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Consider the balanced chemical equation $$ 4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s) $$ What mole ratio would you use to calculate how many moles of oxygen gas would be needed to react completely with a given number of moles of aluminum metal? What mole ratio would you use to calculate the number of moles of product that would be expected if a given number of moles of aluminum metal reacts completely?

Short Answer

Expert verified
To calculate the moles of oxygen gas needed to react completely with a given number of moles of aluminum metal, use the mole ratio \(\frac{3 \:moles \:of\: O_2}{4 \:moles \:of\: Al}\). To calculate the number of moles of aluminum oxide expected if a given number of moles of aluminum metal reacts completely, use the mole ratio \(\frac{1 \:mole \:of\: Al_2O_3}{2\: moles \:of\: Al}\).

Step by step solution

01

Identify the coefficients in the balanced chemical equation.

From the balanced chemical equation, we can see that the coefficients are: - 4 for aluminum (Al) - 3 for oxygen gas (O2) - 2 for aluminum oxide (Al2O3)
02

Find the mole ratio for moles of oxygen gas needed for the given moles of aluminum metal.

To find out how many moles of oxygen gas (O2) would be needed to react completely with given moles of aluminum (Al), we look at the coefficient ratio between Al and O2. The ratio is 4:3. So for every 4 moles of Al, 3 moles of O2 are required. Therefore, the mole ratio for Al to O2 is: $$ \frac{3 \:moles \:of\: O_2}{4 \:moles \:of\: Al} $$
03

Find the mole ratio for the number of moles of aluminum oxide expected for the given moles of aluminum metal.

To find out how many moles of aluminum oxide (Al2O3) would be expected if a given number of moles of aluminum (Al) reacts completely, we look at the coefficient ratio between Al and Al2O3. The ratio is 4:2 or simplified to 2:1. So for every 2 moles of Al, 1 mole of Al2O3 is formed. Therefore, the mole ratio for Al to Al2O3 is: $$ \frac{1 \:mole \:of\: Al_2O_3}{2\: moles \:of\: Al} $$

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Key Concepts

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

Stoichiometry Made Simple
Stoichiometry is a fundamental concept in chemistry that helps us quantify the relationships between reactants and products in chemical reactions.
It might sound complicated, but it's essentially about using ratios derived from balanced equations to make predictions about the amounts of substances involved in a reaction.
This approach allows scientists to calculate how much of a reactant is needed, or how much product will be formed, once they know the quantities of other substances involved.
In the exercise provided, stoichiometry helps us determine the amounts of oxygen gas needed to react with aluminum and the amount of aluminum oxide produced.
By using mole ratios, which are derived from the coefficients in the balanced chemical equation, we can ensure that our calculations are accurate and aligned with the conservation of mass in chemical reactions.
To practice stoichiometry, one must become comfortable finding the mole ratios and applying them to calculate quantities in chemical reactions.
Understanding Balanced Chemical Equations
Balanced chemical equations are the foundation of stoichiometry.
A balanced equation has the same number of each type of atom on both sides of the equation, which reflects the conservation of mass: matter cannot be created or destroyed.
When balancing equations, we adjust the coefficients, which are the numbers in front of molecules or atoms, not the subscripts in the chemical formulas.
In the exercise equation \(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\), the numbers 4, 3, and 2 are coefficients, showing the stoichiometric relationships of reactants and products.
These coefficients tell us that:
  • 4 moles of aluminum react with 3 moles of oxygen gas
  • to form 2 moles of aluminum oxide.
The balanced equation ensures we have the correct mole ratios needed for stoichiometric calculations, making it an essential tool for predicting the outcomes of chemical reactions.
Chemical Reactions and Their Participants
Chemical reactions involve the transformation of reactants into products, and they can take many forms, from combustion to synthesis or decomposition.
In the context of the exercise, we are looking at a synthesis reaction where aluminum reacts with oxygen to form aluminum oxide.
Understanding the basic nature of a chemical reaction helps in identifying the species involved by recognizing their chemical symbols and phases.
The chemical equation \(4 \text{Al}(s) + 3 \text{O}_2(g) \rightarrow 2 \text{Al}_2\text{O}_3(s)\) shows:
  • Aluminum (Al) starting as a solid metal
  • Oxygen (\(\text{O}_2\)) as a gaseous reactant
  • And forming aluminum oxide (\(\text{Al}_2\text{O}_3\)), a solid compound.
Recognizing the states of matter and the type of reaction can guide you in making sense of the process and understanding the transformations that occur during the reaction.

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Most popular questions from this chapter

What quantity serves as the conversion factor between the mass of a sample and how many moles the sample contains?

For each of the following balanced equations, indicate how many moles of the product could be produced by complete reaction of \(1.00 \mathrm{~g}\) of the reactant indicated in boldface. Indicate clearly the mole ratio used for the conversion. a. \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \rightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) b. \(\mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)\) $$ \text { c. } 4 \mathrm{Na}(s)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{Na}_{2} \mathrm{O}(s) $$ d. \(2 \mathbf{P}(s)+3 C l_{2}(g) \rightarrow 2 \mathrm{PCl}_{3}(l)\)

Small quantities of ammonia gas can be generated in the laboratory by heating an ammonium salt with a strong base. For example, ammonium chloride reacts with sodium hydroxide according to the following balanced equation: $$ \mathrm{NH}_{4} \mathrm{Cl}(s)+\mathrm{NaOH}(s) \rightarrow \mathrm{NH}_{3}(g)+\mathrm{NaCl}(s)+\mathrm{H}_{2} \mathrm{O}(g) $$ What mass of ammonia gas is produced if \(1.39 \mathrm{~g}\) of ammonium chloride reacts completely?

Consider the following reaction: \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) If a container were to have only 10 molecules of \(\mathrm{O}_{2}(g)\) and 10 molecules of \(\mathrm{NH}_{3}(g),\) how many total molecules (reactant and product) would be present in the container after the above reaction goes to completion? b. Using "microscopic" pictures, draw the total molecules present inside the container after the reaction occurs. c. What mass of \(\mathrm{NO}(g)\) is present in the container after the reaction occurs? (Report your final answer to 4 significant figures.

Hydrogen peroxide is used as a cleaning agent in the treatment of cuts and abrasions for several reasons. It is an oxidizing agent that can directly kill many microorganisms; it decomposes upon contact with blood, releasing elemental oxygen gas (which inhibits the growth of anaerobic microorganisms); and it foams upon 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. $$ \mathrm{BaO}_{2}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{BaCl}_{2}(a q) $$ What amount of hydrogen peroxide should result when \(1.50 \mathrm{~g}\) of barium peroxide is treated with \(25.0 \mathrm{~mL}\) of hydrochloric acid solution containing \(0.0272 \mathrm{~g}\) of \(\mathrm{HCl}\) per \(\mathrm{mL}\) ?

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