Complete the Following Dimensional Analysis Problem to the Correct Number of Significant Figures

Oct 13, 2025 by wbrum.org 114 views

Complete the Following Dimensional Analysis Problem to the Correct Number of Significant Figures

Understanding Dimensional Analysis

Dimensional analysis is a fundamental concept in chemistry that involves the use of mathematical operations to solve problems involving chemical reactions, stoichiometry, and other related topics. It is a powerful tool that helps chemists to predict the outcomes of chemical reactions, calculate the amounts of substances required, and determine the yields of products. In this article, we will focus on a specific dimensional analysis problem involving the reaction between hydrochloric acid (HCl) and potassium permanganate (KMnO4).

The Reaction Between Hydrochloric Acid and Potassium Permanganate

The reaction between hydrochloric acid (HCl) and potassium permanganate (KMnO4) is a well-known redox reaction that involves the transfer of electrons between the two substances. The balanced chemical equation for this reaction is:

2KMnO4 + 16HCl → 2MnCl2 + 8H2O + 5Cl2 + 2KCl

In this equation, 2 moles of potassium permanganate (KMnO4) react with 16 moles of hydrochloric acid (HCl) to produce 2 moles of manganese(II) chloride (MnCl2), 8 moles of water (H2O), 5 moles of chlorine gas (Cl2), and 2 moles of potassium chloride (KCl).

The Problem

Based on the balanced chemical equation above, we are asked to determine the number of moles of hydrochloric acid (HCl) required to react with 0.64 moles of potassium permanganate (KMnO4).

Step 1: Write Down the Balanced Chemical Equation

The balanced chemical equation for the reaction between hydrochloric acid (HCl) and potassium permanganate (KMnO4) is:

2KMnO4 + 16HCl → 2MnCl2 + 8H2O + 5Cl2 + 2KCl

Step 2: Identify the Mole Ratio

From the balanced chemical equation, we can see that 2 moles of potassium permanganate (KMnO4) react with 16 moles of hydrochloric acid (HCl). Therefore, the mole ratio of potassium permanganate (KMnO4) to hydrochloric acid (HCl) is 2:16 or 1:8.

Step 3: Calculate the Number of Moles of Hydrochloric Acid Required

We are given that 0.64 moles of potassium permanganate (KMnO4) are available. Using the mole ratio of 1:8, we can calculate the number of moles of hydrochloric acid (HCl) required to react with 0.64 moles of potassium permanganate (KMnO4) as follows:

Number of moles of HCl required = (Number of moles of KMnO4 available) x (Mole ratio of HCl to KMnO4) = 0.64 moles x (16 moles of HCl / 2 moles of KMnO4) = 0.64 moles x 8 = 5.12 moles

Step 4: Determine the Number of Significant Figures

The number of significant figures in the answer depends on the number of significant figures in the given values. In this case, the number of moles of potassium permanganate (KMnO4) is given as 0.64 moles, which has 2 significant figures. Therefore, the number of significant figures in the answer should also be 2.

Conclusion

Based on the balanced chemical equation and the mole ratio of potassium permanganate (KMnO4) to hydrochloric acid (HCl), we have calculated that 5.12 moles of hydrochloric acid (HCl) are required to react with 0.64 moles of potassium permanganate (KMnO4). The number of significant figures in the answer is 2, which is consistent with the number of significant figures in the given values.

Key Takeaways

Dimensional analysis is a powerful tool in chemistry that helps chemists to predict the outcomes of chemical reactions, calculate the amounts of substances required, and determine the yields of products.
The balanced chemical equation and the mole ratio of reactants are essential in dimensional analysis problems.
The number of significant figures in the answer depends on the number of significant figures in the given values.

Common Mistakes to Avoid

Failing to write down the balanced chemical equation.
Not identifying the mole ratio of reactants.
Not calculating the number of moles of reactants required.
Not determining the number of significant figures in the answer.

Real-World Applications

Dimensional analysis has numerous real-world applications in chemistry, including:

Predicting the outcomes of chemical reactions.
Calculating the amounts of substances required for chemical reactions.
Determining the yields of products in chemical reactions.
Designing chemical processes and equipment.

Conclusion

In conclusion, dimensional analysis is a fundamental concept in chemistry that involves the use of mathematical operations to solve problems involving chemical reactions, stoichiometry, and other related topics. By understanding the balanced chemical equation and the mole ratio of reactants, chemists can predict the outcomes of chemical reactions, calculate the amounts of substances required, and determine the yields of products. The number of significant figures in the answer depends on the number of significant figures in the given values. By following the steps outlined in this article, chemists can avoid common mistakes and apply dimensional analysis to real-world problems in chemistry.
Dimensional Analysis Q&A

Frequently Asked Questions

Q: What is dimensional analysis?

A: Dimensional analysis is a mathematical technique used to solve problems involving chemical reactions, stoichiometry, and other related topics. It involves the use of mathematical operations to predict the outcomes of chemical reactions, calculate the amounts of substances required, and determine the yields of products.

Q: What is the importance of dimensional analysis in chemistry?

A: Dimensional analysis is a crucial tool in chemistry that helps chemists to predict the outcomes of chemical reactions, calculate the amounts of substances required, and determine the yields of products. It is essential in designing chemical processes and equipment, and in understanding the behavior of chemical systems.

Q: What are the steps involved in dimensional analysis?

A: The steps involved in dimensional analysis are:

Write down the balanced chemical equation.
Identify the mole ratio of reactants.
Calculate the number of moles of reactants required.
Determine the number of significant figures in the answer.

Q: How do I determine the number of significant figures in the answer?

A: The number of significant figures in the answer depends on the number of significant figures in the given values. If the given values have 2 significant figures, the answer should also have 2 significant figures.

Q: What are some common mistakes to avoid in dimensional analysis?

A: Some common mistakes to avoid in dimensional analysis include:

Failing to write down the balanced chemical equation.
Not identifying the mole ratio of reactants.
Not calculating the number of moles of reactants required.
Not determining the number of significant figures in the answer.

Q: How do I apply dimensional analysis to real-world problems in chemistry?

A: Dimensional analysis can be applied to real-world problems in chemistry by following the steps outlined above. Chemists can use dimensional analysis to predict the outcomes of chemical reactions, calculate the amounts of substances required, and determine the yields of products.

Q: What are some real-world applications of dimensional analysis in chemistry?

A: Some real-world applications of dimensional analysis in chemistry include:

Predicting the outcomes of chemical reactions.
Calculating the amounts of substances required for chemical reactions.
Determining the yields of products in chemical reactions.
Designing chemical processes and equipment.

Q: Can dimensional analysis be used to solve problems involving multiple reactants?

A: Yes, dimensional analysis can be used to solve problems involving multiple reactants. The steps involved in dimensional analysis remain the same, but the mole ratio of reactants must be calculated based on the balanced chemical equation.

Q: Can dimensional analysis be used to solve problems involving multiple products?

A: Yes, dimensional analysis can be used to solve problems involving multiple products. The steps involved in dimensional analysis remain the same, but the mole ratio of products must be calculated based on the balanced chemical equation.

Conclusion

Additional Resources

For further information on dimensional analysis, please refer to the following resources:

Chemistry textbooks and online resources.
Online tutorials and videos.
Chemistry courses and workshops.

Key Takeaways

Dimensional analysis is a fundamental concept in chemistry that involves the use of mathematical operations to solve problems involving chemical reactions, stoichiometry, and other related topics.
The balanced chemical equation and the mole ratio of reactants are essential in dimensional analysis problems.
The number of significant figures in the answer depends on the number of significant figures in the given values.
Dimensional analysis can be applied to real-world problems in chemistry by following the steps outlined above.