通用天然气法

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Compressed gases provide vital fuels for industry and for homes and farms in rural areas.
::压缩气体为工业以及农村地区的住宅和农场提供了至关重要的燃料。

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Universal Gas Law
::通用天然气法

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The combined gas law , [Math Processing Error] $\begin{array}{r}PV\propto T\end{array}$ , is true for a particular sample of gas. If any gas is added or allowed to leak out, however, the relationship is lost. In order to get a relationship that is true for any sample of gas, it is necessary to incorporate a term for the amount of gas. From observations as simple as blowing up a balloon, it is clear that increasing the amount of gas increases the volume.
::合并天然气法,[马斯处理错误]PVT,适用于特定的天然气样本。但是,如果添加或允许泄漏任何气体,则关系就会消失。为了建立对任何天然气样本都属实的关系,必须包含一个气体数量的术语。从简单的观测来看,如炸毁气球,很明显,增加气体的数量会增加气量。

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Because different gases have different per molecule, including a term for mass of gas does not produce a consistent equation. If, however, we include a term expressing the number of moles of gas rather than its mass, we can produce a constant proportionality. A mole is a unit representing the number of atoms present. The letter  [Math Processing Error] $\begin{array}{r}n\end{array}$ is used to represent the moles of substance. Incorporating  [Math Processing Error] $\begin{array}{r}n\end{array}$ into the equation yields  [Math Processing Error] $\begin{array}{r}PV\propto nT\end{array}$ . If we insert a letter, [Math Processing Error] $\begin{array}{r}R\end{array}$ , to represent the constant of proportionality, we get the normal form of the universal gas law , [Math Processing Error] $\begin{array}{r}PV=nRT\end{array}$ .
::由于不同气体的分子不同, 包括气体质量的术语并不产生一个一致的方程式。 但是, 如果加入一个表达气体摩尔数而不是其质量的术语, 我们就可以产生一个不变的相称性。 摩尔是一个代表现有原子数的单位。 字母[ Math 处理错误] n 用来代表物质的摩尔。 将 [ Math 处理错误] PV\\nT 纳入方程式的输出 [ Math 处理错误] PVNT 。 如果我们插入一个 字母, [Math 处理错误] R 来代表相称性的常态, 我们就会得到通用气体法的正常形式, [Math 处理错误] PV=nRT 。

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The unit term for  [Math Processing Error] $\begin{array}{r}n\end{array}$ is always moles and   [Math Processing Error] $\begin{array}{r}T\end{array}$ is always in Kelvin. The units for pressure and volume, however, may vary. The value of  [Math Processing Error] $\begin{array}{r}R\end{array}$ depends on the units that are used for pressure and volume.
::[ Math 处理错误] n 的单位术语总是摩尔, [Math 处理错误] T 总是在 Kelvin 。但压力和体积的单位可能不同。 [Math 处理错误] R 的值取决于用于压力和体积的单位。

Values of the Universal Gas Law Constant, R

Pressure Units	Volume Units	Units for  [Math Processing Error] $\begin{array}{r}\underset{\_}{n}\end{array}$	Units for  [Math Processing Error] $\begin{array}{r}\underset{\_}{T}\end{array}$	Value of  [Math Processing Error] $\begin{array}{r}\underset{\_}{R}\end{array}$
atm	liters	moles	Kelvin	0.0821 L•atm/mol•K
atm	milliliters	moles	Kelvin	82.1 mL•atm/mol•K

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Since the product of (liters)(atm) can be converted to joules , we also have a value for  [Math Processing Error] $\begin{array}{r}R\end{array}$ where liters × atm have been converted to joules, [Math Processing Error] $\begin{array}{r}R=8.314\text{J/mol}\cdot \text{K}\end{array}$ .  The two common values of the universal gas law constant [Math Processing Error] $\begin{array}{r}R\end{array}$   are  [Math Processing Error] $\begin{array}{r}0.0821\text{L}\cdot \text{atm/mol}\cdot \text{K}\end{array}$ and [Math Processing Error] $\begin{array}{r}8.314\text{J/mol}\cdot \text{K}\end{array}$ .
::由于(liters(atm)的产物可以转换为焦耳,我们也有[Math处理错误]R的值,其中立方×atm已转换为焦耳,[Math处理错误]R=8.314 J/molK。通用气体法常数[Math处理错误]R的两个共同值是[Math处理错误]0.0821 Latm/molK和[Math处理错误]8.314 J/molK。

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Most universal gas law problems are calculated at STP. STP stands for standard and pressure,  which is the most commonly calculated temperature and pressure value. STP is defined as 1.00 atm and 0°C, or 273 K.
::大部分普遍气体法问题在STTP中计算。 STTP代表标准与压力,这是最常用的计算温度和压力值。 STTP的定义是1.00 原子和 0°C, 或 273 K。

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Examples
::实例

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Example 1  
::例1

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Determine the volume of 1.00 mol of any gas at STP.
::确定在STTP的任何气体的体积为1.00毫摩尔。

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First isolate V from PV=nRT. Then plug in known values and solve.
::首先从 PV=nRT 中分离 V。 然后插入已知值并解析 。

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[Math Processing Error] $$\begin{array}{r}V=\frac{nRT}{P}=\frac{(1.00\text{mol})(0.0821\text{L}\cdot \text{atm/mol}\cdot \text{K})(273\text{K})}{(1.00\text{atm})}=22.4\text{liters}\end{array}$$
::[马氏处理错误]V=nRTP=(1.00 毫升)(0.0821 Latm/mol}K)(273 K)(1.00 小时)=22.4升

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For any gas at STP, one mole has a volume of 22.4 liters. This can be an extremely convenient conversion factor .
::对于在STTP的任何气体,一个内鬼的体积为22.4升,这可以是一个极为方便的转换系数。

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Example 2  
::例2

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A sample of oxygen gas occupies 10.0 liters at STP.  How many moles of oxygen are in the container?
::氧气样品在STTP拥有10升氧气,容器内有多少氧分子?

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[Math Processing Error] $$\begin{array}{r}n=\frac{PV}{RT}=\frac{(1.00\text{atm})(10.0\text{L})}{(0.0821\text{L}\cdot \text{atm/mol}\cdot \text{K})(273\text{K})}=0.446\text{moles}\end{array}$$
::[马氏处理错误]n=PVRT=(1.00 atm)(1.00.0 L)(0.0821 Latm/mol}K)(273 K)=0.446 摩尔

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Use the PLIX Interactive below to change the volume and temperature of gas inside a piston and observe the how pressure, temperature and volume are related to each other in an ideal gas in a closed system :
::使用下面的PLIX互动来改变活塞内气体的体积和温度,并观察在封闭系统中理想气体中的压力、温度和体积如何相互关联:

 

 

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Summary
::摘要

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• The universal gas law is [Math Processing Error] $\begin{array}{r}PV=nRT\end{array}$ , where  [Math Processing Error] $\begin{array}{r}P\end{array}$ is pressure,  [Math Processing Error] $\begin{array}{r}V\end{array}$ is volume,  [Math Processing Error] $\begin{array}{r}n\end{array}$ is number of moles,  [Math Processing Error] $\begin{array}{r}R\end{array}$ is the universal gas law constant, and  [Math Processing Error] $\begin{array}{r}T\end{array}$ is the absolute temperature.
  ::通用天然气法是[马司处理错误]PV=nRT,其中[马司处理错误]P是压力,[马司处理错误]V是体积,[马司处理错误]n是摩尔数,[马司处理错误]R是通用天然气法常数,而[马司处理错误]T是绝对温度。
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• The value of  [Math Processing Error] $\begin{array}{r}R\end{array}$ varies depending on the units used for  [Math Processing Error] $\begin{array}{r}P\end{array}$ and [Math Processing Error] $\begin{array}{r}V\end{array}$ . Two common values are  [Math Processing Error] $\begin{array}{r}0.0821\text{L}\cdot \text{atm/mol}\cdot \text{K}\end{array}$ and [Math Processing Error] $\begin{array}{r}R=8.314\text{J/mol}\cdot \text{K}\end{array}$ .
  ::[ Math 处理错误] R 的值因 [ Math 处理错误] P 和 [ Math 处理错误] V 所使用的单位而异。 两个共同值是 [Math 处理错误] 0.0821 Láatm/ mol}K 和 [Math 处理错误] R=8.314 J/ mol}K。
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• STP is standard temperature and pressure; 273 K and 1.00 atm.
  ::保护受威胁人民协会是标准温度和压力;273 K和1.00 摄氏度。
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• One mole of a gas at STP has a volume of 22.4 liters.
  ::STTP的一个煤气分子有22.4升的体积。

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Review
::回顾

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1. The initial pressure in a helium gas cylinder is 30 atm.  After many balloons have been blown up, the pressure in the cylinder has decreased to 6 atm while the volume and temperature remain the same.  What fraction of the original amount of gas remains in the cylinder?
   ::氢气瓶的初始压力为30 吨。 许多气瓶被炸毁后,气瓶的压力已降至6 吨,而气瓶的体积和温度保持不变。 原气量中有多少部分还留在气瓶中?
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2. Calculate the volume of 8.88 mol of helium gas at 20.0°C and 1.19 atm pressure.
   ::计算在20.0°C和1.19 °C压力下8.88 气的体积。

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Explore More
::探索更多

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Use this resource to answer the questions that follow.
::使用此资源回答下面的问题 。

 

 

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1. Why is it important to have values for R in kPa, atm, and mmHg?
   ::为什么以 kPa、 atm 和 mmHg 表示 R 值很重要?
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2. Why do the units of R include pressure, temperature, volume, and moles?
   ::为什么R的单位包括压力、温度、体积和摩尔?