3.11 密度

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  密度

  

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  How do logs stay afloat in water?
  ::原木如何在水中漂浮?

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  After trees are cut, logging companies often move these materials down a river to a sawmill where they can be shaped into building materials or other products.  The logs float on the water because they are less dense than the water they are in.  Knowledge of density is important in the characterization and separation of materials.  Information about density allows us to make predictions about the behavior of matter.
  ::砍伐树木后,伐木公司往往将这些原料从河流下移到锯木厂,形成成建筑材料或其他产品。原木浮在水上,因为它们比水密度低。对密度的了解在材料的定性和分离中很重要。关于密度的信息使我们能够预测物质的行为。

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  Density
  ::密度

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  A golf ball and a table tennis ball are about the same size. However, the golf ball is much heavier than the table tennis ball. Now imagine a similar size ball made out of lead. That would be very heavy indeed! What are we comparing? By comparing the mass of an object relative to its size, we are studying a property called density. Density is the ratio of the mass of an object to its volume .
  ::高尔夫球和桌球的大小大致相同。 但是, 高尔夫球比桌网球要重得多。 现在想象一下一个由铅制成的类似大小球。 这的确非常沉重 ! 我们比较了什么? 通过比较一个对象的质量与其大小, 我们正在研究一个叫做密度的属性。 密度是对象质量与其体积的比例 。

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  $$\begin{array}{r}\text{Density}=\frac{\text{mass}}{\text{volume}}\end{array}$$

  
  ::密度=质量量

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  Density is an intensive property , meaning that it does not depend on the amount of material present in the sample. Water has a density of 1.0 g/mL. That density is the same whether you have a small glass of water or a swimming pool full of water. Density is a property that is constant for the particular identity of the matter being studied.
  ::密度是一种密集的特性,意味着它不取决于样品中物质的数量,水的密度为1.0克/毫升。无论你是否有小杯水或充斥着水的游泳池,密度是一样的。密度是一种特性,对于所研究的事项的特定特性来说是不变的。

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  The SI units of density are kilograms per cubic meter (kg/m ³ ), since the kg and the m are the SI units for mass and length respectively. In everyday usage in a laboratory, this unit is awkwardly large. Most solids and have densities that are conveniently expressed in grams per cubic centimeter (g/cm ³ ). Since a cubic centimeter is equal to a milliliter, density units can also be expressed as g/mL. are much less dense than solids and liquids, so their densities are often reported in g/L. Densities of some common substances at 20°C are listed in  Table
  ::SI密度单位为每立方米公斤(公斤/立方米),因为公斤和米分别为质量和长度的SI单位,在实验室的日常使用中,这个单位的密度为奇观,大多数固体和密度以每立方厘米克表示(克/立方厘米3),由于立方厘米等于毫升,密度单位也可以以g/毫升表示,比固体和液体的密度要低得多,因此其密度通常以克/升报告。 表中列出了20°C时某些常见物质的密度。

  Densities of Some Common Substances

  Liquids and Solids	Density at 20°C (g/ml)	Gases	Density at 20°C (g/L)
  Ethanol	0.79	Hydrogen	0.084
  Ice (0°C)	0.917	Helium	0.166
  Corn oil	0.922	Air	1.20
  Water	0.998	Oxygen	1.33
  Water (4°C)	1.000	Carbon dioxide	1.83
  Corn syrup	1.36	Radon	9.23
  Aluminum	2.70
  Copper	8.92
  Lead	11.35
  Mercury	13.6
  Gold	19.3

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  Since most materials expand as temperature increases, the density of a substance is temperature dependent and usually decreases as temperature increases.
  ::由于大多数材料随着温度的上升而膨胀,一种物质的密度取决于温度,通常随着温度的上升而下降。

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  You know that ice floats in water and it can be seen from the table that ice is less dense. Alternatively, corn syrup, being denser, would sink if placed into water.
  ::你知道,冰在水中漂浮,从表上可以看到,冰的密度不那么高。 或者,玉米糖浆密度越大,如果被放入水中,就会沉没。

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  Sample Problem: Density Calculations
  ::抽样问题:密度计算

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  An 18.2 g sample of zinc metal has a volume of 2.55 cm ³ . Calculate the density of zinc.
  ::18.2克锌金属样本的体积为2.55厘米,计算锌的密度。

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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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  • mass = 18.2 g
    ::质量=18.2克
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  • volume = 2.55 cm ³
    ::体积= 2.55厘米3

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  Unknown
  ::未知

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  • density = ? g/cm ³
    ::密度=? g/cm3

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  Use the equation for density, $\begin{array}{r}D=\frac{m}{V}\end{array}$ , to solve the problem.
  ::使用密度的方程式D=mV来解决问题。

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  Step 2: Calculate
  ::第2步:计算

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  $\begin{array}{r}D=\frac{m}{V}=\frac{18.2\text{g}}{2.55{\text{cm}}^3}=7.14\text{g}/{\text{cm}}^3\end{array}$
  ::D=mV=18.2 g2.55 cm3=7.14 g/cm3

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

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  If 1 cm ³ of zinc has a mass of about 7 grams, then 2 and a half cm ³ will have a mass about 2 and a half times as great. are expected to have a density greater than that of water and zinc’s density falls within the range of the other metals listed above
  ::如果1厘米3的锌的重量约7克,那么2个半厘米3的重量大约为2倍半。 预计其密度将大于水的密度,而锌的密度则属于上述其他金属的范围。

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  Since density values are known for many substances, density can be used to determine an unknown mass or an unknown volume. will be used to ensure that units cancel appropriately.
  ::由于已知许多物质的密度值,密度可用于确定未知质量或未知体积。 密度将用于确保单位适当取消。

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  Sample Problem: Using Density to Determine Mass and Volume
  ::抽样问题:使用密度确定质量和数量

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  1. What is the mass of 2.49 cm ³ of aluminum?
     ::2.49厘米的铝质量是多少?
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  2. What is the volume of 50.0 g of aluminum?
     ::50.0克铝的体积是多少?

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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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  • density = 2.70 g/cm ³
    ::密度=2.70克/立方厘米
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  • 1. volume = 2.49 cm ³
    ::1. 体积=2.49厘米3
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  • 2. mass = 50.0 g
    ::2. 质量=50.0克

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  Unknown
  ::未知

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  • 1. mass = ? g
    ::1. 质量=? g
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  • 2. volume = ? cm ³
    ::2. 体积=? cm3

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  Use the equation for density, $\begin{array}{r}D=\frac{m}{V}\end{array}$ , and dimensional analysis to solve each problem.
  ::使用密度的方程式、 D=mV 和 尺寸分析来解决每个问题 。

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  Step 2: Calculate
  ::第2步:计算

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  1. $\begin{array}{r}2.49{\text{cm}}^3\times \frac{2.70\text{g}}{1{\text{cm}}^3}=6.72\text{g}\end{array}$
     ::2.49厘米3×2.70克1厘米3=6.72克
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  2. $\begin{array}{r}50.0\text{g}\times \frac{1{\text{cm}}^3}{2.70\text{g}}=18.5{\text{cm}}^3\end{array}$
     ::50.0克×1立方厘米32.70克=18.5立方厘米

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  In problem 1, the mass is equal to the density multiplied by the volume. In problem 2, the volume is equal to the mass divided by the density.
  ::在问题1中,质量等于密度乘以体积。在问题2中,质量等于质量除以密度。

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

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  Because a mass of 1 cm ³ of aluminum is 2.70 g, the mass of about 2.5 cm ³ should be about 2.5 times larger. The 50 g of aluminum is substantially more than its density, so that amount should occupy a relatively large volume.
  ::由于1厘米3的铝质量为2.70克,约2.5厘米3的重量应大于2.5倍左右。50克的铝比其密度高得多,因此,其含量应占较大量。

    

   

   

   

   

   

   

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  Go fishing and explore the variables that affect density in this simulation: 
  ::前往钓鱼并探索此模拟中影响密度的变量 :

   

   

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  Summary
  ::摘要

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  • Density is the ratio of the mass of an object to its volume.
    ::密度是物体质量与体积之比。
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  • Gases are less dense than either solids or liquids
    ::气体密度小于固体或液体。
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  • Both liquid and solid materials can have a variety of densities
    ::液体和固体材料的密度可能不同
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  • For liquids and gases, the temperature will affect the density to some extent.
    ::对于液体和气体,温度将在某种程度上影响密度。

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  Review
  ::回顾

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  1. Define “density.”
     ::“密度”的定义是“密度”。
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  2. Are gases more or less dense that liquids or solids at room temperature?
     ::在室温下液体或固体的气体密度是多少还是多少?
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  3. How does temperature affect the density of a material?
     ::温度如何影响材料的密度?
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  4. A certain liquid sample has a volume of 14.7 mL and a mass of 22.8 grams. Calculate the density.
     ::某种液体样本的体积为14.7毫升,质量为22.8克。计算密度。
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  5. A material with a density of 2.7 grams/mL occupies 35.6 mL. How many grams of the material are there?
     ::密度为2.7克/毫升的材料占35.6毫升。 有多少克材料?
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  6. A certain material has a density of 19.3 g/mL. What is the material?
     ::某种材料的密度为19.3克/毫升。