Modeling a Gas
Learning Objectives
- Use the concept of pressure
- Solve problems using the equation of state of an. idea has
- Understanding the assumptions behind the kinetic model of an ideal gas
- Solving problems using moles, molar mass, and the Avogadro constant
- Describe differences ideal and real gases
- The Avogadro constant
- Ideal Gases
- The Pressure-Volume Law
- The Pressure-Temperature Law
- The Boltzmann Equation
The Avogadro Constant
- Avogadro's number is the number of units in one mole of any substance , equal to 6.02214076 × 1023
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A mole is a unit of measurement, equal to 6.02214076 × 1023. The value of the mole is equal to the number of atoms in exactly 12 grams of pure carbon-12
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Molar mass is the mass of one mole of a substance
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https://www.onlinemathlearning.com/grams-moles.html
Pressure
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/k37ko2/ScreenShot2021-09-04at53131PM.png?enable-io=true&enable=upscale&crop=994%2C445%2Cx0%2Cy0%2Csafe&width=555&height=248)
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/316nb9/3212-The-normal-force-per-unit-area-is-the-pressure-exerted-by-the-force-on-that-area885298fee4450056ac80.png?enable-io=true&enable=upscale&crop=1200%2C454%2Cx0%2Cy0%2Csafe&width=490&height=185)
Ideal Gases
Ideal gases are theoretical model to gases, and they are assumed to obey the followings
- The particles are point particles, each has a negligible volume
- The molecules obey the law of motion
- The are no forces between molecules unless when they collide (molecules do not attract or repel each other)
- The duration of collision is negligible compared with the time between collisions
- The collisions with molecules and other contain walls are elastic
- Molecules have a range of speed and move randomly
An ideal gas can be approximated by an ideal gas when the density is low or when at a high temperature and low pressure. This is because molecules are distant away from each other when density is low, so molecules will exert a weaker force on each other.
The Pressure - Volume Law (Boyle's Law)
- At constant temperature and with a fixed quantity of gas, pressure is inversely proportional to volume and pressure times volume is equal to a constant.
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/3dc8hl/picture1-115.png?enable-io=true&enable=upscale&crop=1686%2C175%2Cx0%2Cy29%2Csafe&width=540&height=56)
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/proxy.png)
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/sxw1d6/d0772b2de7fdf060d3e8b329a6f9e04e.png?enable-io=true&enable=upscale&crop=359%2C359%2Cx0%2Cy0%2Csafe&width=250&height=250)
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Charles' law
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The volume occupied by a fixed amount of gas is directly proportional to its absolute temperature, if the pressure remains constant.
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/quwcln/picture1-116.png?enable-io=true&enable=upscale&crop=1425%2C242%2Cx0%2Cy0%2Csafe&width=442&height=75)
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/o-level-physics-notes-the-absolute-temperature-scale-html-7c84faea.gif?enable-io=true&enable=upscale&crop=433%2C265%2Cx0%2Cy0%2Csafe&width=387&height=237)
Figure 4: Temperature in Celsius
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/ideal_s2_11.gif)
Figure 5: Temperature in Kelvin
The Pressure-Temperature Law
- For a given mass and constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature.
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/hy80qe/picture1-117.png?enable-io=true&enable=upscale&crop=1420%2C229%2Cx0%2Cy0%2Csafe&width=491&height=79)
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/gay-lussacs-law-graph.gif?enable-io=true&enable=upscale&crop=320%2C220%2Cx0%2Cy4%2Csafe&width=320&height=220)
Ideal Gas Equation
- The state of gas can be determined when we know the volume of pressure P, volume V temperature T, and the number of moles present n. The equation related all quantities is known as the equation of state, as shown below.
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/8iyhma/ScreenShot2021-09-04at64939PM.png?enable-io=true&enable=upscale&crop=476%2C94%2Cx0%2Cy13%2Csafe&width=310&height=61)
Gas Laws Summary
![](https://primary.jwwb.nl/public/q/e/c/temp-qxhpqvdlqmczmmnxbocw/nyrkd2/gas-law-formula.png)