Explain the universal gas law?
The universal gas law, or “Ideal Gas Law” shows the interaction of pressure, volume and temperature on a gaseous substance.
In real life, different molecular compositions show different amounts of intermolecular attraction or repulsion that will affect the final state of a gas. This factor is called the fugacity, and it can affect the conditions of some gases markedly (e.g. carbon dioxide). However, it is "Ideal," meaning that no intermolecular interactions are 'allowed'.
Therefore, anytime "non-ideal" gases are used beyond fairly dilute concentrations, caution (and corrections) must be made when calculating values with this equation.
The related Dalton's Law (1766-1844) describes partial pressures, and it was derived by combining the relationships of each of the other general laws (Boyles Law (1627-1691), Charles' Law (1746-1823), and Guy-Lussacs Law (1778-1850).
The other important one to keep in mind is the relationship to moles, which is PV = nRT (Avogadro's Law, 1776–1856). In this case, you must be cautious to use the appropriate "gas constant,” R, as different dimensions have different values for R.
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The universal gas law, also known as the ideal gas law, describes the behavior of ideal gases. It states that the pressure (P) of a gas is directly proportional to its temperature (T) and the amount of gas (n), and inversely proportional to its volume (V). Mathematically, it can be expressed as:
[PV = nRT]
Where:
- P is the pressure of the gas (in Pascals or atmospheres)
- V is the volume of the gas (in liters)
- n is the number of moles of gas
- R is the ideal gas constant ((8.314 , \text{J/mol} \cdot \text{K}))
- T is the temperature of the gas (in Kelvin)
The universal gas law helps to predict the behavior of gases under different conditions, such as changes in pressure, volume, temperature, or the amount of gas.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- The gas inside of a container exerts #9 Pa# of pressure and is at a temperature of #650 ^o K#. If the temperature of the gas changes to #220 ^oC# with no change in the container's volume, what is the new pressure of the gas?
- How are convection currents related to density?
- A container has a volume of #18 L# and holds #15 mol# of gas. If the container is expanded such that its new volume is #24 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?
- The gas inside of a container exerts #8 Pa# of pressure and is at a temperature of #210 ^o K#. If the temperature of the gas changes to #30 ^oC# with no change in the container's volume, what is the new pressure of the gas?
- If #17/6 L# of a gas at room temperature exerts a pressure of #24 kPa# on its container, what pressure will the gas exert if the container's volume changes to #5/4 L#?

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