Derive the ideal gas equation on the basis of the laws of Boyle, Charles, and Avogadro. Calculate the volume occupied by an ideal gas at STP, if 0.25 L of the gas is present at a pressure of 700 mm of Hg and 273℃.
Derive the ideal gas equation on the basis of the laws of Boyle, Charles, and Avogadro. Calculate the volume occupied by an ideal gas at STP, if 0.25 L of the gas is present at a pressure of 700 mm of Hg and 273℃.
An ideal gas is a hypothetical gas dreamed of by chemists and students because it would be much easier if things like intermolecular forces do not exist to complicate the simple Ideal Gas Law. Ideal gases are essentially pointed masses moving in constant, random, straight-line motion. Its behavior is described by the assumptions listed in the kinetic molecular theory of gases.
the Ideal Gas Equation, let us state the four gas variables and one constant for a better understanding. The four gas variables are pressure (P), volume (V), number of moles of gas (n), and temperature (T). Lastly, the constant in the equation shown below is R, known as the gas constant, which will be discussed in depth further later:
PV=nRT
Another way to describe an ideal gas is to describe it mathematically. Consider the following equation:
PV / nRT = 1
The term pV / nRT; pV = nRT is also called the compression factor and is a measure of the ideality of the gas. An ideal gas will always equal 1 when plugged into this equation. The greater it deviates from the number 1, the more
it will behave like a real gas rather than an ideal. A few things should always be kept in mind when working with this equation, as you may find it extremely helpful when checking your answer after working out a gas problem.
- Pressure is directly proportional to the number of molecules and temperature. (Since P is on the opposite side of the equation to n and T)
- Pressure, however, is indirectly proportional to volume. (Since P is on the same side of the equation as V)
Boyle’s law describes the inverse proportional relationship between pressure and volume at a constant temperature and a fixed amount of gas. The law came from a manipulation of the ideal gas law.
P α 1/V
Or expressed from two pressure/ volume points.
P1V1 = P2 V2
The equation would be ideal when working with a problem asking for the initial or final value of pressure or volume of a certain gas when one of the two factors is missing.
Charle’s law
Charles’s law describes the directly proportional relationship between the volume and temperature of a fixed amount of gas when the pressure is held constant.
V α T
Or express from two volume/temperature points
V1/ T1 = V2 / T2
This equation can be used to solve for the initial or final value of temperature under the given condition that pressure and the number of moles of the gas stay the same.
Avogadro’s law
Avogadro’s law states that the volume of a gas is directly proportional to the amount of gas at a constant temperature and pressure.
V α n
Or expressed as two-volume / number points.
Step 2:P1V1 / T1 = P2V2 /T2
At STP pressure = 760 mm Hg = 1 atm
Temperature = 273 K
Here the temperature is given as 273℃ = 546 K
760 X V1 / 273 = 700 X 0.25 / 546
V1 = 0.115 L
Hence, the volume occupied by an ideal gas at STP, if 0.25 L of the gas is present at a pressure of 700 mm of Hg and 273℃ is 0.115 L.
An ideal gas is a hypothetical gas dreamed of by chemists and students because it would be much easier if things like intermolecular forces do not exist to complicate the simple Ideal Gas Law. Ideal gases are essentially pointed masses moving in constant, random, straight-line motion. Its behavior is described by the assumptions listed in the kinetic molecular theory of gases.
the Ideal Gas Equation, let us state the four gas variables and one constant for a better understanding. The four gas variables are pressure (P), volume (V), number of moles of gas (n), and temperature (T). Lastly, the constant in the equation shown below is R, known as the gas constant, which will be discussed in depth further later:
PV=nRT
Another way to describe an ideal gas is to describe it mathematically. Consider the following equation:
PV / nRT = 1
The term pV / nRT; pV = nRT is also called the compression factor and is a measure of the ideality of the gas. An ideal gas will always equal 1 when plugged into this equation. The greater it deviates from the number 1, the more
it will behave like a real gas rather than an ideal. A few things should always be kept in mind when working with this equation, as you may find it extremely helpful when checking your answer after working out a gas problem.
- Pressure is directly proportional to the number of molecules and temperature. (Since P is on the opposite side of the equation to n and T)
- Pressure, however, is indirectly proportional to volume. (Since P is on the same side of the equation as V)
Boyle’s law describes the inverse proportional relationship between pressure and volume at a constant temperature and a fixed amount of gas. The law came from a manipulation of the ideal gas law.
P α 1/V
Or expressed from two pressure/ volume points.
P1V1 = P2 V2
The equation would be ideal when working with a problem asking for the initial or final value of pressure or volume of a certain gas when one of the two factors is missing.
Charle’s law
Charles’s law describes the directly proportional relationship between the volume and temperature of a fixed amount of gas when the pressure is held constant.
V α T
Or express from two volume/temperature points
V1/ T1 = V2 / T2
This equation can be used to solve for the initial or final value of temperature under the given condition that pressure and the number of moles of the gas stay the same.
Avogadro’s law
Avogadro’s law states that the volume of a gas is directly proportional to the amount of gas at a constant temperature and pressure.
V α n
Or expressed as two-volume / number points.
Step 2:P1V1 / T1 = P2V2 /T2
At STP pressure = 760 mm Hg = 1 atm
Temperature = 273 K
Here the temperature is given as 273℃ = 546 K
760 X V1 / 273 = 700 X 0.25 / 546
V1 = 0.115 L
Hence, the volume occupied by an ideal gas at STP, if 0.25 L of the gas is present at a pressure of 700 mm of Hg and 273℃ is 0.115 L.
