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Gas Mixtures  
  
1748   04:15 مساءً   date: 1-11-2020
Author : University of Missouri System
Book or Source : Organic Chemistry ii
Page and Part : .................


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Date: 16-7-2017 1794
Date: 1-7-2017 1256
Date: 17-11-2020 1462

Gas Mixtures

One of the properties of gases is that they mix with each other. When they do so, they become a solution—a homogeneous mixture. Some of the properties of gas mixtures are easy to determine if we know the composition of the gases in the mix.

In gas mixtures, each component in the gas phase can be treated separately. Each component of the mixture shares the same temperature and volume. (Remember that gases expand to fill the volume of their container; gases in a mixture do that as well.) However, each gas has its own pressure. The partial pressure of a gas, Pi, is the pressure that an individual gas in a mixture has. Partial pressures are expressed in torr, millimeters of mercury, or atmospheres like any other gas pressure; however, we use the term pressure when talking about pure gases and the term partial pressure when we are talking about the individual gas components in a mixture.

Dalton’s law of partial pressures states that the total pressure of a gas mixture, Ptot, is equal to the sum of the partial pressures of the components, Pi:

Screen Shot 2014-07-22 at 5.51.15 PM

Although this may seem to be a trivial law, it reinforces the idea that gases behave independently of each other.

Example 15

A mixture of H2 at 2.33 atm and N2 at 0.77 atm is in a container. What is the total pressure in the container?

Solution

Dalton’s law of partial pressures states that the total pressure is equal to the sum of the partial pressures. We simply add the two pressures together:

Ptot = 2.33 atm + 0.77 atm = 3.10 atm

Test Yourself

Air can be thought of as a mixture of N2 and O2. In 760 torr of air, the partial pressure of N2 is 608 torr. What is the partial pressure of O2?

Answer

152 torr

Example 16

A 2.00 L container with 2.50 atm of H2 is connected to a 5.00 L container with 1.90 atm of O2 inside. The containers are opened, and the gases mix. What is the final pressure inside the containers?

Solution

Because gases act independently of each other, we can determine the resulting final pressures using Boyle’s law and then add the two resulting pressures together to get the final pressure. The total final volume is 2.00 L + 5.00 L = 7.00 L. First, we use Boyle’s law to determine the final pressure of H2:

(2.50 atm)(2.00 L) = P2(7.00 L)

Solving for P2, we get

P2 = 0.714 atm = partial pressure of H2

Now we do that same thing for the O2:

(1.90 atm)(5.00 L) = P2(7.00 L)
P2 = 1.36 atm = partial pressure of O2

The total pressure is the sum of the two resulting partial pressures:

Ptot = 0.714 atm + 1.36 atm = 2.07 atm

Test Yourself

If 0.75 atm of He in a 2.00 L container is connected to a 3.00 L container with 0.35 atm of Ne and the connection between the containers is opened, what is the resulting total pressure?

Answer

0.51 atm

One of the reasons we have to deal with Dalton’s law of partial pressures is that gases are frequently collected by bubbling through water.

This partial pressure is called a vapour pressure. Table 1.1 “Vapor Pressure of Water versus Temperature” lists the vapour pressures of H2O versus temperature. Note that if a substance is normally a gas under a given set of conditions, the term partial pressure is used; the term vapour pressure is reserved for the partial pressure of a vapour when the liquid is the normal phase under a given set of conditions.

Table 1.1 Vapor Pressure of Water versus Temperature

Temperature (°C) Vapor Pressure (torr)   Temperature (°C) Vapor Pressure (torr)
5 6.54   30 31.84
10 9.21 35 42.20
15 12.79 40 55.36
20 17.54 50 92.59
21 18.66 60 149.5
22 19.84 70 233.8
23 21.08 80 355.3
24 22.39 90 525.9
25 23.77 100 760.0

Any time a gas is collected over water, the total pressure is equal to the partial pressure of the gas plus the vapour pressure of water. This means that the amount of gas collected will be less than the total pressure suggests.

Example 17

Hydrogen gas is generated by the reaction of nitric acid and elemental iron. The gas is collected in an inverted 2.00 L container immersed in a pool of water at 22°C. At the end of the collection, the partial pressure inside the container is 733 torr. How many moles of H2 gas were generated?

Solution

We need to take into account that the total pressure includes the vapour pressure of water. According to Table 1.1 “Vapor Pressure of Water versus Temperature,” the vapour pressure of water at 22°C is 19.84 torr. According to Dalton’s law of partial pressures, the total pressure equals the sum of the pressures of the individual gases, so

733 torr = PH2 + PH2O = PH2 + 19.84 torr

We solve by subtracting:

PH2 = 713 torr

Now we can use the ideal gas law to determine the number of moles (remembering to convert the temperature to kelvins, making it 295 K):

713torr

All the units cancel except for mol, which is what we are looking for. So

n = 0.0775 mol H2 collected

Test Yourself

CO2, generated by the decomposition of CaCO3, is collected in a 3.50 L container over water. If the temperature is 50°C and the total pressure inside the container is 833 torr, how many moles of CO2 were generated?

Answer

0.129 mol

Finally, we introduce a new unit that can be useful, especially for gases. The mole fraction, χi, is the ratio of the number of moles of component i in a mixture divided by the total number of moles in the sample:

Screen Shot 2014-07-22 at 5.51.24 PM

(χ is the lowercase Greek letter chi.) Note that mole fraction is not a percentage; its values range from 0 to 1. For example, consider the combination of 4.00 g of He and 5.0 g of Ne. Converting both to moles, we get

Screen Shot 2014-07-22 at 5.51.28 PM

The total number of moles is the sum of the two mole amounts:

total moles = 1.00 mol + 0.025 mol = 1.25 mol

The mole fractions are simply the ratio of each mole amount to the total number of moles, 1.25 mol:

Screen Shot 2014-07-22 at 5.51.35 PM

The sum of the mole fractions equals exactly 1.

For gases, there is another way to determine the mole fraction. When gases have the same volume and temperature (as they would in a mixture of gases), the number of moles is proportional to partial pressure, so the mole fractions for a gas mixture can be determined by taking the ratio of partial pressure to total pressure:

Screen Shot 2014-07-22 at 5.51.40 PM

This expression allows us to determine mole fractions without calculating the moles of each component directly.

Example 18

A container has a mixture of He at 0.80 atm and Ne at 0.60 atm. What is the mole fraction of each component?

Solution

According to Dalton’s law, the total pressure is the sum of the partial pressures:

Ptot = 0.80 atm + 0.60 atm = 1.40 atm

The mole fractions are the ratios of the partial pressure of each component to the total pressure:

xhe

Again, the sum of the mole fractions is exactly 1.

Test Yourself

What are the mole fractions when 0.65 atm of O2 and 1.30 atm of N2 are mixed in a container?

Answer

χO2=0.33; χN2=0.67




هي أحد فروع علم الكيمياء. ويدرس بنية وخواص وتفاعلات المركبات والمواد العضوية، أي المواد التي تحتوي على عناصر الكربون والهيدروجين والاوكسجين والنتروجين واحيانا الكبريت (كل ما يحتويه تركيب جسم الكائن الحي مثلا البروتين يحوي تلك العناصر). وكذلك دراسة البنية تتضمن استخدام المطيافية (مثل رنين مغناطيسي نووي) ومطيافية الكتلة والطرق الفيزيائية والكيميائية الأخرى لتحديد التركيب الكيميائي والصيغة الكيميائية للمركبات العضوية. إلى عناصر أخرى و تشمل:- كيمياء عضوية فلزية و كيمياء عضوية لا فلزية.


إن هذا العلم متشعب و متفرع و له علاقة بعلوم أخرى كثيرة ويعرف بكيمياء الكائنات الحية على اختلاف أنواعها عن طريق دراسة المكونات الخلوية لهذه الكائنات من حيث التراكيب الكيميائية لهذه المكونات ومناطق تواجدها ووظائفها الحيوية فضلا عن دراسة التفاعلات الحيوية المختلفة التي تحدث داخل هذه الخلايا الحية من حيث البناء والتخليق، أو من حيث الهدم وإنتاج الطاقة .


علم يقوم على دراسة خواص وبناء مختلف المواد والجسيمات التي تتكون منها هذه المواد وذلك تبعا لتركيبها وبنائها الكيميائيين وللظروف التي توجد فيها وعلى دراسة التفاعلات الكيميائية والاشكال الأخرى من التأثير المتبادل بين المواد تبعا لتركيبها الكيميائي وبنائها ، وللظروف الفيزيائية التي تحدث فيها هذه التفاعلات. يعود نشوء الكيمياء الفيزيائية إلى منتصف القرن الثامن عشر . فقد أدت المعلومات التي تجمعت حتى تلك الفترة في فرعي الفيزياء والكيمياء إلى فصل الكيمياء الفيزيائية كمادة علمية مستقلة ، كما ساعدت على تطورها فيما بعد .