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. Let's assume that one astronaut exhales about 537. 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
The gas is assumed to be at STP.
To solve this question, we will follow several steps:
1. Write and balance the chemical equation:
The unbalanced equation for the reaction is:
CO2 + LiOH → Li2CO3 + H2O
To balance this equation, we need to ensure that the number of atoms of each element is equal on both sides of the equation:
CO2 + 2LiOH → Li2CO3 + H2O
2. Find the molar mass of the compounds involved:
The molar mass of a compound is the sum of the atomic masses of each element in the compound. The atomic masses can be found on the periodic table. The molar masses for the compounds involved are as follows:
- CO2: Carbon has an atomic mass of 12.01 g/mol, and oxygen has an atomic mass of 16.00 g/mol. So, the molar mass of CO2 is (12.01 g/mol) + (16.00 g/mol) + (16.00 g/mol) = 44.01 g/mol.
- LiOH: Lithium has an atomic mass of 6.94 g/mol, oxygen has an atomic mass of 16.00 g/mol, and hydrogen has an atomic mass of 1.01 g/mol. So, the molar mass of LiOH is (6.94 g/mol) + (16.00 g/mol) + (1.01 g/mol) = 23.95 g/mol.
- Li2CO3: Lithium has an atomic mass of 6.94 g/mol, carbon has an atomic mass of 12.01 g/mol, and oxygen has an atomic mass of 16.00 g/mol. So, the molar mass of Li2CO3 is (6.94 g/mol × 2) + (12.01 g/mol) + (16.00 g/mol × 3) = 73.89 g/mol.
3. Use the balanced chemical equation to find the ratio of moles:
From the balanced equation CO2 + 2LiOH → Li2CO3 + H2O, we can see that for every 1 mole of CO2, we need 2 moles of LiOH to react and produce 1 mole of H2O.
4. Calculate the molar mass of CO2:
Since we know the volume of CO2 (537 L), and CO2 is given in liters, we can assume the reaction is under standard conditions (STP). At STP, 1 mole of any ideal gas occupies a volume of 22.4 L. Therefore, the number of moles of CO2 exhales daily can be calculated by dividing the volume of CO2 by 22.4 L/mol:
537 L CO2 / 22.4 L/mol = 23.93 mol CO2
5. Use the ratio of moles to find the number of moles of H2O produced:
From the balanced equation, we see that 1 mole of CO2 reacts to produce 1 mole of H2O. Therefore, the number of moles of H2O produced will also be 23.93 mol.
6. Calculate the mass of water produced:
To find the mass of H2O produced, we multiply the number of moles of H2O (23.93 mol) by its molar mass (18.015 g/mol):
23.93 mol H2O × 18.015 g/mol = 431.88 g H2O.
7. Significant figures:
Since we were given the volume of CO2 (537 L) without any decimal places, we assume it has an infinite number of significant figures and our final answer should also have an infinite number of significant figures. Therefore, our answer for the mass of water produced is 431.88 g, without rounding to a specific number of significant figures.
So, the numerical answer is 431.88 g of water will be produced when the given amount of CO2 reacts with LiOH.
LiOH + CO2 ==> Li2CO3 + H2O
2LiOH + CO2 ==> Li2CO3 + H2O
Note that 537 L CO2 doesn't tell me much since you don't include the pressure nor the temperature of the cabin. The author of the problem forgot to include the conditions of the gas. I understand the cabin pressure is maintained at approximately 1 atm but I KNOW the temperature isn't 0o (273 K). Let's say the temperature is 20 C (293 K). So at NTP (1 atm and 293 K) the molar volume is about 24.05 L/mol. That means mols CO2 iin 537 L @ those conditions is 537/24.05 = 22.3 mols.
Convert this to mols H2O produced using the coefficients in the balanced equation. 22.3 mol CO2 x (1 mol H2O/1 mol CO2) = 22.3 mol H2O
produced. Convert mols H2O to grams H2O.
g H2O = mols H2O x molar mass H2O = 22.3 x 18.02 = ? grams H2O. You can punch the numbers into a calculator to get the answer.
The 18.02 is obtain by used the numbers from the periodic table.
2H + O = 2*1.008) + 16.00 = 18.018 which I rounded to 18.02.
You are allowed 3 significant figures from the 537 number. It has three significant figures.
Note: In the future it would be nice if you would show what you know to do bvy yourself. I don't think you knew NOTHING about this problem.