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Potassium superoxide, \(\mathrm{KO}_{2}\), is used in rebreathing gas masks to generate oxygen. $$ 4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g) $$ If a reaction vessel contains \(0.25 \mathrm{~mol} \mathrm{KO}_{2}\) and \(0.15 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\), what is the limiting reactant? How many moles of oxygen can be produced?

Short Answer

Expert verified
Limiting reactant is \(\mathrm{KO}_{2}\). Moles of \(\mathrm{O}_2\) produced: 0.1875.

Step by step solution

01

Understand the Balanced Equation

The balanced chemical equation for the reaction is: \[ 4 \mathrm{KO}_{2}(s) + 2 \mathrm{H}_{2} \rightarrow 4 \mathrm{KOH}(s) + 3 \mathrm{O}_{2}(g) \]. This indicates that 4 moles of \(\mathrm{KO}_2\) react with 2 moles of \(\mathrm{H}_{2} \mathrm{O}\) to produce 3 moles of \(\mathrm{O}_2\).
02

Determine Mole Ratios

From the balanced equation, 4 moles of \(\mathrm{KO}_2\) require 2 moles of \(\mathrm{H}_2\mathrm{O}\). The ratio of \(\mathrm{KO}_2\) to \(\mathrm{H}_{2} \mathrm{O}\) is 2:1, meaning 1 mole of \(\mathrm{KO}_2\) requires 0.5 moles of \(\mathrm{H}_{2} \mathrm{O}\).
03

Calculate Actual Moles Needed

With 0.25 moles of \(\mathrm{KO}_2\), we'd need \(0.25 \times 0.5 = 0.125\) moles of \(\mathrm{H}_2\mathrm{O}\). We have more than enough \(\mathrm{H}_{2}\mathrm{O}\), as there are 0.15 moles available.
04

Identify the Limiting Reactant

Given 0.25 moles of \(\mathrm{KO}_{2}\) and the need for only 0.125 moles of \(\mathrm{H}_{2}\mathrm{O}\), \(\mathrm{KO}_{2}\) is the limiting reactant because it is present in the lower stoichiometric proportion compared to the \(\mathrm{H}_{2} \mathrm{O}\).
05

Calculate Moles of Oxygen Produced

According to the balanced equation, 4 moles of \(\mathrm{KO}_{2}\) produce 3 moles of \(\mathrm{O}_2\). Hence, 0.25 moles of \(\mathrm{KO}_{2}\) will produce \( \frac{3}{4} \times 0.25 = 0.1875 \) moles of \(\mathrm{O}_{2}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Limiting Reactant
In a chemical reaction, the limiting reactant is the substance that gets completely consumed first, limiting the amount of product that can be formed. It determines the maximum amount of product that can be produced in a given reaction. When you are given specific quantities of reactants, like in this exercise, identifying the limiting reactant is crucial.
We start by using the stoichiometry from the balanced chemical equation. This equation tells us how much of each reactant is needed and in what ratio they interact. In our example with potassium superoxide and water, the balanced equation shows that 4 moles of KOâ‚‚ need 2 moles of Hâ‚‚O.
By comparing the amounts available and the stoichiometric needs calculated from the mole ratio, we can identify the limiting reactant. In this case, KOâ‚‚ is the limiting reactant because the amount of KOâ‚‚ determines how much product (oxygen in this case) can be made before one of the reactants runs out.
Mole Ratio
The concept of mole ratio is central to stoichiometry. It is derived from the coefficients of a balanced chemical equation and tells us how many moles of one substance react with a certain amount of moles of another. It's the bridge that allows us to convert between substances in a chemical equation.
In this particular exercise, the balanced chemical equation provides the mole ratio between KOâ‚‚ and Hâ‚‚O, which is 4:2. This simplifies to a 2:1 ratio. Therefore, for every mole of KOâ‚‚, 0.5 moles of Hâ‚‚O are required.
  • This ratio is used to determine how much of each reactant is necessary for the reaction to proceed completely.
  • By knowing the mole ratio, you can figure out exactly how much of each reactant is needed without any excess.
The mole ratio is especially useful when scaling up reactions for larger batches in a laboratory or industrial setting.
Chemical Equation
A chemical equation is a symbolic representation of a chemical reaction. It shows the substances involved (reactants) and those produced (products). It's crucial for communicating how a reaction proceeds.
The chemical equation in this exercise is given as: \[4 \mathrm{KO}_{2}(s) + 2 \mathrm{H}_{2} \rightarrow 4 \mathrm{KOH}(s) + 3 \mathrm{O}_{2}(g)\]
  • This equation is balanced, meaning the number of atoms for each element is the same on both sides of the equation.
  • The coefficients (the numbers in front of each molecule) are vital. They indicate the smallest whole-number ratios of molecules or moles in the reaction.
Understanding how to read and balance chemical equations is a fundamental skill in chemistry, as it serves as the starting point for stoichiometric calculations.
Oxygen Production
Oxygen production in chemical reactions refers to the formation of oxygen gas as a product. In the context of the reaction between potassium superoxide and water, oxygen is one of the key products.
The balanced chemical equation reveals that for every 4 moles of KOâ‚‚, 3 moles of Oâ‚‚ are generated. Using stoichiometric calculations and considering KOâ‚‚ is the limiting reactant, we can determine the amount of oxygen produced.
With 0.25 moles of KOâ‚‚ available, we applied the mole ratio of KOâ‚‚ to Oâ‚‚, which is 4:3. This ratio lets us calculate the moles of oxygen produced:\[\frac{3}{4} \times 0.25 = 0.1875\] moles of Oâ‚‚.This process shows how understanding stoichiometry and using the limiting reactant concept allows for precise calculations of product formation in chemical reactions.

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Most popular questions from this chapter

Butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\), burns with the oxygen in air to give carbon dioxide and water. $$2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+13 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$$ What is the amount (in moles) of carbon dioxide produced from \(0.30 \mathrm{~mol} \mathrm{C}_{4} \mathrm{H}_{10} ?\)

Alloys, or metallic mixtures, of mercury with another metal are called amalgams. Sodium in sodium amalgam reacts with water. (Mercury does not.) $$ 2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g) $$ If a \(15.23-\mathrm{g}\) sample of sodium amalgam evolves \(0.108 \mathrm{~g}\) of hydrogen, what is the percentage of sodium in the amalgam?

Hydroquinone, used as a photographic developer, is \(65.4 \% \mathrm{C}, 5.5 \% \mathrm{H}\), and \(29.1 \% \mathrm{O}\), by mass. What is the empirical formula of hydroquinone?

Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), burns with the oxygen in air to give carbon dioxide and water. $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ What is the amount (in moles) of water produced from \(0.69 \mathrm{~mol}\) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} ?\)

Potassium superoxide, \(\mathrm{KO}_{2}\), is employed in a selfcontained breathing apparatus used by emergency personnel as a source of oxygen. The reaction is $$ 4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g) $$ Say a self-contained breathing apparatus is charged with \(750 \mathrm{~g}\) \(\mathrm{KO}_{2}\) and then is used to produce \(195 \mathrm{~g}\) of oxygen. Was all of the \(\mathrm{KO}_{2}\) consumed in this reaction? If the \(\mathrm{KO}_{2}\) wasn't all consumed, how much is left over and what mass of additional \(\mathrm{O}_{2}\) could be produced?

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