Textbook Question
A sample that weighs 107.75 g is a mixture of 30% helium atoms and 70% krypton atoms. How many particles are present in the sample?
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Ch.3 - Mass Relationships in Chemical Reactions
McMurry8th EditionChemistryISBN: 9781292336145
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Table of contents
- Ch.1 - Chemical Tools: Experimentation & Measurement143
- Ch.2 - Atoms, Molecules & Ions134
- Ch.3 - Mass Relationships in Chemical Reactions149
- Ch.4 - Reactions in Aqueous Solution157
- Ch.5 - Periodicity & Electronic Structure of Atoms92
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory73
- Ch.7 - Covalent Bonding and Electron-Dot Structures47
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure51
- Ch.9 - Thermochemistry: Chemical Energy104
- Ch.10 - Gases: Their Properties & Behavior138
- Ch.11 - Liquids & Phase Changes43
- Ch.12 - Solids and Solid-State Materials56
- Ch.13 - Solutions & Their Properties98
- Ch.14 - Chemical Kinetics79
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Aqueous Equilibria: Acids & Bases94
- Ch.17 - Applications of Aqueous Equilibria125
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium66
- Ch.19 - Electrochemistry130
- Ch.20 - Nuclear Chemistry73
- Ch.21 - Transition Elements and Coordination Chemistry122
- Ch.22 - The Main Group Elements155
- Ch.23 - Organic and Biological Chemistry43
Chapter 3, Problem 56
An average cup of coffee contains about 125 mg of caffeine, C8H10N4O2. How many moles of caffeine are in a cup? How many molecules of caffeine?
Verified step by step guidance1
Calculate the molar mass of caffeine, C_8H_{10}N_4O_2, by adding the atomic masses of all the atoms in the formula.
Convert the mass of caffeine in the coffee cup from milligrams to grams by dividing by 1000.
Use the formula: number of moles = mass (g) / molar mass (g/mol) to find the number of moles of caffeine.
Use Avogadro's number, 6.022 \(\times\) 10^{23} molecules/mol, to convert the number of moles of caffeine to the number of molecules.
Multiply the number of moles by Avogadro's number to find the total number of caffeine molecules in the cup.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Moles and Molar Mass
A mole is a unit in chemistry that represents 6.022 x 10^23 entities, such as atoms or molecules. The molar mass of a substance, measured in grams per mole (g/mol), is the mass of one mole of that substance. For caffeine (C8H10N4O2), the molar mass can be calculated by summing the atomic masses of its constituent elements, which is essential for converting grams to moles.
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Avogadro's Number
Avogadro's number, approximately 6.022 x 10^23, is the number of particles in one mole of a substance. This constant allows chemists to relate the mass of a substance to the number of molecules it contains. In the context of caffeine, once the number of moles is determined, Avogadro's number can be used to calculate the total number of caffeine molecules in a cup of coffee.
Dimensional Analysis
Dimensional analysis is a mathematical technique used to convert units from one system to another. In chemistry, it is often employed to relate mass, moles, and number of particles. By using conversion factors, such as molar mass and Avogadro's number, one can systematically convert the mass of caffeine in a cup of coffee to moles and then to the number of molecules.
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