(a) If a person wearing such a mask exhales 0.702 g CO2 per minute, How many grams of KO2 are consumed in ten minutes?
28.2 g KO2
To determine the grams of KO2 consumed in ten minutes, we need to set up a conversion using the information given.
First, we need to find the molar mass of CO2, which consists of one carbon atom (C) and two oxygen atoms (O). The atomic masses are:
- Atomic mass of carbon (C) = 12.01 g/mol
- Atomic mass of oxygen (O) = 16.00 g/mol
Hence, the molar mass of CO2 is:
(1 * 12.01 g/mol) + (2 * 16.00 g/mol) = 12.01 g/mol + 32.00 g/mol = 44.01 g/mol
Next, we'll convert the given CO2 mass into moles. We know that the person exhales 0.702 g of CO2 per minute. Using the molar mass, we can convert this to moles:
0.702 g * (1 mol/44.01 g) ≈ 0.01594 mol
Now, let's set up the stoichiometric ratio between CO2 and KO2. The balanced chemical equation for the reaction between CO2 and KO2 is:
2 KO2 + 2 CO2 → K2CO3 + O2
From the equation, we see that 2 moles of KO2 react with 2 moles of CO2. Therefore, the molar ratio is:
2 moles KO2 / 2 moles CO2 = 1 mole KO2 / 1 mole CO2
Since we have 0.01594 moles of CO2, we can conclude that the number of moles of KO2 consumed is also 0.01594 moles.
Finally, we need to convert the moles of KO2 to grams using its molar mass. The molar mass of KO2 is:
39.10 g (atomic mass of K) + (2 * 16.00 g/mol) (atomic mass of O) = 71.10 g/mol
Multiplying the molar mass by the number of moles, we get:
0.01594 mol * 71.10 g/mol ≈ 1.13 g
Therefore, approximately 1.13 grams of KO2 are consumed in ten minutes by a person exhaling 0.702 g of CO2 per minute while wearing a mask.