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Chapter 11: Problem 40

Why are coefficients used in mole ratios instead of subscripts?

Short Answer

Expert verified
Coefficients are used in mole ratios instead of subscripts because they represent the relative amounts of substances participating in a reaction, which directly influence mole ratios. Coefficients in a balanced chemical equation reflect the correct stoichiometry for a given reaction, allowing for conversion between moles of different substances and stoichiometric calculations. In contrast, subscripts represent the number of atoms in a compound's molecule, providing no information about the proportion of substances involved in the reaction. Using coefficients in mole ratios ensures reactants and products are in the correct proportions, respecting the law of conservation of mass.

Step by step solution

01

Define Coefficients and Subscripts

In a chemical equation, coefficients are the numbers written before chemical species (atoms, molecules, or ions) and indicate their relative amounts in a reaction. Subscripts, on the other hand, are small numbers written to the lower right of an element's symbol, representing the number of atoms of that element in one molecule of a compound. For instance, in the chemical equation 2H2 + O2 鈫� 2H2O, the number "2" before H2 and H2O are coefficients, while the subscript "2" in H2 and H2O represent the number of hydrogen atoms in the molecule.
02

Understand Mole Ratios

Mole ratios describe the relationship between the amounts of different substances participating in a chemical reaction. They can be determined from the coefficients of the balanced chemical equation. The mole ratio is helpful for converting the number of moles of a given substance to another substance involved in the same reaction.
03

Importance of Coefficients in Mole Ratios

Coefficients represent the stoichiometric quantities (expressed in moles) of the reactants and products involved in a chemical reaction. They provide information about the mole ratio which, in turn, is vital for determining the amount of product formed or the amount of reactants needed for the reaction. Thus, using coefficients in mole ratios helps ensure that the reactants and products are present in the correct proportions, ultimately respecting the law of conservation of mass.
04

Why Coefficients are Used in Mole Ratios Instead Of Subscripts

The reason coefficients are used in mole ratios rather than subscripts is that coefficients express the relative amounts of substances participating in a reaction, which directly impact the mole ratios. Meanwhile, subscripts merely represent the number of atoms of an element present in one molecule of a compound, which does not provide information about the proportion of the substances involved in the reaction. Using the coefficients for mole ratios allows us to convert between moles of different substances and to perform stoichiometric calculations, which would not be possible if subscripts were used. Additionally, the coefficients in a balanced chemical equation can be adjusted to reflect the correct stoichiometry for a given reaction, while subscripts cannot be changed without altering the compound's identity. Therefore, coefficients are more suitable for providing accurate mole ratio information and enabling stoichiometric calculations for chemical reactions.

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Key Concepts

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

Stoichiometry
Stoichiometry is akin to a recipe for a chemical reaction, ensuring each reactant is measured in the right proportions to react completely without excess. Just like baking a cake requires a specific ratio of flour to sugar, stoichiometry involves using the mole concept to calculate precise quantities of reactants and products involved in a chemical reaction.

Let's consider a simple reaction where hydrogen gas reacts with oxygen to form water. The stoichiometric equation, 2H_2 + O_2 鈫� 2H_2O, represents not just the types of molecules but their quantities as well. The coefficient '2' tells us that two moles of hydrogen gas react with one mole of oxygen gas to produce two moles of water. These coefficients are essential; without them, the stoichiometry would be incomplete, as they dictate the mole ratios necessary for the reaction to occur correctly.

Without stoichiometry, it would be impossible to scale up reactions for practical use in industries or laboratories since the quantities would be estimations rather than precise measurements. This can lead to unreacted excesses or shortages, either of which can have costly or even dangerous implications.
Chemical Equations
Just like a sentence in language has a specific structure, a chemical equation communicates how substances interact, rearrange, and transform during chemical reactions using symbols and formulas. For instance, the equation 2H_2 + O_2 鈫� 2H_2O showcases reactants (hydrogen and oxygen gases) on the left and the product (water) on the right.

A well-balanced chemical equation adheres to the law of conservation of mass, meaning that atoms are neither created nor destroyed. To balance an equation, coefficients are strategically placed to ensure the same number of each type of atom appears on both sides of the equation. This balance is pivotal, as it reflects the reality that in a closed system, mass cannot just disappear or appear from nowhere.

Balancing Matters

The art of balancing chemical equations is a foundational skill in chemistry. It involves adjusting the coefficients in front of compounds until the number of atoms for each element is equal on both the reactant and product sides of the equation. Unbalanced equations can't accurately represent the reaction because they imply a change in mass, which would violate the conservation of mass.
Conservation of Mass
The principle known as the conservation of mass states that mass is neither created nor destroyed in an isolated system. In the context of chemistry, this rule informs us that during a chemical reaction, the total mass of the products must equal the total mass of the reactants.

Returning to our water-forming reaction, 2H_2 + O_2 鈫� 2H_2O, the mass of the hydrogen and the mass of the oxygen before the reaction occurs will be equal to the mass of the water produced. This law is not just a guideline; it is as fundamental to the rules governing chemical reactions as the laws of gravity to motion.

Practical Insights

This principle also has practical implications. For example, in industrial chemical processes, accurately calculating the amounts of starting materials needed, and predicting the quantities of products formed are crucial for economic and safety reasons. Understanding the conservation of mass helps ensure that these processes can be carried out efficiently and without waste.

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Most popular questions from this chapter

Lead(II) oxide is obtained by roasting galena, lead(II) sulfide, in air. The unbalanced equation is: $$\mathrm{PbS}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{PbO}(\mathrm{s})+\mathrm{SO}_{2}(\mathrm{g})$$ a. Balance the equation, and determine the theoretical yield of PbO if 200.0 g of PbS is heated. b. What is the percent yield if 170.0 g of PbO is obtained?

Challenge When copper wire is placed into a silver nitrate solution \(\left(\mathrm{AgNO}_{3}\right)\), silver crystals and copper(II) nitrate \(\left(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\right)\) solution form. a. Write the balanced chemical equation for the reaction. b. If a 20.0-g sample of copper is used, determine the theoretical yield of silver. c. If 60.0 g of silver is recovered from the reaction, determine the percent yield of the reaction.

Challenge For each of the following, balance the chemical equation; interpret the equation in terms of particles, moles, and mass; and show that the law of conservation of mass is observed. a) ____\(\mathrm{Na}(\mathrm{s})+\)____\(\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow\) ____\(\mathrm{NaOH}(\mathrm{aq})+\) ____\(\mathrm{H}_{2}(\mathrm{g})\) b) ____\(Z n(s)+\) ____\(\mathrm{HNO}_{3}(\mathrm{aq}) \rightarrow\) ____\(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+\) ____\(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

What information does a balanced equation provide?

When aluminum is mixed with iron(III) oxide, iron metal and aluminum oxide are produced, along with a large quantity of heat. What mole ratio would you use to determine moles of Fe if moles of Fe_ \(\mathrm{O}_{3}\) is known? \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})+\) heat
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