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Chapter 9: Problem 6

State the number of particles in each of the following: (a) \(1 \mathrm{~mol}\) of silicon atoms, Si (b) \(1 \mathrm{~mol}\) of silane molecules, \(\mathrm{SiH}_{4}\)

Short Answer

Expert verified
(a) \(6.022 \times 10^{23}\) silicon atoms; (b) \(6.022 \times 10^{23}\) silane molecules.

Step by step solution

01

Understanding Moles and Avogadro's Number

Avogadro's number is used to determine the amount of particles in one mole of a substance. It is approximately \(6.022 \times 10^{23}\). This number states how many atoms, molecules, or entities are present in one mole of any substance.
02

Determine the number of silicon atoms in 1 mol Si

Since 1 mole of any substance contains Avogadro's number of particles, and we are asked for 1 mole of silicon atoms, the number of silicon atoms is simply Avogadro's number. Therefore, there are \(6.022 \times 10^{23}\) silicon atoms in 1 mole of silicon.
03

Determine the number of silane molecules in 1 mol SiH4

Similarly, 1 mole of silane molecules, \(\mathrm{SiH_4}\), also contains Avogadro's number of these molecules. Therefore, there are \(6.022 \times 10^{23}\) silane molecules in 1 mole of silane.

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Key Concepts

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

Moles
The concept of a mole is fundamental to understanding chemistry. A mole is simply a unit used to express amounts of a chemical substance. It's similar to how a "dozen" represents 12 items, except "mole" stands for a very large number: approximately Avogadro's number, which is \( 6.022 \times 10^{23} \).
This number signifies how many atoms, molecules, or entities are in one mole of any substance. For example:
  • \(6.022 \times 10^{23}\) water molecules in one mole of water
  • \(6.022 \times 10^{23}\) carbon atoms in one mole of carbon
Therefore, understanding moles allows chemists to count and measure substances at an atomic level, using a system that aligns with the macroscopic world.
Silicon Atoms
Silicon is a widely used element in the technological world, especially in electronics. When discussing silicon atoms in the context of moles, remember that one mole of silicon atoms contains a number of atoms equivalent to Avogadro's number.
This means:
  • In 1 mole of silicon, there are \(6.022 \times 10^{23}\) silicon atoms.
  • Silicon, with its atomic number of 14, plays a crucial role in creating semiconductors.
Understanding how many silicon atoms are present in a given mole is vital in manufacturing processes and in fields like material science.
Silane Molecules
Silane is a chemical compound made up of silicon and hydrogen with the formula \(\mathrm{SiH_4}\). It's interesting because, just like other molecules, one mole of silane also contains Avogadro's number. This means:
  • 1 mole of silane equals \(6.022 \times 10^{23}\) silane molecules.
  • Each silane molecule consists of one silicon atom and four hydrogen atoms.
Silane is often used in the production of silicon-containing materials and is essential in the technology sector for its applications in creating high-purity silicon for semiconductors. Understanding how many silane molecules are in a mole helps manufacturers precisely control reactions and material properties.

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Most popular questions from this chapter

Calculate the number of moles containing each of the following: (a) \(1.00 \times 10^{22}\) atoms of manganese, \(\mathrm{Mn}\) (b) \(2.00 \times 10^{23}\) molecules of sulfur trioxide, \(\mathrm{SO}_{3}\) (c) \(3.00 \times 10^{24}\) formula units of manganese(II) sulfate, \(\mathrm{MnSO}_{4}\)

Refer to the periodic table and state the atomic mass (in amu) of one atom for each of the following metals: (a) lithium (b) titanium (c) gold (d) bismuth

State the molar mass for each of the following: (a) aluminum, Al (b) silicon, Si (c) oxygen, \(\mathrm{O}_{2}\) (d) sulfur, \(S_{8}\)

The volume occupied by each copper atom in a 1 -mole crystal is \(0.0118 \mathrm{nm}^{3}\). If the density of the copper crystal is \(8.92 \mathrm{~g} / \mathrm{cm}^{3},\) what is the experimental value of Avogadro's number?

Calculate the number of particles in each of the following: (a) 7.57 g platinum, \(P\) (b) 3.88 g ethane, \(C_{2} H_{6}\) (c) \(0.152 \mathrm{~g}\) aluminum chloride, \(\mathrm{AlCl}_{3}\)
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