# So as to touch base at the ideal gas equation, the state equation is connected (Kerboua, Kaouther & Hamdaoui, 2018).

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Ideal gas law

So as to touch base at the ideal gas equation, the state equation is connected (Kerboua, Kaouther & Hamdaoui, 2018). The condition of a given substance test can be indicated by giving the estimations of the accompanying components:

P – Pressure

T – Temperature

V – Volume

N – Amount of substance

These components are dependent of each other. Whenever the temperature, amount, and volume are chosen, then an accepted pressure has to be utilized as a requirement.

It is presently evident that to ascertain the density of air given the Temperature, Air Pressure and its Specific gas constant, we should actualize the formula underneath:

Þ=P/(R*T)

Þ = Density of Air

P = Atmospheric Pressure (Pa)

T = Temperature (°K)

R = Specific Gas Constant for the various gases.

The density for Oxygen for instance at temperature 20°C is:

P = 101.3E3 kg/m3

R = 259.8 J kg−1 K−1

T = 20°C: 20+273 =293 K

Þ=101.3E3/( 259.8*293)= 101.3E3/( 76121.4) =1.330769008 kg/m3

Density for Nitrogen at temperature 10°C is:

P = 101.3E3 kg/m3

R = 296.8 J kg−1 K−1

T = 10°C: 10+273 =283 K

Þ 101.3E3/( 296.8*283) =101.3E3/( 83994.4) = 1.206032783 kg/m3

Density for Hydrogen at temperature 30°C is:

P = 101.3E3 kg/m3

R = 4124 J kg−1 K−1

T = 30°C: 30+273 =303 K

Þ=101.3E3/( 4124.8*303) = 101.3E3/( 1249572 ) = 0.081067758 kg/m3

Density for Air at temperature -100°C is:

P = 101.3E3 kg/m3

R = 286.9 J kg−1 K−1

T = -100°C: -100+273 =173 K

Þ=101.3E3/( 286.9*173) = 101.3E3/( 49633.7)= 2.040952014 kg/m3

The above made calculations were implemented on all the cells from temperatures -100°C to 100°C for the densities of all the four gases. The average gas constant for Oxygen and Hydrogen is:

(259.8+4124)/( 2) = 2191.9 J kg−1 K−1

Proof of all the above made calculations are seen in the attached excel file and the screenshot on this report as well.

Below is a screenshot for the excel file:

The formula implemented in excel for example is =C10/(C11*B17) for the density of Air at temperature -60°C. From this formula, C10 represents the Standard atmospheric pressure and C11 is the gas constant while B17 is the temperature of air in Kelvin. This equation was connected on the cells of different gases in agreement to their gas constants and temperature in Kelvin (Timberlake & Karen, 2015).

From the excel calculations done, the lowest gas density for air is at 100°C and is highest at -100°C. For Nitrogen gas, the highest density is at -100°C and the lowest density in the given range is at 100°C. On the other hand, the highest and lowest gas densities for Oxygen and Hydrogen are at -100.1°C and 100°C respectively.

Given the distinctions in gas constants for every one of the gases, they all have diverse densities. The gas having the littlest gas contains higher densities than alternate gases when the temperature is the same. Oxygen consequently has the most astounding densities while Hydrogen has the least densities.

The diagram below shows proof of the above conclusions.

References

Kerboua, Kaouther, and Oualid Hamdaoui. “Numerical estimation of ultrasonic production of hydrogen: Effect of ideal and real gas based models.” Ultrasonics sonochemistry 40 (2018): 194-200.

Timberlake, Karen C. General, organic, and biological chemistry: structures of life. Pearson Education, 2015.