Course: 14.8 理想天然气法

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理想天然气法

A yellow and gray gas cylinder labeled with hazard symbols for ammonia.

What chemical reactions require ammonia?
::什么化学反应需要氨?

There are a number of that require ammonia. In order to carry out the reaction efficiently, we need to know how much ammonia we have for stoichiometric purposes. Using laws, we can determine the number of moles present in the tank if we know the volume , temperature , and pressure of the system .
::为了高效地进行反应,我们需要知道我们有多少氨用于测量声学目的。根据法律,如果我们知道这个系统的数量、温度和压力,我们可以确定罐中存在多少摩尔。

Ideal Gas Law
::理想天然气法

The shows that the pressure of a gas is inversely proportional to volume and directly proportional to temperature. Avogadro’s law shows that volume or pressure is directly proportional to the number of moles of gas. Putting these together leaves us with the following equation:
::这表明气体的压力与体积成反比,直接与温度成正比。 Avogadro的法律显示,气的体积或压力与气的摩尔数量成正比。把这些组合起来,我们就可以得出以下公式:

\begin{aligned} \frac{P_{1} \times V_{1}}{T_{1} \times n_{1}} = \frac{P_{2} \times V_{2}}{T_{2} \times n_{2}} \end{aligned}

::P1xV1T1xn1 = P2xV2T2xn2

As with the other gas laws, we can also say that $\begin{aligned} \frac{(P \times V)}{(T \times n)} \end{aligned}$ is equal to a constant. The constant can be evaluated provided that the gas being described is considered to be ideal.
::与其他气体法一样,我们也可以说(PxV)(Txn)等于常数。只要所描述的气体被认为是理想的,就可以对常数进行评估。

The ideal gas law is a single equation which relates the pressure, volume, temperature, and number of moles of an ideal gas . If we substitute in the variable $\begin{aligned} R \end{aligned}$ for the constant, the equation becomes:
::理想气体法是一个单一的方程式,它涉及到理想气体的压力、体积、温度和摩尔数量。如果我们用变量R代替常数,则公式变成:

\begin{aligned} \frac{P \times V}{T \times n} = R \end{aligned}

::PxVTxn=R (R)

The ideal gas law is conventionally rearranged to look this way, with the multiplication signs omitted:
::理想的天然气法通常被重新排列为这样看, 乘法符号省略了:

\begin{aligned} P V = n R T \end{aligned}

::PV=nRT

The variable $\begin{aligned} R \end{aligned}$ in the equation is called the ideal gas constant .
::方程中的变量R称为理想气体常数。

Evaluating the Ideal Gas Constant
::评估理想气体常量

The value of $\begin{aligned} R \end{aligned}$ , the ideal gas constant, depends on the units chosen for pressure, temperature, and volume in the ideal gas equation. It is necessary to use Kelvin for the temperature and it is conventional to use the SI unit of liters for the volume. However, pressure is commonly measured in one of three units: kPa, atm, or mmHg. Therefore, $\begin{aligned} R \end{aligned}$ can have three different values.
::R 值是理想气体常量,值取决于理想气体方程式中为压力、温度和体积选择的单位。温度需要使用Kelvin, 量使用SI 升数单位是常规的。但是, 压力通常在三个单位中的一个单位中测量: kPa、 atm 或 mmHg。因此, R 可以有三个不同的值。

We will demonstrate how $\begin{aligned} R \end{aligned}$ is calculated when the pressure is measured in kPa. Recall that the volume of 1.00 mol of any gas at STP is measured to be 22.414 L. We can substitute 101.325 kPa for pressure, 22.414 L for volume, and 273.15 K for temperature into the ideal gas equation and solve for $\begin{aligned} R \end{aligned}$ .
::我们将会证明在用千帕测量压力时如何计算R。回顾在STTP测量到的任何气体的体积为1.00毫升为22.414L。我们可以用101.325千帕代替压力,用22.414升代替体积,用273.15K代替温度,进入理想气体方程式和R溶液中。

\begin{aligned} R = \frac{P V}{n T} = \frac{101.325 kPa \times 22.414 L}{1.000 mol \times 273.15 K} = 8.314 kPa \cdot L/K \cdot mol \end{aligned}

::R=PVnT=101.325 kPax22.414 L1.000 mol×273.15 K=8.314 kPaL/Kmol

This is the value of $\begin{aligned} R \end{aligned}$ that is to be used in the ideal gas equation when the pressure is given in kPa. Table shows a summary of this and the other possible values of $\begin{aligned} R \end{aligned}$ . It is important to choose the correct value of $\begin{aligned} R \end{aligned}$ to use for a given problem.
::这是在千帕给出压力时用于理想气体方程式的 R 值。表显示此值和其他R 可能值的汇总。选择 R 的正确值对于特定问题很重要。

Values of the Ideal Gas Constant
Unit of $\begin{aligned} P \end{aligned}$	Unit of $\begin{aligned} V \end{aligned}$	Unit of $\begin{aligned} n \end{aligned}$	Unit of $\begin{aligned} T \end{aligned}$	Value and unit of $\begin{aligned} R \end{aligned}$
kPa	L	mol	K	$\begin{aligned} 8.314 J/K \cdot mol \end{aligned}$
atm	L	mol	K	$\begin{aligned} 0.08206 L \cdot atm/K \cdot mol \end{aligned}$
mmHg	L	mol	K	$\begin{aligned} 62.36 L \cdot mmHg/K \cdot mol \end{aligned}$

Notice that the unit for $\begin{aligned} R \end{aligned}$ when the pressure is in kPa has been changed to J/K • mol. A kilopascal multiplied by a liter is equal to the SI unit for energy , a joule (J).
::请注意,当压力在千帕中时,R的单位已改为 J/K / mol。千帕斯卡乘以一升等于 SI 的能量单位,即焦耳(J)。

Sample Problem: Ideal Gas Law
::问题:理想天然气法

What volume is occupied by 3.760 g of oxygen gas at a pressure of 88.4 kPa and a temperature of 19°C? Assume the oxygen is ideal.
::3.760克氧气在88.4千帕的压力和19摄氏度的温度下被3.760克氧气占用的体积是多少?假设氧气是理想的。

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

Known
::已知已知

$\begin{aligned} P = 88.4 kPa \end{aligned}$
::P=88.4千帕

$\begin{aligned} T = 19^{\circ} C = 292 K \end{aligned}$
::T=19°C=292K

$\begin{aligned} mass O_{2} = 3.760 g \end{aligned}$
::质量O2=3.760克

$\begin{aligned} O_{2} = 32.00 g/mol \end{aligned}$
::O2=32.00克/摩尔

$\begin{aligned} R = 8.314 J/K \cdot mol \end{aligned}$
::R=8.314 J/Kmol

Unknown
::未知

$\begin{aligned} V = ? L \end{aligned}$
::V=? L=L=L=L=L=L=L=Y=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L=L

In order to use the ideal gas law, the number of moles of O ₂ "> $\begin{aligned} (n) \end{aligned}$ must be found from the given mass and the . Then, use $\begin{aligned} P V = n R T \end{aligned}$ to solve for the volume of oxygen.
::为了使用理想气体法,必须从给定质量和。然后,使用PV=nRT 来解决氧气量问题。

Step 2: Solve .
::步骤2:解决。

\begin{aligned} 3.760 g \times \frac{1 mol O_{2}}{32.00 g O_{2}} = 0.1175 mol O_{2} \end{aligned}

::3.760克×1摩尔 O232.00克 O2=0.1175摩尔 O2

Rearrange the ideal gas law and solve for $\begin{aligned} V \end{aligned}$ .
::重新排列理想的天然气法并解决V。

\begin{aligned} V = \frac{n R T}{P} = \frac{0.1175 mol \times 8.314 J/K \cdot mol \times 292 K}{88.4 kPa} = 3.23 L O_{2} \end{aligned}

::V=nRTP=0.1175 molx8.314 J/Kmolx292 K88.4 kPa=3.23 L O2

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

The number of moles of oxygen is far less than one mole, so the volume should be fairly small compared to molar volume (22.4 L/mol) since the pressure and temperature are reasonably close to standard. The result has three because of the values for $\begin{aligned} T \end{aligned}$ and $\begin{aligned} P \end{aligned}$ . Since a joule (J) = kPa • L, the units cancel correctly, leaving a volume in liters.
::氧的摩尔数远远少于1摩尔,因此,与摩尔体积(22.4升/摩尔)相比,其体积应相当小,因为压力和温度相当接近标准。其结果有3个,因为T和P的值。由于焦耳(J)=kPa = kPa = 升,单位取消正确,在升数中留下一个体积。

Ever wonder why soda goes flat? Explore the ideal gas law in action inside a soda bottle in this simulation:
::在模拟中探索一个苏打水瓶内最理想的气体法:

Summary
::摘要

The ideal gas constant is calculated.
::计算出理想气体常数。

An example of calculations using the ideal gas law is shown.
::展示了使用理想气体法进行计算的例子。

Review
::回顾

Which value of $\begin{aligned} R \end{aligned}$ will you use if the pressure is given in atm?
::如果压力以原子表示, 你会使用哪个 R 值 ?

You are doing a calculation where the pressure is given in mm Hg. You select 8.314 J/K • mol as your value for $\begin{aligned} R \end{aligned}$ . Will you get a correct answer?
::您正在计算以毫米汞给出的压力。您选择了8. 314 J/ K / 摩尔作为 R 的值。您是否能得到正确的答案 ?

How would you check that you have chosen the correct value of $\begin{aligned} R \end{aligned}$ for your problem?
::您如何确定您选择 R 正确值来解决您的问题 ?

Section outline

General

理想天然气法

What chemical reactions require ammonia? ::什么化学反应需要氨?

Ideal Gas Law ::理想天然气法

Evaluating the Ideal Gas Constant ::评估理想气体常量

Sample Problem: Ideal Gas Law ::问题:理想天然气法

Summary ::摘要