14.7 《阿沃加德罗法》

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• 选择节Avogadro法

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  Avogadro法

  

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  How much air do you put into a tire?
  ::你在轮胎里放多少空气?

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  A flat tire is not very useful. It does not cushion the rim of the wheel and creates a very uncomfortable ride. When air is added to the tire, the pressure increases as more molecules of are forced into the rigid tire. How much air should be put into a tire depends on the pressure rating for that tire. Too little pressure and the tire will not hold its shape. Too much pressure and the tire could burst.
  ::平板轮胎不是非常有用的。 它不会缓冲轮盘的边缘, 并造成非常不舒适的骑车。 当空气被添加到轮胎上时, 压力会随着更多的分子被强制进入硬质轮胎而增加。 多少空气应该放入轮胎取决于轮胎的压力等级。 压力太小, 轮胎不会保持形状。 太多的压力和轮胎可能爆裂。

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  Avogadro’s Law
  ::阿沃加德罗法

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  You have learned about Avogadro’s hypothesis : equal volumes of any gas at the same temperature and pressure contain the same number of molecules. It follows that the volume of a gas is directly proportional to the number of moles of gas present in the sample. Avogadro’s law states that the volume of a gas is directly proportional to the number of moles of gas when the temperature and pressure are held constant. The mathematical expression of Avogadro’s law is
  ::你已了解到Avogadro的假设:在相同的温度和压力下,任何气体在相同的温度和压力下都含有相同数量的分子。 由此推论,气体的量与样品中天然气的摩尔数量直接成正比。 Avogadro的法律规定,当温度和压力保持不变时,气体的量与气体的摩尔数量直接成正比。 Avogadro的法律的数学表达方式是:在温度和压力保持不变时,气体的量与气体的摩尔数量成正比。

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  $$\begin{align*}V=k \times n \quad \text{and} \quad \frac{V_1}{n_1}=\frac{V_2}{n_2}\end{align*}$$
  ::V=kxnandV1n1=V2n2

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  where  $\begin{align*}n\end{align*}$ is the number of moles of gas and  $\begin{align*}k\end{align*}$ is a constant. Avogadro’s law is in evidence whenever you blow up a balloon. The volume of the balloon increases as you add moles of gas to the balloon by blowing it up.
  ::在 n 处, 气和 k 的摩尔数量是一个常数。 Avogadro 的法律在每次炸毁气球时都是证据。 气球的量随着气球的爆炸而增加,气球的量随着气球的量的增加而增加。

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  If the container holding the gas is rigid rather than flexible, pressure can be substituted for volume in Avogadro’s law. Adding gas to a rigid container makes the pressure increase.
  ::如果持有气体的容器是硬质的而不是灵活的,那么根据Avogadro的法律,压力可以代替体积。 将气体添加到硬质容器会增加压力。

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  Sample Problem: Avogadro’s Law
  ::抽样问题:阿沃加德罗法

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  A balloon has been filled to a volume of 1.90 L with 0.0920 mol of helium gas. If 0.0210 mol of additional helium is added to the balloon while the temperature and pressure are held constant, what is the new volume of the balloon?
  ::气球以0.0920 毫升的气填充到1.90升的体积。如果在温度和压力保持不变的情况下将0.0210 毫升的额外的添加到气球中,气球的新体积是多少?

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

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  Known
  ::已知已知

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  • $\begin{align*}V_1=1.90 \text{ L}\end{align*}$
    ::V1=1.90升
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  • $\begin{align*}n_1=0.0920 \text{ mol}\end{align*}$
    ::n1=0.0920 摩尔
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  • $\begin{align*}n_2=0.0920+0.0210=0.1130 \text{ mol}\end{align*}$
    ::n2=0.0920+0.0210=0.1130摩尔

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  Unknown
  ::未知

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  • $\begin{align*}V_2=? \text{ L}\end{align*}$
    ::V2=L吗?

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  Note that the final number of moles has to be calculated by adding the original number of moles to the moles of added helium. Use Avogadro’s law to solve for the final volume.
  ::请注意, 最终的摩尔数必须计算方法是将最初的摩尔数加到添加的摩尔数中。 使用 Avogadro 的法律来解决最后的量 。

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  Step 2: Solve.
  ::步骤2:解决。

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  First, rearrange the equation algebraically to solve for $\begin{align*}V_2\end{align*}$ .
  ::首先,重新排列方程式代数以解析 V2 。

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  $$\begin{align*}V_2=\frac{V_1 \times n_2}{n_1}\end{align*}$$
  ::V2=V1xn2n1

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  Now substitute the known quantities into the equation and solve.
  ::现在将已知数量替换为方程式和解析 。

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  $$\begin{align*}V_2=\frac{1.90 \text{ L} \times 0.1130 \text{ mol}}{0.0920 \text{ mol}}=2.33 \text{ L}\end{align*}$$
  ::V2=1.90 Lx0.1130 mol0.0920 mol=2.33 L

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

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  Since a relatively small amount of additional helium was added to the balloon, its volume increases slightly.
  ::由于在气球中添加了相对较少量的增,其数量略有增加。

   

   

   

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  Summary
  ::摘要

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  • Calculations are shown for relationships between volume and number of moles of a gas.
    ::对气体的摩尔数量和数量之间的关系进行了计算。

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  Review
  ::回顾

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  1. What is held constant in the Avogadro’s Law relationship?
     ::在阿沃加德罗的法律关系中,什么是不变的?
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  2. What happens if you add gas to a rigid container?
     ::如果你把煤气加到硬质容器里会怎么样?
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  3. Why does a balloon expand when you add air to it?
     ::为什么气球在增加空气时会膨胀呢?