To determine how many moles of lithium hydroxide (LiOH) are required to react with 20 moles of carbon dioxide (CO₂), we can use the stoichiometric relationship given in the balanced chemical equation:
[tex]\[ CO_2(g) + 2 LiOH(s) \rightarrow Li_2CO_3(s) + H_2O(l) \][/tex]
From the balanced equation, we see that 1 mole of CO₂ reacts with 2 moles of LiOH. This gives us the stoichiometric ratio:
[tex]\[ 1 \text{ mole of } CO_2 : 2 \text{ moles of } LiOH \][/tex]
Now, let's determine how many moles of LiOH are needed to react with 20 moles of CO₂.
Step-by-step procedure:
1. Identify the given quantity: We know that we have 20 moles of CO₂.
2. Use the stoichiometric ratio to find the required amount of LiOH:
[tex]\[ \text{Moles of LiOH} = 2 \times \text{Moles of CO₂} \][/tex]
3. Substitute the given quantity (20 moles of CO₂) into the equation:
[tex]\[ \text{Moles of LiOH} = 2 \times 20 \text{ moles of CO₂} \][/tex]
4. Calculate the result:
[tex]\[ \text{Moles of LiOH} = 40 \text{ moles of LiOH} \][/tex]
Therefore, 40 moles of lithium hydroxide (LiOH) are required to react with 20 moles of carbon dioxide (CO₂), which is the average amount exhaled by a person each day.
Based on our calculation, the correct answer is:
- 40 moles
