课程： 10.2 摩尔和原子之间的转换

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选择节摩尔和原子之间的转换

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摩尔和原子之间的转换
Big numbers or little numbers?
::大数字还是小数字?

Do you hate to type subscripts and superscripts? Even with a good word-processing program, having to click on an icon to get a superscript and then remembering to click off after you type the number can be a real hassle. If we did not know about moles and just knew about numbers of atoms or molecules (those big numbers that require lots of superscripts), life would be much more complicated and we would make many more typing errors.
::您是否讨厌输入下标和上标 ? 即使有一个好的文字处理程序, 需要点击一个图标来获得上标, 然后记住在您键入后点击该数字会是一个真正的麻烦。如果我们不知道内鬼, 并且只是知道原子或分子的数量( 那些需要大量上标的大数字), 生命会更加复杂得多, 我们会做更多的打字错误。

Conversions Between Moles and Atoms
::摩尔和原子之间的转换

Conversions Between Moles and Number of Particles
::模块和粒子数量之间的转换

Using our unit conversion techniques, we can use the mole label to convert back and forth between the number of particles and moles.
::使用我们的单位转换技术, 我们可以使用摩尔标签来回转换粒子和摩尔的数量。

Sample Problem 1: Converting Number of Particles to Moles
::问题1:将粒子数量转换成模块

The carbon exists in two primary forms: graphite and diamond. How many moles of carbon atoms is 4.72 × 10 ²⁴ atoms of carbon?
::碳以两种基本形式存在:石墨和钻石。有多少碳原子的摩尔是4.72×1024碳原子?

Step 1: List the known quantities and plan the problem.
::第1步:列出已知数量并规划问题。

Known
::已知已知

number of C atoms = 4.72 × 10 ²⁴
::C原子数 = 4.72 × 1024

1 mole = 6.02 × 10 ²³ atoms
::1摩尔=6.02×1023原子

Unknown
::未知

4.72 × 10 ²⁴ = ? mol C
::4.72 × 1024 =? mol C

One conversion factor will allow us to convert from the number of C atoms to moles of C atoms.
::一个转换系数将使我们能够从C原子的数量转换为C原子的摩尔。

Step 2: Calculate.
::第2步:计算。

$\begin{aligned} 4.72 \times 10^{24} atoms C \times \frac{1 mol C}{6.02 \times 10^{23} atoms C} = 7.84 mol C \end{aligned}$
$\begin{align*}4.72 \times 10^{24}\ \text{atoms C} \times \frac{1 \ \text{mol C}}{6.02 \times 10^{23}\ \text{atoms C}}=7.84 \ \text{mol C}\end{align*}$
::4.72×1024 原子 Cx1 mol C6.02×1023 原子 C= 7.84 mol C

Step 3: Think about your result.
::步骤3:想想你的结果。

The given number of carbon atoms was greater than Avogadro’s number , so the number of moles of C atoms is greater than 1 mole. Since Avogadro’s number is a measured quantity with three , the result of the calculation is rounded to three significant figures.
::给定的碳原子数量大于Avogadro的数量,因此C原子的摩尔数量大于1摩尔。由于Avogadro的数量是一个测量数量,有3个,计算结果四舍五入为3个重要数字。

Suppose that you wanted to know how many hydrogen atoms were in a mole of water molecules. First, you would need to know the for water, which is H ₂ O. There are two atoms of hydrogen in each molecule of water. How many atoms of hydrogen would there be in two water molecules? There would be 2 × 2 = 4 hydrogen atoms. How about in a dozen? In that case a dozen is 12 so 12 × 2 = 24 hydrogen atoms in a dozen water molecules. To get the answers, (4 and 24) you had to multiply the given number of molecules by two atoms of hydrogen per molecule. So to find the number of hydrogen atoms in a mole of water molecules, the problem could be solved using conversion factors.
::假设你想知道水分子的分子中有多少氢原子。首先,你需要知道水中有多少氢原子, 也就是H2O。每个水分子中有两个氢原子。两个水分子中有多少氢原子? 12个氢原子中有多少氢原子? 12个原子中有多少氢原子? 12个原子中12个原子中24个氢原子中12个原子中12个原子中12个原子中12个原子中12个原子中24个氢原子中12个原子中12个原子中12个原子中12个原子中24个氢原子中12个原子中12个原子中24个氢原子中12个原子中12个原子中24个氢原子中有多少氢原子中12个原子中水分子中有多少氢原子中2个原子中2个分子中有多少氢分子中2个原子中有多少氢分子中有多少氢分子中有多少氢原子, 问题可以通过转换因素来解决。

$\begin{aligned} 1 mol H_{2} O \times \frac{6.02 \times 10^{23} molecules H_{2} O}{1 mol H_{2} O} \times \frac{2 atoms H}{1 molecule H_{2} O} = 1.20 \times 10^{24} atoms H \end{aligned}$
$\begin{align*}1 \ \text{mol}\ \text{H}_2\text{O} \times \frac{6.02 \times 10^{23}\ \text{molecules}\ \text{H}_2\text{O}}{1 \ \text{mol} \ \text{H}_2\text{O}} \times \frac{2 \ \text{atoms H}}{1 \ \text{molecule}\ \text{H}_2\text{O}}=1.20 \times 10^{24} \ \text{atoms H}\end{align*}$
::1 摩尔 H2O×6.02×1023分子 H2O1 摩尔 H2O×2原子 H1 分子 H2O= 1.20×1024 原子 H

The first conversion factor converts from moles of particles to the number of particles. The second conversion factor reflects the number of atoms contained within each molecule.
::第一个转换系数从粒子的摩尔转换成粒子的数量。第二个转换系数反映每个分子所含原子的数量。

Two water molecules contain 4 hydrogen atoms and 2 oxygen atoms. A mole of water molecules contains 2 moles of hydrogen atoms and 1 mole of oxygen atoms.
::两个水分子含有4个氢原子和2个氧原子,一个水分子的摩尔含有2个氢原子和1个氧原子的摩尔。

Sample Problem 2: Atoms, Molecules, and Moles
::问题2:原子、分子和摩尔斯

Sulfuric has the chemical formula H ₂ SO ₄ . A certain quantity of sulfuric acid contains 4.89 × 10 ²⁵ atoms of oxygen. How many moles of sulfuric acid is the sample?
::一定数量的硫酸含有4.89×1025原子的氧气,样本中有多少硫酸的摩尔?

Step 1: List the known quantities and plan the problem.
::第1步:列出已知数量并规划问题。

Known
::已知已知

4.89 × 10 ²⁵ = O atoms
::4.89 × 1025 = O原子

1 mole = 6.02 × 10 ²³ molecules H ₂ SO ₄
::1 摩尔= 6.02 × 1023 分子 H2SO4

Unknown
::未知

mol of H ₂ SO ₄ molecules
::H2SO4分子 mol

Two conversion factors will be used. First, convert atoms of oxygen to molecules of sulfuric acid. Then, convert molecules of sulfuric acid to moles of sulfuric acid.
::首先,将氧原子转换成硫酸分子,然后将硫酸分子转换成硫酸分子。

Step 2: Calculate.
::第2步:计算。

$\begin{aligned} 4.89 \times 10^{25} atoms O \times \frac{1 molecule H_{2} {SO}_{4}}{4 atoms O} \times \frac{1 mol H_{2} {SO}_{4}}{6.02 \times 10^{23} molecules H_{2} SO 4} = 20.3 mol H_{2} {SO}_{4} \end{aligned}$
$\begin{align*}4.89 \times 10^{25}\ \text{atoms O}\ \times \frac{1 \ \text{molecule}\ \text{H}_2\text{SO}_4}{4 \ \text{atoms O}} \times \frac{1 \ \text{mol}\ \text{H}_2\text{SO}_4}{6.02 \times 10^{23}\ \text{molecules}\ \text{H}_2\text{SO}4}=20.3 \ \text{mol}\ \text{H}_2\text{SO}_4\end{align*}$
::4.89×1025原子 O ×1分子 H2SO44原子 Ox1 mol H2SO46.02×1023分子 H2SO4=20.3 mol H2SO4

Step 3: Think about your result.
::步骤3:想想你的结果。

The original number of oxygen atoms was about 80 times larger than Avogadro’s number. Since each sulfuric acid molecule contains 4 oxygen atoms, there are about 20 moles of sulfuric acid molecules.
::最初的氧原子数量大约比Avogadro的数字高80倍。由于每个硫酸分子都含有4个氧原子,因此大约有20个硫酸分子的摩尔。

Summary
::摘要

Methods are described for conversions between moles, atoms, and molecules.
::说明了摩尔、原子和分子之间的转换方法。

Review
::回顾

What conversion factor would we need to convert moles of helium to atoms of helium?
::用什么转换系数来将的摩尔转换成的原子?

I want to convert atoms to moles. My friend tells me to multiply the number of atoms by 6.02 × 10 ²³ atoms/mole. Is my friend correct?
::我要将原子转换为内鬼。我的朋友让我将原子数乘以6.02×1023原子/摩尔。我的朋友是正确的吗 ?

Why do you need to know the formula for a molecule in order to calculate the number of moles of one of the atoms?
::为什么你需要知道分子的公式才能计算出一个原子的摩尔数量?

How many atoms of fluorine are in 5.6×10 ²² molecules of MgF ₂ ?
::在5.6×1022 分子中有多少氟原子是 MgF2 中的原子?

章节大纲

常规

摩尔和原子之间的转换

Big numbers or little numbers? ::大数字还是小数字?

Conversions Between Moles and Atoms ::摩尔和原子之间的转换

Conversions Between Moles and Number of Particles ::模块和粒子数量之间的转换

Sample Problem 1: Converting Number of Particles to Moles ::问题1:将粒子数量转换成模块

Sample Problem 2: Atoms, Molecules, and Moles ::问题2:原子、分子和摩尔斯

Summary ::摘要

Review ::回顾

Big numbers or little numbers?
::大数字还是小数字?

Conversions Between Moles and Atoms
::摩尔和原子之间的转换

Conversions Between Moles and Number of Particles
::模块和粒子数量之间的转换

Sample Problem 1: Converting Number of Particles to Moles
::问题1:将粒子数量转换成模块

Sample Problem 2: Atoms, Molecules, and Moles
::问题2:原子、分子和摩尔斯

Summary
::摘要

Review
::回顾