Question

Hydrogen peroxide is used as a cleansing agent in the treatment of cuts and abrasions for several reasons. It is an oxidizing agent that can directly kill many microorganisms; it decomposes on contact with blood, releasing elemental oxygen gas (which inhibits the growth of anaerobic microorganisms); and it foams on contact with blood, which provides a cleansing action. In the laboratory, small quantities of hydrogen peroxide can be prepared by the action of an acid on an alkaline earth metal peroxide, such as barium peroxide: $$ \mathrm{BaO}_{2}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{BaCl}_{2}(a q) $$ What mass of hydrogen peroxide should result when 1.50 \(\mathrm{g}\) barium peroxide is treated with 88.0 \(\mathrm{mL}\) hydrochloric acid solution containing 0.0272 \(\mathrm{g} \mathrm{HCl}\) per mL? What mass of which reagent is left unreacted?

Short answer

In conclusion, 1.14 g of hydrogen peroxide is produced, and 0.91 g of barium peroxide is left unreacted.

Step-by-step solution

Calculate the number of moles of both reactants

First, we need to find the molecular weights of the reactants, which can be found using the periodic table: BaO2: \(137.33 \, (Ba) + 2 \times 16.00 \, (O) = 169.33 \, g/mol\) HCl: \(1.01 \, (H) + 35.45 \, (Cl) = 36.46 \, g/mol\) Now we can calculate the number of moles for both reactants: For BaO2: \(\frac{1.50 \, g}{169.33 \, g/mol} = 0.00886 \, mol\) For HCl: \(88.0 \, mL \times \frac{0.0272 \, g}{mL} \times{\frac{1 \, mol}{36.46 \, g}} = 0.0671 \, mol\)

Determine the limiting reagent

Using the stoichiometric coefficients from the balanced chemical equation, we can see that 1 mole of BaO2 reacts with 2 moles of HCl. To determine the limiting reagent, we can calculate the mole ratio between the reactants: Mole ratio = \(\frac{0.0671 \, mol \, HCl}{0.00886 \, mol \, BaO2} = 7.57\) Since 1 mole of BaO2 reacts with 2 moles of HCl, the mole ratio must be 2 or lower for BaO2 to be the limiting reagent. Since the mole ratio is greater than 2 (7.57), this means that HCl is the limiting reagent.

Calculate the mass of hydrogen peroxide produced and the mass of the reagent left unreacted

Now that we know HCl is the limiting reagent, we can calculate the moles of H2O2 produced using the stoichiometry of the balanced chemical equation: Moles of H2O2 produced = \(\frac{0.0671 \, mol \, HCl}{2} = 0.0335 \, mol\) Now we can calculate the mass of H2O2 produced: Mass of H2O2 = \(0.0335 \, mol \times 34.02 \, g/mol = 1.14 \, g\) To find the mass of unreacted BaO2, let us see how many moles of BaO2 reacted with the given moles of HCl: Moles of BaO2 reacted = \(\frac{0.0671 \, mol \, HCl}{2} = 0.0335 \, mol\) Now we can calculate the mass of BaO2 left unreacted: Mass of BaO2 left unreacted = \(0.00886 \, mol - 0.0335 \, mol) \times 169.33 \, g/mol = 0.91 \, g\) In conclusion, 1.14 g of hydrogen peroxide is produced, and 0.91 g of barium peroxide is left unreacted.

Key concepts

Chemical Reaction Stoichiometry

Understanding the stoichiometry of a chemical reaction is like following a recipe. Every chemical equation tells a story about the reactants and products involved, much like ingredients and finished dishes. In our specific hydrogen peroxide synthesis reaction, the equation is given as: \[ \text{BaO}_{2}(s) + 2 \text{HCl}(aq) \rightarrow \text{H}_{2}\text{O}_{2}(aq) + \text{BaCl}_{2}(aq) \] This tells us that one mole of barium peroxide reacts with two moles of hydrochloric acid to form one mole of hydrogen peroxide and one mole of barium chloride. The coefficients in the equation reflect how much of each substance is needed or produced. Stoichiometry helps us calculate the quantity of reactants needed or products formed. Therefore, understanding stoichiometry is key when balancing chemical reactions, predicting quantities of products, and recognizing limiting reagents.

Oxidizing Agents

Oxidizing agents play an essential role in chemical reactions. They gain electrons during a reaction, causing another substance to lose electrons, which is known as oxidation. In the production of hydrogen peroxide, though we don't directly refer to an oxidizing agent in the balanced reaction discussed, hydrogen peroxide itself is a well-known oxidizing agent. It kills microorganisms by disrupting their cell walls and, when broken down to release oxygen, particularly combats anaerobic microorganisms, which cannot survive in the presence of oxygen. Understanding the behavior of oxidizing agents is crucial when analyzing their biological and chemical applications. These properties make oxidizing agents indispensable in disinfection, bleaching, and other industrial processes.

Balanced Chemical Equation

Balancing chemical equations is like making sure a scale stays even. A balanced equation ensures conservation of mass; meaning, atoms are neither created nor destroyed in a chemical reaction. Without a balanced equation, we can't accurately use stoichiometry to determine reactant and product quantities. Consider our initial reaction: \[ \text{BaO}_{2} + 2\text{HCl} \rightarrow \text{H}_{2}\text{O}_{2} + \text{BaCl}_{2} \] For the equation to be balanced, the number of atoms must be the same on both sides—for example, two hydrogen atoms and two chlorine atoms on both sides. Balancing equations forms the foundation of solving stoichiometric problems, ensuring each calculation we derive, such as isolating the limiting reagent, is precise and scientifically sound.

Hydrogen Peroxide Production

The production of hydrogen peroxide involves intricate chemical processes. In our example, an acidic reaction with an alkaline earth metal peroxide, specifically barium peroxide, yields hydrogen peroxide. This process can easily be replicated in a laboratory setting by reacting barium peroxide with hydrochloric acid. Hydrogen peroxide (\(\text{H}_{2}\text{O}_{2}\)) is not only practical in household cleaning but also industrial applications, ranging from bleaching textiles to rocket propellants due to its decomposable nature into water and oxygen. It's crucial to understand these chemical processes to comprehend how this common yet powerful compound is synthesized and utilized effectively. Moreover, the knowledge of how much product results from given reactants, as provided in stoichiometry, allows scientists and manufacturers to optimize production processes and costs.