Obviously, to calculation the volume/space populated by a mole of (an ideal) gas, you"ll need to specify temperature ($T$) and pressure ($P$), uncover the gas constant ($R$) value through the ideal units and also plug them all in the ideal gas equation $$PV = nRT.$$

The problem? It appears to it is in some kind of common "wisdom" all over the Internet, that one mole that gas occupies $22.4$ liters of space. But the standard problems (STP, NTP, or SATP) mentioned lack consistency over multiple sites/books. Typical claims: A mole of gas occupies,

$pu22.4 L$ in ~ STP$pu22.4 L$ at NTP$pu22.4 L$ in ~ SATP$pu22.4 L$ in ~ both STP and also NTP

Even Chem.SE is rife v the "fact" that a mole of right gas rectal $pu22.4 L$, or some expansion thereof.

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Being so completely frustrated through this situation, I made decision to calculate the volumes populated by a mole of ideal gas (based ~ above the appropriate gas equation) because that each of the 3 standard conditions; namely: traditional Temperature and Pressure (STP), common Temperature and Pressure (NTP) and Standard approximately Temperature and Pressure (SATP).

Knowing that,

STP: $pu0 ^circ C$ and $pu1 bar$NTP: $pu20 ^circ C$ and $pu1 atm$SATP: $pu25 ^circ C$ and also $pu1 bar$

And making use of the equation, $$V = frac nRTP,$$where $n = pu1 mol$, by default (since we"re talking around one mole the gas).

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I"ll draw ideal values of the gas continuous $R$ indigenous this Wikipedia table:

*

The volume inhabited by a mole the gas must be:

At STPeginalignT &= pu273.0 K,&P &= pu1 bar,&R &= pu8.3144598 imes 10^-2 together bar K^-1 mol^-1.endalignPlugging in all the values, I acquired $$V = pu22.698475 L,$$ which come a reasonable approximation, gives$$V = pu22.7 L.$$

At NTPeginalignT &= pu293.0 K,&P &= pu1 atm,&R &= pu8.2057338 imes 10^-2 together atm K^-1 mol^-1.endalignPlugging in all the values, I acquired $$V = pu24.04280003 L,$$ which come a reasonable approximation, gives $$V = pu24 L.$$

At SATPeginalignT &= pu298.0 K,&P &= pu1 bar,&R &= pu8.3144598 imes 10^-2 l bar K^-1 mol^-1.endalignPlugging in all the values, I acquired $$V = pu24.7770902 L,$$ which to a reasonable approximation, gives $$V = pu24.8 L.$$

Nowhere walk the miracle "$pu22.4 L$" number in the three situations I"ve analyzed appear. Due to the fact that I"ve viewed the "one mole occupies $pu22.4 L$ at STP/NTP" dictum so many times, I"m wondering if I"ve to let go something.

My question(s):

Did i screw up through my calculations?(If i didn"t screw up) Why is it that the "one mole occupies $pu22.4 L$" idea is for this reason widespread, despite not being close (enough) to the worths that ns obtained?