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Chapter 7: Problem 4

Calculate each of the following: a. number of \(\mathrm{O}\) atoms in 0.0180 moles of dry ice b. number of \(\mathrm{K}\) atoms in \(14.5 \mathrm{moles}\) of \(\mathrm{K}_{2} \mathrm{CO}_{3}\) c. moles of \(\mathrm{O}\) in \(8.60 \times 10^{21}\) molecules of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) d. moles of \(\mathrm{C}_{6} \mathrm{H}_{6}\) in \(6.90 \times 10^{23}\) molecules of \(\mathrm{C}_{6} \mathrm{H}_{6}\)

Short Answer

Expert verified
a. \(2.17 \times 10^{22} \) O atoms; b. \(1.75 \times 10^{25} \) K atoms; c. \(5.71 \times 10^{-3} \) moles O; d. \(1.15 \) moles \(\text{C}_6\text{H}_6\)

Step by step solution

01

Calculate number of \textbf{O} atoms in 0.0180 moles of dry ice (CO\textbf{2})

First, note that each molecule of CO\textbf{2} contains 2 O atoms. Use Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol) to find the number of molecules in 0.0180 moles of CO\textbf{2}. Then multiply the number of molecules by 2 to determine the number of O atoms.\[ \text{Molecules of CO\textbf{2}} = 0.0180 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \] \[ \text{Number of O atoms} = 2 \times (\text{Number of molecules of CO\textbf{2}}) \]
02

Calculate number of \textbf{K} atoms in 14.5 moles of K\textbf{2}CO\textbf{3}

Each molecule of K\textbf{2}CO\textbf{3} contains 2 K atoms. Use Avogadro's number to find the number of molecules in 14.5 moles of K\textbf{2}CO\textbf{3}. Then multiply the number of molecules by 2 to determine the number of K atoms.\[ \text{Molecules of K\textbf{2}CO\textbf{3}} = 14.5 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \] \[ \text{Number of K atoms} = 2 \times (\text{Number of molecules of K\textbf{2}CO\textbf{3}}) \]
03

Calculate moles of \textbf{O} in 8.60 \times 10^{21} molecules of H\textbf{2}SO\textbf{4}

Each molecule of H\textbf{2}SO\textbf{4} contains 4 O atoms. To find the moles of O atoms, first convert the total number of molecules to moles using Avogadro's number. Then multiply by the number of O atoms per molecule.\[ \text{Moles of H\textbf{2}SO\textbf{4}} = \frac{8.60 \times 10^{21}}{6.022 \times 10^{23}} \] \[ \text{Moles of O} = (\text{Moles of H\textbf{2}SO\textbf{4}}) \times 4 \]
04

Calculate moles of \textbf{C}\textsubscript{6}\textbf{H}\textsubscript{6} in 6.90 \times 10^{23} molecules of \textbf{C}\textsubscript{6}\textbf{H}\textsubscript{6}

Use Avogadro's number to convert the total number of molecules (6.90 \times 10^{23}) to moles.\[ \text{Moles of } \textbf{C}\textsubscript{6}\textbf{H}\textsubscript{6} = \frac{6.90 \times 10^{23}}{6.022 \times 10^{23}} \]

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Key Concepts

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

Avogadro's Number
Avogadro's number is one of the fundamental constants of chemistry. It represents the number of atoms or molecules in one mole of a substance. This number is approximately \( 6.022 \times 10^{23} \). By knowing Avogadro's number, we can easily convert between the number of particles (atoms, molecules) and moles.

For example, if we want to find out how many molecules are present in 0.0180 moles of CO\textsubscript{2}, we use the following calculation:

\[ \text{Molecules of CO}_2 = 0.0180 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} = 1.084 \times 10^{22} \text{ molecules} \]

Understanding this conversion is key in many chemistry problems and applications.
Molecular Composition
Molecular composition refers to the types and numbers of atoms that make up a molecule. For instance, a molecule of CO\textsubscript{2} has 1 carbon atom and 2 oxygen atoms.

Let's apply this to a problem. If we have 0.0180 moles of CO\textsubscript{2}, each molecule contains 2 oxygen atoms. So, the total number of oxygen atoms can be calculated as follows:

\[ \text{Number of O atoms} = 2 \times \text{Number of molecules of CO}_2 = 2 \times 1.084 \times 10^{22} = 2.168 \times 10^{22} \text{ O atoms} \]

By understanding molecular composition, we can determine the number of each type of atom in a given amount of substance.
Chemical Formula
A chemical formula represents the composition of a molecule. For example, K\textsubscript{2}CO\textsubscript{3} consists of 2 potassium (K) atoms, 1 carbon (C) atom, and 3 oxygen (O) atoms.

This helps in determining the total number of specific atoms in a given number of moles. For instance, for 14.5 moles of K\textsubscript{2}CO\textsubscript{3}, the total number of K atoms would be calculated as:

\[ \text{Number of K atoms} = 2 \times (14.5 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol}) = 1.748 \times 10^{25} \text{ K atoms} \]

Knowing the chemical formula is crucial in stoichiometry and various chemical calculations.
Stoichiometry
Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. It allows us to predict the amounts of substances consumed and produced in a given reaction.

For example, if we need to find the moles of oxygen atoms in 8.60 脳 10\textsuperscript{21} molecules of H\textsubscript{2}SO\textsubscript{4}, we can use stoichiometric relationships:

First, convert molecules to moles of H\textsubscript{2}SO\textsubscript{4}:

\[ \text{Moles of H}_2\text{SO}_4 = \frac{8.60 \times 10^{21}}{6.022 \times 10^{23}} \]

Then, multiply by the number of oxygen atoms per molecule:

\[ \text{Moles of O} = (\text{Moles of H}_2 \text{SO}_4) \times 4 \]

By understanding stoichiometry, we can handle various problems related to amounts of substances in chemical reactions effectively.

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Most popular questions from this chapter

Nitrogen gas reacts with hydrogen gas to produce ammonia. $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ a. If you have \(3.64 \mathrm{~g}\) of \(\mathrm{H}_{2}\), how many grams of \(\mathrm{NH}_{3}\) can be produced? b. How many grams of \(\mathrm{H}_{2}\) are needed to react with \(2.80 \mathrm{~g}\) of \(\mathrm{N}_{2} ?\) c. How many grams of \(\mathrm{NH}_{3}\) can be produced from \(12.0 \mathrm{~g}\) of \(\mathrm{H}_{2} ?\)

Ibuprofen, an anti-inflammatory drug in Advil, has the formula \(\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2} .(7.1,7.2,7.3)\) a. What is the molar mass of ibuprofen? b. How many grams of ibuprofen are in 0.525 mole? c. How many moles of \(\mathrm{C}\) are in \(12.0 \mathrm{~g}\) of ibuprofen? d. How many moles of ibuprofen contain \(1.22 \times 10^{23}\) atoms of C?

Classify each of the following as exothermic or endothermic: a. The energy level of the products is lower than that of the reactants. b. In the body, the synthesis of proteins requires energy. c. A reaction absorbs \(125 \mathrm{~kJ}\).

Classify each of the following as exothermic or endothermic: a. \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \stackrel{\Delta}{\longrightarrow} 3 \mathrm{C} \mathrm{O}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)+2220 \mathrm{~kJ}\) b. \(2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NaCl}(s)+819 \mathrm{~kJ}\) c. \(\mathrm{PCl}_{5}(g)+67 \mathrm{~kJ} \longrightarrow \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\)

During heavy exercise and workouts, lactic acid, \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3}\), accumulates in the muscles where it can cause pain and soreness. (7.1,7.2) a. How many molecules are in 0.500 mole of lactic acid? b. How many atoms of \(\mathrm{C}\) are in 1.50 moles of lactic acid? c. How many moles of lactic acid contain \(4.5 \times 10^{24}\) atoms of \(\mathrm{O} ?\) d. What is the molar mass of lactic acid?
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