The reaction between potassium superoxide, \(\mathrm{KO}_{2},\) and \(\mathrm{CO}_{2}\) $$ 4 \mathrm{KO}_{2}+2 \mathrm{CO}_{2} \longrightarrow 2 \mathrm{K}_{2} \mathrm{CO}_{3}+3 \mathrm{O}_{2} $$ is used as a source of \(\mathrm{O}_{2}\) and absorber of \(\mathrm{CO}_{2}\) in self-contained breathing equipment used by rescue workers. (a) How many moles of \(\mathrm{O}_{2}\) are produced when 0.400 \(\mathrm{mol}\) of \(\mathrm{KO}_{2}\) reacts in this fashion? (b) How many grams of \(\mathrm{KO}_{2}\) are needed to form 7.50 \(\mathrm{g}\) of \(\mathrm{O}_{2} ?\) (c) How many grams of \(\mathrm{CO}_{2}\) are used when 7.50 \(\mathrm{g}\) of \(\mathrm{O}_{2}\) are produced?

Step by step solution

01

(a) Calculate moles of O₂ produced

To calculate the moles of O₂ produced when 0.400 mol of KO₂ reacts, we can use the stoichiometry of the balanced chemical equation. From the balanced equation, we see that 4 moles of KO₂ produce 3 moles of O₂. So, for 0.400 mol of KO₂, Moles of O₂ = (Moles of KO₂ × Moles of O₂ produced) / (Moles of KO₂ reacting) Moles of O₂ = (0.400 mol × 3) / 4 Moles of O₂ produced = 0.300 mol

02

(b) Calculate grams of KO₂ needed to produce 7.50 g O₂

First, we need to convert the given mass of O₂ to moles: Moles of O₂ = mass of O₂ / molar mass of O₂ Moles of O₂ = 7.50 g / 32.00 g/mol Moles of O₂ = 0.2344 mol Now, we find how many moles of KO₂ are needed to produce 0.2344 moles of O₂. From the balanced equation, 4 moles of KO₂ produce 3 moles of O₂. So, Moles of KO₂ = (Moles of O₂ × Moles of KO₂ reacting) / Moles of O₂ produced Moles of KO₂ = (0.2344 mol × 4) / 3 Moles of KO₂ = 0.3125 mol Now, we convert moles of KO₂ to grams: Mass of KO₂ = moles of KO₂ × molar mass of KO₂ Mass of KO₂ = 0.3125 mol × (39.10 g/mol + 16.00 g/mol) Mass of KO₂ = 17.24 g

03

(c) Calculate grams of CO₂ used to produce 7.50 g O₂

We know that 0.2344 mol of O₂ is produced, which we found in part (b). We will now find the moles of CO₂ used in the reaction. From the balanced equation, 4 moles of KO₂ react with 2 moles of CO₂ to produce 3 moles of O₂. Moles of CO₂ = (Moles of O₂ × Moles of CO₂ reacting) / Moles of O₂ produced Moles of CO₂ = (0.2344 mol × 2) / 3 Moles of CO₂ = 0.1563 mol Now, we convert moles of CO₂ to grams: Mass of CO₂ = moles of CO₂ × molar mass of CO₂ Mass of CO₂ = 0.1563 mol × (12.01 g/mol + 2 * 16.00 g/mol) Mass of CO₂ = 7.00 g

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