Gas density and PV=nRT, the ideal gas law

What is gas density and how does it fit mathematically into PV=nRT? Also included are two practice problems using d=mP/nRT and d=MP/RT including molar mass and identifying the gas.
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-More on gas density--Wikipedia July 2019-
The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume: ρ = m/V
where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume,[2] although this is scientifically inaccurate - this quantity is more specifically called specific weight.
For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser.
To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water.
The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid. This causes it to rise relative to more dense unheated material.
The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.
An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interactions are perfectly elastic collisions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.
In most usual conditions (for instance at standard temperature and pressure), most real gases behave qualitatively like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases, and some heavier gases like carbon dioxide can be treated like ideal gases within reasonable tolerances.[1] Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure,[1] as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them. One mole of an ideal gas has a volume of 22.710947(13) litres[2] at standard temperature and pressure (a temperature of 273.15 K and an absolute pressure of exactly 105 Pa) as defined by IUPAC since 1982.
WIKIPEDIA Jan 18 2019

[@aarishhanif1837]

Finally, someone talks about the relationships of density. Thanks!

[@adnonalumbert9008]

agreed

[@smartscience5305]

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[@CrashChemistryAcademy]

This is for a chemistry class. It could easily be given in a physics class as well. It depends on your school/teacher, but usually it is chemistry.

[@smartscience5305]

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[@smartscience5305]

Hi again, we'll gonna take this lesson in grade 10 or 11 or 12 or college?

[@CrashChemistryAcademy]

usually grade 10, although not all teachers would teach it--it depends on the level of the introductory chem class. The higher the level, the more likely it will be taught.

[@smartscience5305]

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[@adnonalumbert9008]

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[@uveselic200]

Excellent! May I ask which "blackboard" software do you use for explanations. Looking for suggestions for me for my students

[@CrashChemistryAcademy]

I use microsoft powerpoint. It has a lot of drawing and animation features.

[@হিরোআলম-ণ৮ভ]

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[@marigeo24]

@3:14 how the value for R differed based on wether the pressure was measured in atm vs. kPa, how can we convert between units of measurement? In other words, how did you know that “under these conditions, the pressure would be 101.3 kPa”? Or better, what can I search on KZbin to find videos explaining this? To add on to this: If you’re given the values for R, V, T, and n, which give you a value of 101.3 for P, but you don’t know the unit of measurement, how do you know it’s kPa rather than atm?

[@CrashChemistryAcademy]

I think this video should give you your answers kzbin.info/www/bejne/f5Tbp2uolql6eLM

[@marigeo24]

@@CrashChemistryAcademy So from what I understand, no matter how high or low the atm/kPa for a given ideal gas, the rest of the variables including R will be proportional to it (the given pressure), in the same ratios. In other words, you either have an R of 0.082 when using atm, or 8.314 when using kPa, no matter what the exact values for P, V, N, and T happen to be for that problem. So we can just plug in either of the two Rs depending on which measurement of pressure is being used. Did I understand correctly?

[@CrashChemistryAcademy]

Yes that is correct!

[@bubbahotep6316]

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[@TechnicalGamerDino99]

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[@pauldolinko9905]

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[@chemistfatimasmartscientis3923]

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[@ааа-п4н5ч]

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[@bobbleheadgary]

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[@minniemouse7348]

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[@MutoniRitah18]

Thnx so much

[@CrashChemistryAcademy]

You're welcome! Thanks for watching.

[@Sunita73-cx5vb]

Is kg/L = kg/m³

[@CrashChemistryAcademy]

No. There are 1000 g in 1 kg, there 1000 L in 1 m^3. So 1 g/L = 1 kg/m^3. And 1 kg/L = 1000 kg/m^3.

[@Sunita73-cx5vb]

@@CrashChemistryAcademy sir i used D = PM/RT D= kpa*kg/mol whole divided by Lkpa/mol*k * k After cancelling kpa , mol, K I got kg/l But si unit is kg/m³ so what do I do Sir can u help me by Commenting or making a video on it Sir I am very thankful to you because you replied me on every comment ❤

[@CrashChemistryAcademy]

the relationship between kg/L and kg/m^3 is 1:1000, so you multiply your amount of kg/L by 1000 to get the amount of kg/m^3

[@Sunita73-cx5vb]

Si unit of density is kg/m³ by MP/RT how plzz tell

[@CrashChemistryAcademy]

It depends on the unit used for R. I use units for R that result in density expressed in g/L, which is a common way to express gas density. If you use R with m³ instead of L, then you would have to express molar mass as kg/mol in order to get to kg/m³. If you notice that there are 1000 g in 1 kg, and there are 1000 L in 1 m³, that means 1 g/L = 1 kg/m³. So whatever density you get from the math that is expressed as g/L, you can use the same value to express it as kg/m³. So for example 3.07 g/L = 3.07 kg/m³, etcetera.

[@Sunita73-cx5vb]

@@CrashChemistryAcademy when I solved the equation I got kg/L so how can i make it kg/m³

[@CrashChemistryAcademy]

What unit for R are you using?

[@Sunita73-cx5vb]

@@CrashChemistryAcademy kpa/mol.k

[@CrashChemistryAcademy]

Your unit is missing volume. The R you gave must have a volume unit (usually liters) in the numerator.

[@returnofthemomos]

First

[@CrashChemistryAcademy]

Thanks Owen, wherever you are...