The ideal gas law is an equation of state that describes a relationship between the state functions associated with the ideal gas; such as temperature, pressure, volume, and number of moles. This law allows to study real gaseous systems comparing them with their idealized versions.
An ideal gas is a theoretical gas, composed of point or spherical particles that move at random; with high kinetic energy, where the only interaction between them is completely elastic shocks. In addition, they comply with the ideal gas law.
At standard pressure and temperature (STP): 1 atm of pressure, and a temperature of 0 ºC, most of the real gases behave qualitatively as ideal gases; as long as their densities are low. Large intermolecular or interatomic distances (for noble gases) facilitate such approximations..
Under STP conditions, oxygen, nitrogen, hydrogen, noble gases and some gases in compound form, such as carbon dioxide, behave as an ideal gas..
The ideal gas model tends to fail at low temperatures, high pressures, and high particle densities; when intermolecular interactions, as well as particle size, become important.
The ideal gas law is a composition of three gas laws: Boyle and Mariotte's law, Charles and Gay-Lussac's law, and Avogadro's law..
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The gas law is expressed mathematically with the formula:
PV = nRT
Where P is the pressure exerted by a gas. It is usually expressed with the unit of atmosphere (atm), although it can be expressed in other units: mmHg, pascal, bar, etc..
The volume V occupied by a gas is usually expressed in units of the liter (L). While n is the number of moles, R the universal gas constant, and T the temperature expressed in Kelvin (K).
The most used expression in gases for R equals 0.08206 L atm K-1Mole-1. Although the SI unit for the gas constant has a value of 8.3145 J mol-1K-1. Both are valid as long as care is taken with the units of the other variables (P, T and V).
The ideal gas law is a combination of Boyle-Mariotte's law, Charles-Gay-Lussac's law, and Avogadro's law.
It was formulated independently by the physicist Robert Boyle (1662) and the physicist and botanist Edme Mariotte (1676). The law is stated as follows: at constant temperature, the volume of a fixed mass of a gas is inversely proportional to the pressure it exerts.
PV ∝ k
By using a colon:
P1V1 = PtwoVtwo
The law was published by Gay-Lussac in 1803, but it made reference to the unpublished work by Jacques Charles (1787). For this reason the law is known as Charles's law..
The law states that at constant pressure, there is a direct proportional relationship between the volume occupied by a gas and its temperature.
V ∝ ktwoT
By using a colon:
V1/ T1 = Vtwo/ Ttwo
V1Ttwo = VtwoT1
The law was enunciated by Amadeo Avogadro in 1811, pointing out that equal volumes of all gases, at the same pressure and temperature, have the same number of molecules.
V1/ n1 = Vtwo/ ntwo
The ideal gas law establishes a relationship between four independent physical properties of gas: pressure, volume, temperature, and quantity of the gas. It is enough to know the value of three of them, to be able to obtain that of the remaining.
The Law establishes the conditions that indicate when a gas behaves ideally, and when it moves away from this behavior.
For example, the so-called compression factor (PV / nRT) has a value of 1 for ideal gases. A departure from the value of 1 for the compression factor indicates that the behavior of the gas is far from that shown by an ideal gas.
Therefore, a mistake would be made when applying the ideal gas equation to a gas that does not behave according to the model.
The ideal gas law equation can be used in calculating the density of a gas and its molar mass. By making a simple modification, a mathematical expression can be found that relates the density (d) of a gas and its molar mass (M):
d = MP / RT
And clearing M:
M = dRT / P
Stoichiometry is the branch of chemistry that relates the amount of each of the reactants present with the products that take part in a chemical reaction, generally expressed in moles..
The use of the ideal gas equation allows the determination of the volume of a gas produced in a chemical reaction; since the number of moles can be obtained from the chemical reaction. Then the volume of the gas can be calculated:
PV = nRT
V = nRT / P
By measuring V the yield or progress of said reaction can be determined. When there are no more gases, it is an indication that the reagents are completely depleted.
The Ideal Gas Law can be used, together with Dalton's partial pressure law, to calculate the partial pressures of the different gases present in a gas mixture..
The relation applies:
P = nRT / V
To find the pressure of each of the gases present in the mixture.
A reaction is carried out that produces a gas, which is collected by means of an experimental design in water. The total pressure of the gas plus the water vapor pressure is known. The value of the latter can be obtained in a table and by subtraction the pressure of the gas can be calculated.
From the stoichiometry of the chemical reaction, the number of moles of the gas can be obtained, and applying the relationship:
V = nRT / P
The volume of gas produced is calculated.
A gas has a density of 0.0847 g / L at 17 ° C, and a pressure of 760 torr. What is its molar mass? What is gas?
We start from the equation
M = dRT / P
We first convert the units of temperature to kelvin:
T = 17 ºC + 273.15 K = 290.15 K
And the pressure of 760 torr corresponds to that of 1 atm. Now you only need to substitute the values and solve:
M = (0.0847 g / L) (0.08206 L atm K-1Mole-1) (290.15 K) / 1 atm
M = 2.016 g / mol
This molar mass may correspond to a single species: the diatomic hydrogen molecule, Htwo.
A mass of 0.00553 g of mercury (Hg) in the gas phase is found in a volume of 520 L, and at a temperature of 507 K. Calculate the pressure exerted by Hg. The molar mass of Hg is 200.59 g / mol.
The problem is solved by using the equation:
PV = nRT
Information about the number of moles of Hg does not appear; but they can be obtained by using their molar mass:
Number of moles of Hg = (0.00553 g of Hg) (1 mole Hg / 200.59 g)
= 2,757 10-5 moles
Now we just have to solve for P and substitute the values:
P = nRT / V
= (2,757 10-5 moles) (8,206 · 10-two L atm K-1Mole-1) (507 K) / 520 L
= 2.2 10-6 atm
Calculate the pressure generated by the hydrochloric acid produced by reacting 4.8 g of chlorine gas (Cltwo) with hydrogen gas (Htwo), in a volume of 5.25 L, and at a temperature of 310 K. The molar mass of Cltwo is 70.9 g / mol.
H2 g) + Cl2 g) → 2 HCl(g)
The problem is solved by using the ideal gas equation. But the amount of HCl is expressed in grams and not in moles, so the proper transformation is made.
Moles of HCl = (4.8 g Cltwo) (1 mole of Cltwo/ 70.9 g Cltwo) (2 mol HCl / 1 mol Cltwo)
= 0.135 moles of HCl
Applying the ideal gas law equation:
PV = nRT
P = nRT / V
= (0.135 moles of HCl) (0.08206 L atm K-1Mole-1) (310 K) / 5.25 L
= 0.65 atm
A 0.130 g sample of a gaseous compound occupies a volume of 140 mL at a temperature of 70 ° C and a pressure of 720 torr. What is its molar mass?
To apply the ideal gas equation, several changes must first be made:
V = (140 mL) (1 L / 1000 mL)
= 0.14 L
Taking the volume in liters, we now have to express the temperature in kelvin:
T = 70 ºC + 273.15 K = 243.15 K
And finally, we must convert the pressure in units of atmosphere:
P = (720 torr) (1 atm / 760 torr)
= 0.947 atm
The first step in solving the problem is to obtain the number of moles of the compound. For this, the ideal gas equation is used and we solve for n:
PV = nRT
n = PV / RT
= (0.947 atm) (0.14 L) / (0.08206 L atm K-1Mole-1) (243.15 K)
= 0.067 moles
You only need to calculate the molar mass by dividing the grams by the moles obtained:
Molar mass = grams of compound / number of moles.
= 0.130 g / 0.067 moles
= 19.49 g / mol
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