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Without doing any detailed calculations (but using a periodic table to give atomic weights), rank the following samples in order of increasing numbers of atoms: \(0.5 \mathrm{~mol} \mathrm{BCl}_{3}\) molecules, \(197 \mathrm{~g}\) gold, \(6.0 \times 10^{23} \mathrm{CCl}_{4}\) molecules.

Short Answer

Expert verified
The order is: 197 g gold < 0.5 mol \(\text{BCl}_3\) < \(6.0 \times 10^{23} \text{CCl}_4\).

Step by step solution

01

Understand the Problem

We need to rank three different samples by the number of atoms they contain: \(0.5 \text{ mol} \text{ BCl}_3\) molecules, \(197 \text{ g}\) of gold, and \(6.0 \times 10^{23} \text{ CCl}_4\) molecules. To do this, we need to calculate the number of atoms in each sample.
02

Calculate Number of Atoms in \(0.5 \text{ mol} \text{ BCl}_3\)

One mole of \(\text{BCl}_3\) contains Avogadro's number of molecules, which is \(6.022 \times 10^{23}\). Since each molecule of \(\text{BCl}_3\) contains 4 atoms (1 B and 3 Cl), \(0.5 \text{ mol} \text{ BCl}_3\) will contain:\[0.5 \times 6.022 \times 10^{23} \times 4 \text{ atoms}\]
03

Calculate Number of Atoms in \(197 \text{ g}\) Gold

Gold has an atomic weight of approximately \(197 \text{ g/mol}\), which means \(197 \text{ g}\) of gold corresponds to \(1 \text{ mol}\). Each mole of gold has an Avogadro's number of atoms, which is \(6.022 \times 10^{23}\) atoms.
04

Calculate Number of Atoms in \(6.0 \times 10^{23} \text{ CCl}_4\) Molecules

Each molecule of \(\text{CCl}_4\) contains 5 atoms (1 C and 4 Cl). Therefore, \(6.0 \times 10^{23} \text{ CCl}_4\) molecules contain:\[6.0 \times 10^{23} \times 5 \text{ atoms}\]
05

Rank the Samples by Number of Atoms

To rank them, compare the calculated numbers:1. \(0.5 \text{ mol} \text{ BCl}_3\) has \((0.5 \times 6.022 \times 10^{23} \times 4 = 1.204 \times 10^{24})\) atoms.2. \(197 \text{ g}\) of gold, which is \(1 \text{ mol}\), has \(6.022 \times 10^{23}\) atoms.3. \(6.0 \times 10^{23} \text{ CCl}_4\) molecules have \(6.0 \times 10^{23} \times 5 = 3.0 \times 10^{24}\) atoms.Therefore, the order of increasing number of atoms is: \(197 \text{ g gold} < 0.5 \text{ mol } \text{BCl}_3 < 6.0 \times 10^{23} \text{ CCl}_4\).

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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 a fundamental constant in chemistry that helps us understand the scale of the atomic world. It is defined as the number of atoms, ions, or molecules in one mole of a substance, which is precisely \(6.022 \times 10^{23}\). This enormous number allows chemists to count particles at an atomic level by using observable measurements.

Consider it the bridge between the atomic and macroscopic worlds, making it possible to convert grams and moles into individual particles. For example, when you have one mole of any element, you know it contains \(6.022 \times 10^{23}\) atoms. This concept is crucial in stoichiometry, which involves calculating quantities in chemical reactions.
  • It relates the mass and energy of atoms to a tangible quantity.
  • Helps in understanding the atomic scale measurements such as atoms, molecules, and formula units.
  • Useful in many scientific calculations like determining gas volume at Standard Temperature and Pressure (STP).
Periodic Table
The periodic table is a powerful tool that organizes all known elements by their atomic number, electron configurations, and recurring chemical properties. It allows chemists to quickly find crucial information about elements, such as atomic weights and relationships between various elements. Reading along rows and columns, you can predict how elements will react chemically.

One key feature of the periodic table is that it helps you determine molar masses. For example, the atomic weight of gold is approximately 197 g/mol, which tells us that 197 grams of gold is one mole of gold, containing Avogadro's number of atoms.
  • Elements are arranged in order of increasing atomic number.
  • Provides information about electron configurations and valency.
  • Amazing tool for visualizing trends in element properties.
Molecules vs. Atoms
In chemistry, it is crucial to differentiate between molecules and atoms. These terms often come into play when discussing substances and their behaviors.

An atom is the smallest unit of an element, while a molecule is a chemical combination of two or more atoms. For instance, a molecule of \( \text{BCl}_3 \) contains one boron atom and three chlorine atoms, making up four atoms in total. On the other hand, a molecule of \( \text{CCl}_4 \) consists of one carbon atom and four chlorine atoms, totaling five atoms altogether.
  • Atoms are individual particles, while molecules are a set of bonded atoms.
  • Molecules determine the chemical properties of a substance, not just the elements they contain.
  • Different atoms in a molecule can influence the molecule's shape and reactivity.
This distinction between atoms and molecules allows chemists to predict reactions and properties of substances based on their molecular composition.

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Most popular questions from this chapter

Balance the following equations: (a) \(\mathrm{SiCl}_{4}(l)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Si}(\mathrm{OH})_{4}(s)+\mathrm{HCl}(a q)\) (b) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(l) \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (d) \(\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\)

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;\) (b) barium carbonate decomposes into barium oxide and carbon dioxide gas when heated; \((\mathbf{c})\) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l),\) is combusted in air; \((\mathbf{d})\) dimethylether, \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(g),\) is combusted in air.

A sample of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) contains \(1.250 \times 10^{21}\) carbon atoms. (a) How many atoms of hydrogen does it contain? (b) How many molecules of glucose does it contain? (c) How many moles of glucose does it contain? (d) What is the mass of this sample in grams?

Cinnamaldehyde is a compound that is responsible for the characteristic aroma of cinnamon. It contains \(81.79 \% \mathrm{C}\), \(6.10 \% \mathrm{H},\) and the remaining is oxygen. Its molar mass is \(132 \mathrm{~g} / \mathrm{mol}\). Determine its molecular formula.

Determine the empirical and molecular formulas of each of the following substances: (a) Ibuprofen, a headache remedy, contains \(75.69 \% \mathrm{C}\) \(8.80 \% \mathrm{H},\) and \(15.51 \% \mathrm{O}\) by mass and has a molar mass of \(206 \mathrm{~g} / \mathrm{mol}\). (b) Cadaverine, a foul-smelling substance produced by the action of bacteria on meat, contains \(58.55 \% \mathrm{C}\), \(13.81 \% \mathrm{H},\) and \(27.40 \% \mathrm{~N}\) by mass; its molar mass is \(102.2 \mathrm{~g} / \mathrm{mol}\) (c) Epinephrine (adrenaline), a hormone secreted into the bloodstream in times of danger or stress, contains \(59.0 \%\) C, \(7.1 \%\) H, \(26.2 \%\) O, and \(7.7 \%\) N by mass; its molar mass is about \(180 \mathrm{u}\).

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