH canister has reached 71.7 % of its CO₂ absorption capacity.