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Chapter 6: Problem 6

Can the coefficients in a balanced chemical equation be fractions? Explain.

Short Answer

Expert verified
In a balanced chemical equation, coefficients cannot be fractions because it would imply a partial or fractional number of molecules or moles involved, which is inconsistent with the fundamental principles of stoichiometry. Coefficients are whole numbers to accurately represent and maintain the stoichiometric relationships between reactants and products, as dictated by the Law of Conservation of Mass.

Step by step solution

01

Understand Balanced Chemical Equations

A chemical equation represents a chemical reaction using chemical symbols for the reactants and products, with their respective coefficients. A balanced chemical equation has the same number of atoms for each element on both sides of the equation, which obeys the Law of Conservation of Mass that states that matter cannot be created or destroyed in a chemical reaction.
02

The Role of Coefficients in a Chemical Equation

Coefficients are the numbers placed before the chemical symbols or formulas in a chemical equation. They represent the stoichiometric relationships between the reactants and products. Coefficients are used to balance the atoms' number for each element on both sides of the equation.
03

Analyzing the Possibility of Fractions as Coefficients

When balancing a chemical equation, coefficients are adjusted to make sure the number of atoms for each element is the same on both sides. As we are looking for whole number quantities of molecules or moles, it is essential to use whole number coefficients to maintain the stoichiometric relationships between reactants and products.
04

Conclusion

In a balanced chemical equation, coefficients cannot be fractions. Using fractions as coefficients would imply that there's a partial or fractional number of molecules or moles involved, which goes against the fundamental principles of stoichiometry. Chemical equations represent the real-world chemical reactions happening at a molecular level; therefore, integer coefficients are essential to accurately represent and maintain the stoichiometric relationships between reactants and products.

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Key Concepts

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

Coefficients in Chemical Equations
Coefficients in chemical equations play a crucial role in defining the stoichiometric relationships between the reactants and products. When writing a chemical equation, the coefficients are the numbers placed in front of the chemical symbols or formulas. These numbers indicate the proportion of molecules or moles involved in the reaction.

It is important to note that coefficients must be whole numbers. This is because chemical reactions occur in discrete units of atoms and molecules. Fractions would imply splitting these indivisible particles, which is physically impossible.
  • Coefficients help balance the equation by ensuring equal numbers of each type of atom on both sides.
  • They convey the idea of ratios in chemical reactions, maintaining the integrity of the equation.
  • Adjusting coefficients is the key step in balancing equations accurately.
Stoichiometry
Stoichiometry is the study of the quantitative relationships in chemical reactions, based on the balanced chemical equation. It involves using the coefficients in the chemical equation to calculate the amounts of reactants needed or products formed in a reaction.

Understanding stoichiometry is essential for predicting reaction yields and determining the proportions of compounds involved:
  • The coefficients serve as conversion factors between moles of reactant and product substances.
  • This makes it possible to assess the precise amount of a reactant needed to produce a desired quantity of product.
  • Stoichiometry can also help identify the limiting reactant, which determines the maximum yield of the reaction.
Knowing how to apply stoichiometric principles is fundamental for anyone engaging with chemical reactions, from laboratory scientists to industrial engineers.
Law of Conservation of Mass
The law of conservation of mass is a foundational principle in chemistry, declaring that mass is neither created nor destroyed in a chemical reaction. This law directly influences the way chemical equations must be balanced.

Balance in a chemical equation is achieved through the use of coefficients, ensuring that the mass of reactants equals the mass of products. Here's how the law of conservation of mass is maintained in practice:
  • All atoms present in the reactants must be accounted for in the products.
  • Each side of the equation has the same number of each type of atom.
  • This conservation ensures the correct stoichiometry for the equation.
This fundamental law underscores the idea that during chemical reactions, although the substances involved may change, the total quantity of matter remains constant.

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Most popular questions from this chapter

Which of the following correctly describes the balanced chemical equation given below? There may be more than one true statement. If a statement is incorrect, explain why it is incorrect. $$ 4 \mathrm{Al}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3} $$ a. For every 4 atoms of aluminum that react with 6 atoms of oxygen, 2 molecules of aluminum oxide are produced. b. For every 4 moles of aluminum that reacts with 3 moles of oxygen, 2 moles of aluminum (III) oxide is produced. c. For every 4 grams of aluminum that reacts with 3 grams of oxygen, 2 grams of aluminum oxide is produced.

How is the balancing of chemical equations related to the law of conservation of mass?

Which of the following correctly balances the chemical equation given below? There may be more than one correct balanced equation. If a balanced equation is incorrect, explain why it is incorrect. $$\mathrm{CaO}+\mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}$$ a. \(\mathrm{CaO}_{2}+3 \mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}\) b. \(2 \mathrm{CaO}+5 \mathrm{C} \rightarrow 2 \mathrm{CaC}_{2}+\mathrm{CO}_{2}\) c. \(\mathrm{CaO}+2 ^{1/2} \mathrm{C} \rightarrow \mathrm{CaC}_{2}+1 / 2 \mathrm{CO}_{2}\)d. \(4 \mathrm{CaO}+10 \mathrm{C} \rightarrow 4 \mathrm{CaC}_{2}+2 \mathrm{CO}_{2}\)

Given the equation for the reaction: \(\mathrm{N}_{2}+\mathrm{H}_{2} \rightarrow \mathrm{NH}_{3}\) draw a molecular diagram that represents the reaction (make sure it is balanced).

Consider the generic chemical equation aA \(+\mathrm{bB} \rightarrow\) \(\mathrm{cC}+\mathrm{dD}\) (where a, b, \(\mathrm{c},\) and \(\mathrm{d}\) represent coefficients for the chemicals \(A, B, C,\) and \(D,\) respectively). a. How many possible values are there for "c"? Explain your answer. b. How many possible values are there for "c/d"? Explain your answer.
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