Question

Answer the following question: In a space shuttle, the CO2 that the crew exhales is removed from the air by a reaction within canisters of lithium hydroxide. On average, each astronaut exhales about 650 L of CO2 daily. What mass of water will be produced
when this amount reacts with LiOH? The other product of the reaction is

Li2CO3. When answering this question include the following:

Have both the unbalanced and balanced chemical equations.
Explain how to find the molar mass of the compounds.
Explain how the balanced chemical equation is used to find the ratio of moles (hint: step 3 in the video).
Explain how many significant figures your answer needs to have.
The numerical answer

Answer 1

Answer:

$\boxed{\text{520 g H _{2} O}}$

Explanation:

(a) Unbalanced equation

$\rm LiOH + CO _{2} \longrightarrow \, Li _{2} CO _{3} + H _{2} O$

(b) Balanced equation

$\rm 2LiOH + CO _{2} \longrightarrow \, Li _{2} CO _{3} + H _{2} O$

(c) Molar masses

The only compound for which you need an atomic mass is water.

You look up the atomic masses of each element in the Periodic Table, multiply by their subscripts in the formula, and add.

$\begin{array}{rcrcr}\text{2H} & = & 2 \times 1.008 & = & 2.02\\\text{1O} & = & 1 \times 16.00 & = & 16.00\\\text{H _{2} O} & = & & & \mathbf{18.02}\\\end{array}$

(d) Molar Ratio

You want to convert moles of carbon dioxide to moles of water.

The balanced equation tells you that the molar ratio is 1 mol H₂O:1 mol CO₂.

(e) Significant figures

The only measurement you are given is "about 650 L." That tells you that the trailing zero is not significant.

The volume has only two significant figures, so the mass of water can have only two significant figures.

Note: Intermediate calculations should carry at least one extra digit (a guard digit) to prevent cumulative round-off errors, answers to be reported must have the correct number of significant figures.

(f) The calculation

You don't give the temperature and pressure of the gas, so I shall assume STP (1 bar and 0 °C). At STP, the molar volume of a gas

is 22.71 L.

$\text{Moles of CO _{2} } = \text{650 L CO _{2} } \times \dfrac{\text{1 mol CO _{2} }}{\text{22.71 L CO _{2} }} = \text{28.6 mol CO _{2} }\\\\\text{Moles of H _{2} O} = \text{28.6 mol CO _{2} } \times \dfrac{\text{1 mol H _{2} O}}{\text{1 mol CO _{2} }} = \text{28.6 mol H _{2} O}\\\\\text{Mass of H _{2} O} = \text{28.6 mol H _{2} O} \times \dfrac{\text{18.02 g H _{2} O}}{\text{1 mol H _{2} O}} = \boxed{\textbf{520 g H _{2} O}}$