14.15 传播、传播和格雷厄姆法

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  传播、传播和格雷厄姆法

  

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  How do we know how fast a gas moves?
  ::我们怎么知道煤气移动的速度有多快?

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  We usually cannot see , so we need ways to detect their movements indirectly. The relative rates of diffusion of ammonia to hydrogen chloride can be observed in a simple . Cotton balls are soaked with solutions of ammonia and hydrogen chloride (hydrochloric acid) and attached to two different rubber stoppers. These are simultaneously plugged into either end of a long glass tube. The vapors of each travel down the tube at different rates. Where the vapors meet, they react to form ammonium chloride (NH ₄ Cl), a white solid that appears in the glass tube as a ring.
  ::通常我们看不到, 所以我们需要一些方法来间接检测它们的移动情况。 氨向氯化氢的相对扩散速度可以通过简单的方式观测到。 棉花球被浸泡在氨和氯化氢(氢氯酸)的溶液中, 并附在两种不同的橡胶阻截器上。 这些溶液同时被塞入一个长玻璃管的两端。 每根玻璃管的蒸气以不同的速度流过管。 当蒸气体相遇时, 它们反应形成氯化铵(NH4Cl), 一种白色的固体, 以玻璃管为环出现。

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  Graham’s Law
  ::格雷汉姆的法律

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  When a person opens a bottle of perfume in one corner of a large room, it doesn’t take very long for the scent to spread throughout the entire room. Molecules of the perfume evaporate and the vapor spreads out to fill the entire space. Diffusion is the tendency of molecules to move from an area of high to an area of low concentration until the concentration is uniform. While gases diffuse rather quickly, diffuse much more slowly. Solids essentially do not diffuse.
  ::当一个人在一个大房间的一个角落打开一瓶香水瓶时,气味会在整个房间里扩散不会花很长时间。 香水蒸发和蒸气的微粒会扩散以填满整个空间。 扩散是分子从高点向低浓度地区移动直到浓度一致的倾向。 虽然气体扩散速度相当快,但扩散速度要慢得多。 固体基本上不会扩散。

   

   

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  A related process to diffusion is the effusion . Effusion is the process of a confined gas escaping through a tiny hole in its container. Effusion can be observed by the fact that a helium-filled balloon will stop floating and sink to the floor after a day or so. This is because the helium gas effuses through tiny pores in the balloon. Both diffusion and effusion are related to the speed at which various gas molecules move. Gases that have a lower effuse and diffuse at a faster rate than gases that have a higher molar mass.
  ::与扩散相关的一个过程是渗出。渗出是一个封闭气体通过容器中一个小洞渗出的过程。渗出可以观察到一个事实,即一个装满氦的气球一天或一天后将停止漂浮并沉到地板上。这是因为氦气在气球中通过微孔发泡。扩散和渗出都与各种气体分子移动的速度有关。气体的磨损和扩散速度都比其摩尔质量较高的气体快。

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  Scottish chemist Thomas Graham (1805-1869) studied the rates of effusion and diffusion of gases. Graham’s law states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of the molar mass of the gas. Graham’s law can be understood by comparing two gases ( $\begin{align*}A\end{align*}$ and $\begin{align*}B\end{align*}$ ) at the same temperature , meaning the gases have the same . The kinetic energy of a moving object is given by the equation $\begin{align*}KE =\frac{1}{2}mv^2\end{align*}$ ,
  ::苏格兰化学家托马斯·格雷厄姆(Thomas Graham (1805-1869))研究了气体的分解和扩散速度。格雷厄姆的法律规定,气体的分解或扩散速度与气体摩尔质量的平方根成反比。格雷厄姆的法律可以通过在相同的温度上比较两种气体(A和B)来理解,这意味着气体具有相同的特性。移动物体的动能由方程式 KE=12mv2给出。

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  where  $\begin{align*}m\end{align*}$ is mass and  $\begin{align*}v\end{align*}$ is velocity. Setting the kinetic energies of the two gases equal to one another gives:
  ::m 是质量, v 是速度。 设定两种气体的电动能量 。

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  $$\begin{align*}\frac{1}{2}m_Av^2_A=\frac{1}{2}m_Bv^2_B\end{align*}$$
  ::12 mAvA2=12mB2

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  The equation can be rearranged to solve for the ratio of the velocity of gas  $\begin{align*}A\end{align*}$ to the velocity of gas  $\begin{align*}B\left(\frac{v_A}{v_B}\right)\end{align*}$ .
  ::该方程式可以重新排列,以解决气体A的速度与气体B(vAvB)的速度之比。

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  $$\begin{align*}\frac{v^2_A}{v^2_B}=\frac{m_B}{m_A} \text{ which becomes } \frac{v_A}{v_B}=\sqrt{\frac{m_B}{m_A}}\end{align*}$$
  ::vA2vB2=mBma, 成为 vAvB=mBA 。

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  For the purposes of comparing the rates of effusion or diffusion of two gases at the same temperature, the molar masses of each gas can be used in the equation for $\begin{align*}m\end{align*}$ .
  ::为了比较同一温度两种气体的分解或扩散速度,每种气体的摩尔质量可用于m方程。

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  Sample Problem: Graham’s Law
  ::抽样问题:格雷厄姆的法律

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  Calculate the ratio of diffusion rates of ammonia gas (NH ₃ ) to hydrogen chloride (HCl) at the same temperature and pressure .
  ::计算氨气(NH3)和氯化氢(HCl)在相同温度和压力下扩散率的比率。

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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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  • molar mass NH ₃ = 17.04 g/mol
    ::3 NH3 = 17.04克/摩尔
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  • molar mass HCl = 36.46 g/mol
    ::摩拉质量HCl = 36.46克/摩尔

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  Unknown
  ::未知

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  • velcoity ratio  $\begin{align*}\dfrac{v_{\text{NH}_3}}{v_{\text{HCl}}}\end{align*}$
    ::速度比率 vNH3vHCl

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  Substitute the molar masses of the gases into Graham’s law and solve for the ratio.
  ::以Graham的法律取代气体的摩尔含量,

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  Step 2: Solve.
  ::步骤2:解决。

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  $$\begin{align*}\frac{v_{NH_3}}{v_{HCl}}=\sqrt{\frac{36.46 \text{ g/mol}}{17.04 \text{ g/mol}}}=1.46\end{align*}$$
  ::vNH3vHCl=36.46克/摩尔17.04克/摩尔=1.46

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  The rate of diffusion of ammonia is 1.46 times faster than the rate of diffusion of hydrogen chloride.
  ::氨的传播速度比氯化氢的传播速度快1.46倍。

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

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  Since ammonia has a smaller molar mass than hydrogen chloride, the velocity of its molecules is greater and the velocity ratio is larger than 1.
  ::由于氨的摩尔质量小于氯化氢,其分子的速度更高,速度比大于1。

   

   

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  Summary
  ::摘要

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  • The processes of gas diffusion and effusion are described.
    ::介绍了气体扩散和渗漏的过程。
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  • Graham’s law relates the molecular mass of a gas to its rate of diffusion or effusion.
    ::Graham的法律将气体的分子质量与其扩散或分解速度联系起来。

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  Review
  ::回顾

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  1. Why can you smell food cooking when you are in the next room?
     ::为什么你能闻到食物烹饪的味道 当你在隔壁的房间?
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  2. Why does a helium-filled balloon gradually sink?
     ::为什么一个充气球会逐渐沉没?
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  3. What does temperature have to do with gas kinetic energies?
     ::温度和气体动能有什么关系?