Domanda del libro di testo
(a) What is the length of the pencil in the following figure if the ruler reads in centimeters? How many significant figures are there in this measurement?
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Ch.1 - Introduction: Matter, Energy, and Measurement
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement146
- Ch.2 - Atoms, Molecules, and Ions200
- Ch.3 - Chemical Reactions and Reaction Stoichiometry176
- Ch.4 - Reactions in Aqueous Solution155
- Ch.5 - Thermochemistry126
- Ch.6 - Electronic Structure of Atoms131
- Ch.7 - Periodic Properties of the Elements126
- Ch.8 - Basic Concepts of Chemical Bonding123
- Ch.9 - Molecular Geometry and Bonding Theories143
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces91
- Ch.12 - Solids and Modern Materials122
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics174
- Ch.15 - Chemical Equilibrium101
- Ch.16 - Acid-Base Equilibria139
- Ch.17 - Additional Aspects of Aqueous Equilibria146
- Ch.18 - Chemistry of the Environment72
- Ch.19 - Chemical Thermodynamics129
- Ch.20 - Electrochemistry142
- Ch.21 - Nuclear Chemistry101
- Ch.22 - Chemistry of the Nonmetals68
- Ch.23 - Transition Metals and Coordination Chemistry66
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry10
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Non è quello che usi tu?Cambia libro di testo
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Brown 15th EditionCh.1 - Introduction: Matter, Energy, and MeasurementProblema 12
Brown 15th EditionCh.1 - Introduction: Matter, Energy, and MeasurementProblema 12Capitolo 1, Problema 12
Consider the jar of jelly beans in the photo. To get an estimate of the number of beans in the jar you weigh six beans and obtain masses of 3.15, 3.12, 2.98, 3.14, 3.02, and 3.09 g. Then you weigh the jar with all the beans in it, and obtain a mass of 2082 g. The empty jar has a mass of 653 g. Based on these data, estimate the number of beans in the jar. Justify the number of significant figures you use in your estimate.
Guida verificata passo dopo passo1
Calculate the average mass of a single jelly bean by adding the masses of the six beans and dividing by six: \( \text{Average mass} = \frac{3.15 + 3.12 + 2.98 + 3.14 + 3.02 + 3.09}{6} \).
Determine the total mass of the jelly beans by subtracting the mass of the empty jar from the mass of the jar with beans: \( \text{Total mass of beans} = 2082 \text{ g} - 653 \text{ g} \).
Estimate the number of beans in the jar by dividing the total mass of the beans by the average mass of a single bean: \( \text{Number of beans} = \frac{\text{Total mass of beans}}{\text{Average mass of a bean}} \).
Consider the significant figures: The average mass of a bean should be calculated to the same number of significant figures as the least precise measurement, which is two decimal places in this case.
The final estimate of the number of beans should be rounded to the appropriate number of significant figures based on the precision of the measurements used in the calculation.
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Mass and Average Calculation
To estimate the number of jelly beans, first calculate the average mass of the six beans weighed. This is done by summing the individual masses and dividing by the number of beans. The average mass provides a representative value that can be used to estimate the total number of beans in the jar based on the total mass of the beans.
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Percorso guidato
02:42
Average Rate Calculation Example
Total Mass Calculation
The total mass of the jelly beans can be determined by subtracting the mass of the empty jar from the mass of the jar filled with beans. This calculation gives the total mass of the jelly beans alone, which is essential for estimating the number of beans using the average mass calculated earlier.
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03:12Molar Mass Calculation Example
Significant Figures
Significant figures are important in scientific measurements as they convey the precision of the data. When performing calculations, the result should reflect the least number of significant figures from the measurements used. In this case, the average mass of the beans and the total mass of the jelly beans must be reported with the appropriate number of significant figures to ensure accuracy in the final estimate of the number of beans.
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Percorso guidato
01:09Significant Figures Example
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(a) How many significant figures should be reported for the volume of the metal bar shown here?
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