4.20 计算平均原子量

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  计算平均原子量

  

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  Have you ever tried to move a boulder?
  ::你有没有试过移动巨石?

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  You have a pile of rocks to move and need to decide what equipment you want to rent to move them.  If the rocks are fairly small, you can get a shovel to pick them up.  Larger rocks could be moved by hand, but big boulders will need some sort of mechanical scoop.  The amount of each kind of rock will also determine how much time you will need to get the job done.  Knowing the relative amounts of large, medium, and small rocks can be very useful in deciding how to approach the job.
  ::您有一堆石头可以移动, 并且需要决定您要租赁哪些设备来移动它们。 如果这些石头很小, 您可以得到一把铲子来捡起来。 更大的石头可以手工移动, 但大石头需要某种机械式的挖掘。 每种石头的数量也会决定您需要多长时间才能完成任务 。 了解大、 中、小石头的相对数量对于决定如何接近工作非常有用 。

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  Most occur naturally as a of two or more isotopes. Table shows the natural isotopes of several elements, along with the percent natural abundance of each.
  ::大多数是自然地作为两个或两个以上的同位素产生。表格显示了若干元素的自然同位素,以及每种元素的自然丰度百分比。

  Atomic Masses and Percent Abundances of Some Natural Isotopes

  Element	播放段落 (symbol) :符号)	播放段落 Percent natural ::自然百分比 播放段落 abundance ::丰度	播放段落 Atomic ::原子原子 播放段落 mass (amu) ::质量( AMu)	播放段落 Average ::平均平均数 播放段落 atomic mass (amu) ::原子质量( AMU)
  Hydrogen	播放段落 $\begin{align*}^{1}_{1}\text{H}\end{align*}$ ::11H 11H 播放段落 $\begin{align*}^{2}_{1}\text{H}\end{align*}$ ::12H 12H 播放段落 $\begin{align*}^{3}_{1}\text{H}\end{align*}$ ::13H 13H	99.985 0.015 播放段落 negligible ::微小	1.0078 2.0141 3.0160	1.0079
  Carbon	播放段落 $\begin{align*}^{12}_{6}\text{C}\end{align*}$ ::612C 612C 播放段落 $\begin{align*}^{13}_{6}\text{C}\end{align*}$ ::613C 613C 播放段落 $\begin{align*}^{14}_{6}\text{C}\end{align*}$ ::614C 614C	98.89 1.11 播放段落 trace ::微微	12.000 13.003 14.003	12.011
  Oxygen	播放段落 $\begin{align*}^{16}_{8}\text{O}\end{align*}$ ::816O 播放段落 $\begin{align*}^{17}_{8}\text{O}\end{align*}$ ::817O 播放段落 $\begin{align*}^{18}_{8}\text{O}\end{align*}$ ::818O	99.759 0.037 0.204	15.995 16.995 17.999	15.999
  Chlorine	播放段落 $\begin{align*}^{35}_{17}\text{Cl}\end{align*}$ ::1735Cl 播放段落 $\begin{align*}^{37}_{17}\text{Cl}\end{align*}$ ::1737Cll	75.77 24.23	34.969 36.966	35.453
  Copper	播放段落 $\begin{align*}^{63}_{29}\text{Cu}\end{align*}$ ::2963库 播放段落 $\begin{align*}^{65}_{29}\text{Cu}\end{align*}$ ::2965Cu	69.17 30.83	62.930 64.928	63.546

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  For some elements, one particular isotope predominates greatly over the other isotopes. Naturally occurring hydrogen is nearly all hydrogen-1 and naturally occurring oxygen is nearly all oxygen-16. For many other elements, however, more than one isotope may exist in more substantial quantities. Chlorine ( 17) is a yellowish-green toxic . About three quarters of all chlorine atoms have 18 neutrons, giving those atoms a of 35. About one quarter of all chlorine atoms have 20 neutrons, giving those atoms a mass number of 37. Were you to simply calculate the arithmetic average of the precise atomic masses , you would get 36.
  ::对于某些元素,一种特定的同位素大大高于其他同位素。自然产生的氢几乎全部是氢-1,自然产生的氧几乎全部是氧-16。然而,对于许多其他元素来说,一个以上的同位素可能存在数量更多。氯(17)是一种黄绿色毒性。大约四分之三的氯原子有18个中子,这些原子有35个,大约四分之一的氯原子有20个中子,这些原子有37个质量数。如果你简单地计算精确原子质量的算术平均数,你就会得到36个。

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  $\begin{align*}\frac{(34.969+36.966)}{2}=35.968 \ \text{amu}\end{align*}$
  :34.969+36.9662=35.968 amu)

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  Clearly the actual average atomic mass from the last column of the table is significantly lower. Why? We need to take into account the percent natural abundances of each isotope in order to calculate what is called the weighted average. The atomic mass of an element is the weighted average of the atomic masses of the naturally occurring isotopes of that element. The sample problem below demonstrates how to calculate the atomic mass of chlorine.
  ::显然,表格最后一列的实际平均原子质量要低得多。为什么?我们需要考虑每种同位素的自然丰度百分比,以便计算所谓的加权平均值。元素的原子质量是该元素自然产生的同位素原子质量的加权平均值。下面的样本问题说明了如何计算氯原子质量。

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  Sample Problem: Calculating Average Atomic Mass
  ::问题:计算平均原子量

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  Use the atomic masses of each of the two isotopes of chlorine along with their percent abundances to calculate the average atomic mass of chlorine.
  ::使用两种氯同位素的原子质量及其百分比丰度来计算平均原子的氯质量。

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  Step 1: List the known and unknown quantities and plan the problem.
  ::第1步:列出已知和未知的数量并规划问题。

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  Known
  ::已知已知

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  • chlorine-35: atomic mass = 34.969 amu and % abundance = 75.77%
    ::氯-35:原子质量=34.969 AMU和%丰度=75.77%
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  • chlorine-37: atomic mass = 36.966 amu and % abundance = 24.23%
    ::氯-37:原子质量 = 36.966 amu,丰度% = 24.23%

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  Unknown
  ::未知

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  • Average atomic mass of chlorine
    ::氯平均原子量

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  Change each percent abundance into decimal form by dividing by 100. Multiply this value by the atomic mass of that isotope. Add together for each isotope to get the average atomic mass.
  ::将每一百分比的丰度改变为小数点形式, 以100 乘以该同位素的原子质量乘以这个值。 将每个同位素加在一起, 以获得平均原子质量 。

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  Step 2: Calculate.
  ::第2步:计算。

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  $$\begin{array}{rlrl}& \text{chlorine-35}& & 0.7577\times 34.969=26.50\text{amu}\\ & \text{chlorine-37}& & 0.2423\times 36.966=8.957\text{amu}\\ & \text{average atomic mass}& & 26.50+8.957=35.45\text{amu}\end{array}$$

  $$\begin{align*}& \text{chlorine-35} && 0.7577 \times 34.969=26.50 \ \text{amu}\\ & \text{chlorine-37} && 0.2423 \times 36.966=8.957 \ \text{amu}\\ & \text{average atomic mass} && 26.50 + 8.957=35.45 \ \text{amu}\end{align*}$$
  ::350.7577×34.969=26.50 贵宾-370.2423×36.966=8.957AM平均原子质量26.50+8.957=35.45 AMU

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  Note: Applying significant figure rules results in the 35.45 amu result without excessive error . In one step:
  ::注:应用重要数字规则可得出35.45 amu结果,无过多误差。

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  $\begin{align*}(0.7577 \times 34.969)+(0.2423 \times 36.966)=35.45 \ \text{amu}\end{align*}$
  :0.7577x34.34.969+(0.2423x36.36.966)=35.45 amu

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

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  The calculated average atomic mass is closer to 35 than to 37 because a greater percentage of naturally occurring chlorine atoms have the mass number of 35. It agrees with the value from the Table .
  ::计算的平均原子质量接近35比37,因为较大比例的自然产生的氯原子质量数为35, 与表中的数值相同。

   

   

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  Summary
  ::摘要

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  • The atomic mass of an element is the weighted average of the atomic masses of the naturally occurring isotopes of that element.
    ::一个元素的原子质量是该元素自然产生的同位素原子质量的加权平均值。
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  • Calculations of atomic mass use the percent abundance of each isotope.
    ::原子质量的计算使用每种同位素的丰度百分比。

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  Review 
  ::回顾

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  1. Define atomic mass.
     ::确定原子质量。
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  2. What information do you need to calculate atomic mass for an element?
     ::您需要什么信息来计算元素的原子质量 ?
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  3. Calculate the atomic mass for carbon using the data provided in the table below.
     ::使用下表提供的数据计算碳原子质量。

  播放段落 Isotope ::同位素同位素同位素	播放段落 Atomic Mass ::原子原子质量	播放段落 Percent Abundance ::百分比丰度
  播放段落 carbon-12 ::碳-12	12.000000	98.90
  播放段落 carbon-13 ::碳- 13	13.003355	1.100