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Ideal Gases
Storyboard 
In the case of an ideal gas, where the interactions between its particles are negligible, there are direct and simple relationships between pressure, volume, temperature, and the amount of gas.
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Ideal gas
Image
A gas in which its particles do not interact is known as an ideal gas. We can envision it as follows:
• It consists of a series of spheres contained within a container ERROR:5226.1.
• The speed of these particles depends on the absolute temperature ($T$).
• They generate a pressure of the pressure ($p$) through collisions with the walls of the container.
An ideal gas is characterized by the absence of potential energies between the particles. In other words, the potential energies that could exist between particles $i$ and $j$ with positions $q_i$ and $q_j$ are null:
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The moles
Note
By utilizing the concept of a mole, we can directly relate the amount of substance of a gas to the number of the number of particles ($N$) particles present in it. This simplifies calculations and allows for a more intuitive connection between the quantity of gas and its defining properties, such as the pressure ($p$), the volume ($V$), and the absolute temperature ($T$).
The constant the avogadro's number ($N_A$), which is approximately equal to $6.02\times 10^{23}$, is a fundamental constant in chemistry and is used to bridge the gap between the macroscopic and microscopic scales of atoms and molecules.
The value of the número de Moles ($n$) can be calculated from the number of particles ($N$) and the mass ($M$). In the first case, it is obtained by dividing by ERROR:5403 using the formula:
| $ n \equiv\displaystyle\frac{ N }{ N_A }$ |
While in the second case, the molar Mass ($M_m$) is used with the formula:
| $ n = \displaystyle\frac{ M }{ M_m }$ |
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Pressure
Quote
Pressure is the result of multiple collisions between gas particles and the walls of the container. Each collision contributes to the total pressure exerted by the gas. The faster the particles move and the more collisions that occur within a specific time period, the higher the pressure will be.
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Volume
Exercise
Volume is a fundamental property of a gas and can be understood as the three-dimensional space that the gas occupies in a container.
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Gas mixture
Equation
In the case of an ideal gas, where there is no interaction between particles, a mixture of different types of gases will behave as if it were a larger quantity of the same type of gas.
Specifically, if we have three components with their respective partial pressures, when they are mixed, the total pressure will be the sum of the partial pressures:
This image illustrates how the partial pressures of gases add up in a mixture. Each gas exerts an independent pressure and contributes to the total pressure of the mixture.
This concept is fundamental in understanding the behavior of gas mixtures, as it allows us to calculate the total pressure based on the partial pressures of the individual components.
According to Dalton's Law [1], the total pressure of a gas mixture is equal to the sum of the individual pressures of the gases, where a pressure ($p$) is equal to the sum of the partial pressure of component i ($p_i$). This leads us to conclude that the gas behaves as if the particles of the different gases were identical. In this way, the pressure ($p$) is the sum of the partial pressure of component i ($p_i$):
| $ p = \displaystyle\sum_i p_i $ |
Therefore, it can be concluded that the gas behaves as if the different gases were identical and the number of moles corresponds to the sum of the moles of the different components:
| $ n =\displaystyle\sum_i n_i $ |
[1] "Experimental Essays on the Constitution of Mixed Gases; on the Force of Steam or Vapour from Water and Other Liquids in Different Temperatures, Both in a Torricellian Vacuum and in Air; on Evaporation; and on the Expansion of Gases by Heat", John Dalton, Memoirs of the Literary and Philosophical Society of Manchester, Volume 5, Issue 2, Pages 535-602 (1802).
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Gas Laws
Script
The state of a system is described by the so-called equation of state, which establishes the relationship between the parameters that characterize the system.
In the case of gases, the parameters that describe their state are the pressure ($p$), the volume ($V$), the absolute temperature ($T$), and the number of moles ($n$). Typically, the latter parameter remains constant as it is associated with the amount of gas present.
The equation of state, therefore, relates pressure, volume, and temperature, and it establishes that there are only two degrees of freedom, as the equation of state allows for the calculation of the third parameter. In particular, if the volume is fixed, one can choose, for example, temperature as the variable, which enables the calculation of the corresponding pressure.
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Ideal Gases
Storyboard
In the case of an ideal gas, where the interactions between its particles are negligible, there are direct and simple relationships between pressure, volume, temperature, and the amount of gas.
Variables
Calculations
to 
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then, select the variable: 
to 
Calculations
Variable
Given
Calculate
Target :
Equation
To be used
Equations
The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):
If we multiply both the numerator and the denominator by the particle mass ($m$), we obtain:
$n=\displaystyle\frac{N}{N_A}=\displaystyle\frac{Nm}{N_Am}=\displaystyle\frac{M}{M_m}$
So it is:
The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):
If we multiply both the numerator and the denominator by the particle mass ($m$), we obtain:
$n=\displaystyle\frac{N}{N_A}=\displaystyle\frac{Nm}{N_Am}=\displaystyle\frac{M}{M_m}$
So it is:
The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):
If we multiply both the numerator and the denominator by the particle mass ($m$), we obtain:
$n=\displaystyle\frac{N}{N_A}=\displaystyle\frac{Nm}{N_Am}=\displaystyle\frac{M}{M_m}$
So it is:
Examples
In the ideal gas model, gases are represented as small spheres bouncing off the walls of the container. Since they do not interact, the type of gas is irrelevant what matters is the number of collisions they produce. Therefore, the key factor is the total number of particles, regardless of type, that impact the surface.
Experiment:
You can activate or deactivate different gases, or deactivate one component and transfer its particle count to another. This allows observation that the average number of impacts per unit time remains unchanged, illustrating the principle of partial pressures.
A gas in which its particles do not interact is known as an ideal gas. We can envision it as follows:
• It consists of a series of spheres contained within a container ERROR:5226.1.
• The speed of these particles depends on the absolute temperature ($T$).
• They generate a pressure of the pressure ($p$) through collisions with the walls of the container.
An ideal gas is characterized by the absence of potential energies between the particles. In other words, the potential energies that could exist between particles $i$ and $j$ with positions $q_i$ and $q_j$ are null:
By utilizing the concept of a mole, we can directly relate the amount of substance of a gas to the number of the number of particles ($N$) particles present in it. This simplifies calculations and allows for a more intuitive connection between the quantity of gas and its defining properties, such as the pressure ($p$), the volume ($V$), and the absolute temperature ($T$).
The constant the avogadro's number ($N_A$), which is approximately equal to $6.02\times 10^{23}$, is a fundamental constant in chemistry and is used to bridge the gap between the macroscopic and microscopic scales of atoms and molecules.
The value of the número de Moles ($n$) can be calculated from the number of particles ($N$) and the mass ($M$). In the first case, it is obtained by dividing by the avogadro's number ($N_A$) using the formula:
While in the second case, the molar Mass ($M_m$) is used with the formula:
In the case of an ideal gas, where there is no interaction between particles, a mixture of different types of gases will behave as if it were a larger quantity of the same type of gas.
Specifically, if we have three components with their respective partial pressures, when they are mixed, the total pressure will be the sum of the partial pressures:
This image illustrates how the partial pressures of gases add up in a mixture. Each gas exerts an independent pressure and contributes to the total pressure of the mixture.
This concept is fundamental in understanding the behavior of gas mixtures, as it allows us to calculate the total pressure based on the partial pressures of the individual components.
According to Dalton's Law [1], the total pressure of a gas mixture is equal to the sum of the individual pressures of the gases, where a pressure ($p$) is equal to the sum of the partial pressure of component i ($p_i$). This leads us to conclude that the gas behaves as if the particles of the different gases were identical. In this way, the pressure ($p$) is the sum of the partial pressure of component i ($p_i$):
Therefore, it can be concluded that the gas behaves as if the different gases were identical and the number of moles corresponds to the sum of the moles of the different components:
[1] "Experimental Essays on the Constitution of Mixed Gases; on the Force of Steam or Vapour from Water and Other Liquids in Different Temperatures, Both in a Torricellian Vacuum and in Air; on Evaporation; and on the Expansion of Gases by Heat", John Dalton, Memoirs of the Literary and Philosophical Society of Manchester, Volume 5, Issue 2, Pages 535-602 (1802).
The number of moles ($n$) is determined by dividing the mass ($M$) of a substance by its the molar Mass ($M_m$), which corresponds to the weight of one mole of the substance.
Therefore, the following relationship can be established:
The molar mass is expressed in grams per mole (g/mol).
The number of moles ($n$) is determined by dividing the mass ($M$) of a substance by its the molar Mass ($M_m$), which corresponds to the weight of one mole of the substance.
Therefore, the following relationship can be established:
The molar mass is expressed in grams per mole (g/mol).
The number of moles ($n$) is determined by dividing the mass ($M$) of a substance by its the molar Mass ($M_m$), which corresponds to the weight of one mole of the substance.
Therefore, the following relationship can be established:
The molar mass is expressed in grams per mole (g/mol).
The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):
the avogadro's number ($N_A$) is a universal constant with a value of 6.028E+23 1/mol, and is therefore not included among the variables used in the calculation.
The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):
the avogadro's number ($N_A$) is a universal constant with a value of 6.028E+23 1/mol, and is therefore not included among the variables used in the calculation.
The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):
the avogadro's number ($N_A$) is a universal constant with a value of 6.028E+23 1/mol, and is therefore not included among the variables used in the calculation.
The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):
the avogadro's number ($N_A$) is a universal constant with a value of 6.028E+23 1/mol, and is therefore not included among the variables used in the calculation.
In the case of an ideal gas, the pressure the pressure ($p$) is proportional to the number of moles the number of moles ($n$) contained in a given volume. By introducing the pressure constant per mole ($C_{pn}$), this relationship can be expressed as:
In the case of an ideal gas, the pressure the pressure ($p$) is proportional to the number of moles the number of moles ($n$) contained in a given volume. By introducing the pressure constant per mole ($C_{pn}$), this relationship can be expressed as:
In the case of an ideal gas, the pressure the pressure ($p$) is proportional to the number of moles the number of moles ($n$) contained in a given volume. By introducing the pressure constant per mole ($C_{pn}$), this relationship can be expressed as:
In the case of an ideal gas, the pressure the pressure ($p$) is proportional to the number of moles the number of moles ($n$) contained in a given volume. By introducing the pressure constant per mole ($C_{pn}$), this relationship can be expressed as:
The total pressure of all components ($p$) is the sum of the partial pressure of component 1 ($p_1$), the partial pressure of component 2 ($p_2$), and the partial pressure of component 3 ($p_3$):
The total number of particles ($N$) is equal to the sum of the number of particles of component 1 ($N_1$), the number of particles of component 2 ($N_2$), and the number of particles of component 3 ($N_3$):
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