Course: 14.3 Boyle法 | The Way To Learn

Section outline

Select section General

Collapse Expand
General

Collapse all Expand all
- Select activity 新闻通告
  
  新闻通告 Forum

Boyle法

How important is it to check the weather?
::检查天气有多重要?

Each day, hundreds of weather balloons are launched. Made of a synthetic rubber and carrying a box of instruments, the helium-filled balloon rises up into the sky. As it gains altitude, the becomes less and the balloon expands. At some point the balloon bursts due to the expansion, the instruments drop (aided by a parachute) to be retrieved and studied for information about the weather.
::每天有数百个天气气球被发射。由合成橡胶制成,并携带一箱仪器,由氦填充的气球升入天空。随着高度升高,气球变小,气球膨胀。在某些时候,气球由于膨胀而喷发,仪器(由降落伞助助推 ) 的落落(由降落伞助推 ) , 用于检索和研究天气信息。

Boyle’s Law
::Boyle法

Robert Boyle (1627-1691), an English chemist, is widely considered to be one of the founders of the modern experimental science of chemistry . He discovered that doubling the pressure of an enclosed sample of while keeping its temperature constant caused the volume of the gas to be reduced by half. Boyle’s law states that the volume of a given mass of gas varies inversely with the pressure when the temperature is kept constant. An inverse relationship is described in this way. As one variable increases in value, the other variable decreases.
::罗伯特·博伊勒(Robert Boyle,英国化学家,1627-1691年)被广泛认为是现代化学实验科学的创始人之一。他发现,在保持温度常数的同时,将封闭样本的压力增加一倍,导致气体的体积减半。博伊尔的法律规定,特定气体的体积与温度保持恒定时的压力的体积有反差。以这种方式描述了一种反比关系。另一种变数随着价值的变数增加而下降。

Physically, what is happening? The gas molecules are moving and are a certain distance apart from one another. An increase in pressure pushes the molecules closer together, reducing the volume. If the pressure is decreased, the gases are free to move about in a larger volume.
::物理上, 正在发生什么? 气分子在移动, 并且彼此之间有一定的距离。压力的增加会拉近分子的距离, 从而降低其体积。如果压力降低, 气体就可以在更大的体积中自由移动。

Mathematically, Boyle’s law can be expressed by the equation:
::Boyle的法律在数学上可以用下列等式来表达:

\begin{aligned} P \times V = k \end{aligned}

::PxV=k (k)

The $\begin{aligned} k \end{aligned}$ is a constant for a given sample of gas and depends only on the mass of the gas and the temperature. Table shows pressure and volume data for a set amount of gas at a constant temperature. The third column represents the value of the constant $\begin{aligned} (k) \end{aligned}$ for this data and is always equal to the pressure multiplied by the volume. As one of the variables changes, the other changes in such a way that the product of $\begin{aligned} P \times V \end{aligned}$ always remains the same. In this particular case, that constant is 500 atm · ml.
::k 是特定气体样本的常数, 仅取决于气体质量和温度。表格显示在恒定温度下一组气体的压力和体积数据。第三列代表该数据中的常数(k)值, 并且始终等于压力乘以体积。作为变量之一, 其它变化使PxV的产物始终保持不变。在此特定情况下, 该常数为500 AM / 毫升。

Pressure-Volume Data
Pressure (atm)	Volume (mL)	$\begin{aligned} P \times V = k (atm \cdot mL) \end{aligned}$
0.5	1000	500
0.625	800	500
1.0	500	500
2.0	250	500
5.0	100	500
8.0	62.5	500
10.0	50	500

A graph of the data in the table further illustrates the inverse relationship nature of Boyle’s Law (see Figure ). Volume is plotted on the $\begin{aligned} x \end{aligned}$ -axis, with the corresponding pressure on the $\begin{aligned} y \end{aligned}$ -axis.
::表中的数据图表进一步说明了Boyle法的反关系性质(见图 )。卷用x轴绘制,对y轴施加相应的压力。

Boyle’s Law can be used to compare changing conditions for a gas. We use $\begin{aligned} P_{1} \end{aligned}$ and $\begin{aligned} V_{1} \end{aligned}$ to stand for the initial pressure and initial volume of a gas. After a change has been made, $\begin{aligned} P_{2} \end{aligned}$ and $\begin{aligned} V_{2} \end{aligned}$ stand for the final pressure and volume. The mathematical relationship of Boyle’s Law becomes:
::Boyle法可以用来比较气体的不断变化的条件。我们用P1和V1代表气体的初始压力和初始体积。改变后,P2和V2代表最终压力和体积。 Boyle法的数学关系是:

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

::P1xV1=P2xV2

This equation can be used to calculate any one of the four quantities if the other three are known.
::如果已知其他三个数量,本方程式可用于计算四个数量中的任何一个。

Sample Problem: Boyle’s Law
::抽样问题:博伊勒法

A sample of oxygen gas has a volume of 425 mL when the pressure is equal to 387 kPa. The gas is allowed to expand into a 1.75 L container. Calculate the new pressure of the gas.
::当压力等于387千帕时,氧气样本的体积为425毫升。允许气体膨胀成1.75升容器。计算气体的新压力。

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

$\begin{aligned} P_{1} = 387 kPa \end{aligned}$
::P1=387千帕

$\begin{aligned} V_{1} = 425 mL \end{aligned}$
::V1=425毫升

$\begin{aligned} V_{2} = 1.75 L = 1750 mL \end{aligned}$
::V2=1.75 L=1750毫升

Unknown
::未知

$\begin{aligned} P_{2} = ? kPa \end{aligned}$
::P2=? kPa(千帕)

Use Boyle’s Law to solve for the unknown pressure $\begin{aligned} (P_{2}) \end{aligned}$ . It is important that the two volumes ( $\begin{aligned} V_{1} \end{aligned}$ and $\begin{aligned} V_{2} \end{aligned}$ ) are expressed in the same units, so $\begin{aligned} V_{2} \end{aligned}$ has been converted to mL.
::使用 Boyle 的法律来解决未知的压力(P2) 。这两卷(V1和V2)必须用相同的单位表示, 所以V2 已被转换为 mL 。

Step 2: Solve.
::步骤2:解决。

First, rearrange the equation algebraically to solve for $\begin{aligned} P_{2} \end{aligned}$ .
::首先,重新排列方程式代数,以解答P2。

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

::P2=P1xV1V2

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。

\begin{aligned} P_{2} = \frac{387 kPa \times 425 mL}{1750 mL} = 94.0 kPa \end{aligned}

::P2=387千帕×425毫升1750毫升=94.0千帕

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

The volume has increased to slightly over 4 times its original value and so the pressure is decreased by about $\begin{aligned} \frac{1}{4} t h \end{aligned}$ . The pressure is in kPa and the value has three . Note that any pressure or volume units can be used as long as they are consistent throughout the problem.
::体积已略微增加为原值的四倍以上, 因此压力会减少14倍左右。压力以千帕为单位, 值为三。请注意, 只要压力或体积单位在整个问题中始终一致, 任何压力或体积单位都可以使用。

Summary
::摘要

The volume of a gas is inversely proportional to the pressure of that gas in a closed system in which only temperature and pressure are changing .
::气体的体积与封闭系统中气体的压力成反比,封闭系统中只有温度和压力在变化。

Review
::回顾

What does “inversely” mean in this law?
::本法中“反面”的含义是什么?

Explain Boyle’s law in terms of the kinetic-molecular theory of gases.
::解释Boyle在气体动能分子理论方面的法律。

Does it matter what units are used?
::使用哪个单位有关系吗?

Section outline

General

Boyle法

How important is it to check the weather? ::检查天气有多重要?

Boyle’s Law ::Boyle法

Sample Problem: Boyle’s Law ::抽样问题:博伊勒法

Summary ::摘要

Review ::回顾

How important is it to check the weather?
::检查天气有多重要?

Boyle’s Law
::Boyle法

Sample Problem: Boyle’s Law
::抽样问题:博伊勒法

Summary
::摘要

Review
::回顾