Book cover for Introductory Chemistry: An Active Learning Approach

Introductory Chemistry: An Active Learning Approach

Mark S. Cracolice, Edward I. Peters

ISBN #9781305079250

6th Edition

1,627 Questions

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9,334 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter emphasizes the importance of both qualitative understanding and quantitative analysis in chemistry. It discussed the necessity of accurate measurement through techniques such as scientific notation, conversion factors, and significant figures. Mastering these concepts enables precise calculation and effective problem-solving in chemical investigations, echoing Lavoisier’s legacy in measurement and scientific inquiry.

Learning Objectives

1

Explain the dual qualitative and quantitative nature of chemistry, emphasizing measurement and calculation.

2

Write numbers in scientific notation and convert them back to ordinary decimal form.

3

Perform arithmetic operations (addition, subtraction, multiplication, and division) with numbers expressed in scientific notation.

4

Apply conversion factors and metric units to solve quantitative chemistry problems.

5

Develop problem-solving skills essential for accurate scientific measurements and calculations.

Key Concepts

CONCEPT

DEFINITION

Scientific Notation

A method of writing very large or very small numbers in the form a × 10^b, where 1 ≤ |a| < 10 and b is an integer.

Conversion Factors

Ratios that express how many of one unit are equal to another unit, used to convert measurements between different systems or units.

Metric Units

Units of measurement in the metric system (e.g., meter, liter, gram) that provide a standardized method for measuring physical quantities.

Significant Figures

The digits in a number that carry meaningful information about its precision, including all non-zero digits and any zeros that are known with certainty.

Measurement Accuracy and Precision

Accuracy refers to how close a measured value is to the true value, while precision indicates the reproducibility of measurements.

Example Problems

Example 1

Write the following numbers in scientific notation: (a) 0.000322 (b) 6,030,000,000 (c) 0.00000000000619

Example 2

Write each of the following numbers in scientific notation: (a) 70,300 (b) 0.0231 (c) 0.000154 (d) 5,040

Example 3

Write the following numbers in ordinary decimal form: $$\text { (a) } 5.12 \times 10^{6}$$ $$\text { (b) } 8.40 \times 10^{-7}$$ $$\text { (c) } 1.92 \times 10^{21}$$

Example 4

Write the ordinary form of the following numbers: (a) $2.32 \times 10^{-2}$ (b) $9.27 \times 10^{4}$ (c) $2.54 \times 10^{3}$ (d) $8.96 \times 10^{-4}$

Example 5

Complete the following operations: a) $\left(7.87 \times 10^{4}\right)\left(9.26 \times 10^{-8}\right)=$ b) $\left(5.67 \times 10^{-6}\right)\left(9.05 \times 10^{-7}\right)=$ c) $(309)\left(9.64 \times 10^{6}\right)=$ d) $\left(4.07 \times 10^{3}\right)\left(8.04 \times 10^{-8}\right)\left(1.23 \times 10^{-2}\right)=$
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Step-by-Step Explanations

QUESTION

How do you convert 0.00000000000000000000000665 grams to scientific notation?

STEP-BY-STEP ANSWER:

Step 1: Identify the first non-zero digit in the number.
Step 2: Place the decimal point immediately after this digit to form the coefficient.
Step 3: Count the number of places the decimal has moved to the right to reach its original position.
Step 4: Express the number as the product of the coefficient and 10 raised to the power of the negative count.
Final Answer: 6.65 Ă— 10^-24 grams.

Scientific Notation Conversion (Decimal to Scientific)

QUESTION

How do you multiply (2.0 Ă— 10^3) by (3.0 Ă— 10^4) using scientific notation?

STEP-BY-STEP ANSWER:

Step 1: Multiply the coefficients: 2.0 Ă— 3.0 = 6.0.
Step 2: Add the exponents: 3 + 4 = 7.
Step 3: Combine the results to express in scientific notation.
Final Answer: 6.0 Ă— 10^7.

Arithmetic with Scientific Notation

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Common Mistakes

  • Incorrectly positioning the decimal point when converting a number to scientific notation.
  • Adding or subtracting exponents instead of multiplying when performing multiplication operations.
  • Overlooking or misapplying conversion factors between metric and USCS units.
  • Rounding numbers too early, which leads to loss of significant figures and decreased precision in calculations.