Proving Using Ideal Gas Law That Molar Volume At NTP Is 22.4 Litres

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Learn more about Teams Proving using ideal gas law that molar volume at NTP is 22.4 litres Ask Question Asked 7 years ago Modified 5 years ago Viewed 24k times 0 $\begingroup$

The definition of NTP as given by IUPAC is

NTP – Normal Temperature and Pressure – is defined as air at $20\ ^\circ\mathrm C$ ($\pu{293.15 K}$, $\pu{68^{\circ}F}$) and $\pu{1 atm}$ ($\pu{101.325 kN/m2}$, $101.325\ \mathrm{kPa}$, $14.7\ \mathrm{psia}$, $0\ \mathrm{psig}$, $29.92\ \mathrm{inHg}$, $407\ \mathrm{in}\ce{H2O}$, $760\ \mathrm{Torr}$).

It is also known that volume occupied by $1$ mole of gas at NTP is $\pu{22.4 L}$.

My attempt at proving the above statement,

For $1$ mole, $PV=RT$

Substituting $P=\pu{1 atm}$, $T=\pu{293 K}$, $R=0.0821\ \mathrm{L\ atm\ K^{-1}\ mol^{-1}}$, we get $V=\pu{24.05 L}$ as the molar volume.

On putting $T=\pu{273 K}$ and $P=\pu{1 bar}$ (conditions of STP), we get $V=\pu{22.2 L}$

Therefore, molar volume at STP is $\pu{22.4L}$.

Why is the above calculation in NTP condition giving wrong results? How else to prove that molar volume at NTP is ${22.4\ \mathrm L}$?

• gas-laws

Share Cite Improve this question Follow edited Jun 11, 2020 at 10:20 CommunityBot 1 asked Jun 15, 2017 at 2:04 ArishtaArishta 4,19599 gold badges4141 silver badges5858 bronze badges $\endgroup$ 1

• $\begingroup$ see the whole article and the linked section in particular en.wikipedia.org/wiki/… $\endgroup$ – MaxW Commented Oct 6, 2017 at 15:56

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Sorted by: Reset to default Highest score (default) Date modified (newest first) Date created (oldest first) 2 $\begingroup$

The issue is that one mole of a gas at NTP should not be 22.4 L based on the ideal gas. This is only true for a gas at STP. The key difference between the two conditions is they are defined by different temperatures (STP is for 273 K while NTP is for 293 K).

They are also different in that the IUPAC now defines STP with respect to 1 bar while NTP is defined with respect to 1 atm.

See The Engineering ToolBox for more info.

Share Cite Improve this answer Follow edited Jun 20, 2019 at 13:37 andselisk♦ 38.4k1414 gold badges133133 silver badges222222 bronze badges answered Jun 15, 2017 at 2:20 Tyberius♦Tyberius 11.8k1010 gold badges4343 silver badges8686 bronze badges $\endgroup$ 4

• 2 $\begingroup$ And to add further point, the pressure is one bar, not one atm. So at STP it would be more correctly $\pu{22.7L}$. $\endgroup$ – Pritt says Reinstate Monica Commented Jun 15, 2017 at 2:37
• $\begingroup$ @PrittBalagopal good point, I will make note of that explicitly. $\endgroup$ – Tyberius ♦ Commented Jun 15, 2017 at 2:54
• $\begingroup$ You should use 298K for NTP! $\endgroup$ – Vaibhav Dixit Commented Jun 15, 2017 at 8:15
• 1 $\begingroup$ @Vaibhav Dixit all the definitions I have seen for NTP define it at 20C or 293K. $\endgroup$ – Tyberius ♦ Commented Jun 15, 2017 at 19:52

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