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Tyberius ♦
Tyberius ♦
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The common saying is a hold over from when STP was defined to be $\pu{273.15 K}$ and $\pu{1 atm}$. However, IUPAC changed the definition in 1982 so that $\pu{1 atm}$ became $\pu{1 bar}$. I think the main issue is a lot of educators didn't get the memo and went right along either teaching STP as $\pu{1 atm}$ or continuing with the line they were taught ("1 mole"$\pu{1 mol}$ of any gas under STP occupies $\pu{22.4 L}$") without realizing it didn't hold under the new conditions.

Just as a "proof" of this working for the old definition. \begin{align} V &=\frac{nRT}{P}\\ &=\frac{\pu{1 mol} \times \pu{8.2057338 \times 10^-2 L * atm//K * mol} \times \pu{273.15 K}}{\pu{1 atm}}\\ &=\pu{22.41396 L}\\ &\approx \pu{22.4 L} \end{align}

The common saying is a hold over from when STP was defined to be $\pu{273.15 K}$ and $\pu{1 atm}$. However, IUPAC changed the definition in 1982 so that $\pu{1 atm}$ became $\pu{1 bar}$. I think the main issue is a lot of educators didn't get the memo and went right along either teaching STP as $\pu{1 atm}$ or continuing with the line they were taught ("1 mole of any gas under STP occupies $\pu{22.4 L}$") without realizing it didn't hold under the new conditions.

Just as a "proof" of this working for the old definition. \begin{align} V &=\frac{nRT}{P}\\ &=\frac{\pu{1 mol} \times \pu{8.2057338 \times 10^-2 L * atm//K * mol} \times \pu{273.15 K}}{\pu{1 atm}}\\ &=\pu{22.41396 L}\\ &\approx \pu{22.4 L} \end{align}

The common saying is a hold over from when STP was defined to be $\pu{273.15 K}$ and $\pu{1 atm}$. However, IUPAC changed the definition in 1982 so that $\pu{1 atm}$ became $\pu{1 bar}$. I think the main issue is a lot of educators didn't get the memo and went right along either teaching STP as $\pu{1 atm}$ or continuing with the line they were taught ("$\pu{1 mol}$ of any gas under STP occupies $\pu{22.4 L}$") without realizing it didn't hold under the new conditions.

Just as a "proof" of this working for the old definition. \begin{align} V &=\frac{nRT}{P}\\ &=\frac{\pu{1 mol} \times \pu{8.2057338 \times 10^-2 L * atm//K * mol} \times \pu{273.15 K}}{\pu{1 atm}}\\ &=\pu{22.41396 L}\\ &\approx \pu{22.4 L} \end{align}

converted MathJaxe to use align for better readability
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Martin - マーチン ♦
Martin - マーチン ♦
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The common saying is a hold over from when STP was defined to be $273.15~\mathrm{K}$$\pu{273.15 K}$ and $1~\mathrm{atm}$$\pu{1 atm}$. However, IUPAC changed the definition in 1982 so that $1~\mathrm{atm}$$\pu{1 atm}$ became $1~\mathrm{bar}$$\pu{1 bar}$. I think the main issue is a lot of educators didn't get the memo and went right along either teaching STP as $1~\mathrm{atm}$$\pu{1 atm}$ or continuing with the line they were taught ("1 mole of any gas under STP occupies $22.4~\mathrm{L}$$\pu{22.4 L}$") without realizing it didn't hold under the new conditions.

Just as a "proof" of this working for the old definition.

$$V=\frac{nRT}{P}=\frac{1 \mathrm{mol}{\times}8.2057338{\times}{10}^{-2}\frac{\mathrm{L}{\cdot}\mathrm{atm}}{\mathrm{K}{\cdot}\mathrm{mol}}{\times}273.15\mathrm{K}}{1~\mathrm{atm}}=22.41396~\mathrm{L}{\approx}22.4~\mathrm{L}$$ \begin{align} V &=\frac{nRT}{P}\\ &=\frac{\pu{1 mol} \times \pu{8.2057338 \times 10^-2 L * atm//K * mol} \times \pu{273.15 K}}{\pu{1 atm}}\\ &=\pu{22.41396 L}\\ &\approx \pu{22.4 L} \end{align}

The common saying is a hold over from when STP was defined to be $273.15~\mathrm{K}$ and $1~\mathrm{atm}$. However, IUPAC changed the definition in 1982 so that $1~\mathrm{atm}$ became $1~\mathrm{bar}$. I think the main issue is a lot of educators didn't get the memo and went right along either teaching STP as $1~\mathrm{atm}$ or continuing with the line they were taught ("1 mole of any gas under STP occupies $22.4~\mathrm{L}$") without realizing it didn't hold under the new conditions.

Just as a "proof" of this working for the old definition.

$$V=\frac{nRT}{P}=\frac{1 \mathrm{mol}{\times}8.2057338{\times}{10}^{-2}\frac{\mathrm{L}{\cdot}\mathrm{atm}}{\mathrm{K}{\cdot}\mathrm{mol}}{\times}273.15\mathrm{K}}{1~\mathrm{atm}}=22.41396~\mathrm{L}{\approx}22.4~\mathrm{L}$$

The common saying is a hold over from when STP was defined to be $\pu{273.15 K}$ and $\pu{1 atm}$. However, IUPAC changed the definition in 1982 so that $\pu{1 atm}$ became $\pu{1 bar}$. I think the main issue is a lot of educators didn't get the memo and went right along either teaching STP as $\pu{1 atm}$ or continuing with the line they were taught ("1 mole of any gas under STP occupies $\pu{22.4 L}$") without realizing it didn't hold under the new conditions.

Just as a "proof" of this working for the old definition. \begin{align} V &=\frac{nRT}{P}\\ &=\frac{\pu{1 mol} \times \pu{8.2057338 \times 10^-2 L * atm//K * mol} \times \pu{273.15 K}}{\pu{1 atm}}\\ &=\pu{22.41396 L}\\ &\approx \pu{22.4 L} \end{align}

Fixed \mathrm{} tags to be around units (rather than variables); fixed temp@STP to 273.15K; Wikipedia link for STP; formatting.
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edit approved Aug 3, 2017 at 6:37
Nat
edit approved Aug 3, 2017 at 6:37
Nat
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The common saying is a hold over from when STP STP was defined to be $273$K$273.15~\mathrm{K}$ and $1$ atm$1~\mathrm{atm}$. However, IUPAC changed the definition in 1982 so that $1$ atm$1~\mathrm{atm}$ became $1$ bar$1~\mathrm{bar}$. I think the main issue is a lot of educators didn't get the memo and went right along either teaching STP as $1$ atm$1~\mathrm{atm}$ or continuing with the line they were taught ("1 mole of any gas under STP occupies 22.4L"$22.4~\mathrm{L}$") without realizing it didn't hold under the new conditions.

Just as a "proof" of this working for the old definition.

$$\mathrm{V=\frac{nRT}{P}}=\frac{1 mol\times8.2057338\times10^{-2}\frac{L*atm}{K*mol}\times273K}{1atm}=22.40165L\approx22.4L$$$$V=\frac{nRT}{P}=\frac{1 \mathrm{mol}{\times}8.2057338{\times}{10}^{-2}\frac{\mathrm{L}{\cdot}\mathrm{atm}}{\mathrm{K}{\cdot}\mathrm{mol}}{\times}273.15\mathrm{K}}{1~\mathrm{atm}}=22.41396~\mathrm{L}{\approx}22.4~\mathrm{L}$$

The common saying is a hold over from when STP was defined to be $273$K and $1$ atm. However, IUPAC changed the definition in 1982 so that $1$ atm became $1$ bar. I think the main issue is a lot of educators didn't get the memo and went right along either teaching STP as $1$ atm or continuing with the line they were taught ("1 mole of any gas under STP occupies 22.4L") without realizing it didn't hold under the new conditions.

Just as a "proof" of this working for the old definition.

$$\mathrm{V=\frac{nRT}{P}}=\frac{1 mol\times8.2057338\times10^{-2}\frac{L*atm}{K*mol}\times273K}{1atm}=22.40165L\approx22.4L$$

The common saying is a hold over from when STP was defined to be $273.15~\mathrm{K}$ and $1~\mathrm{atm}$. However, IUPAC changed the definition in 1982 so that $1~\mathrm{atm}$ became $1~\mathrm{bar}$. I think the main issue is a lot of educators didn't get the memo and went right along either teaching STP as $1~\mathrm{atm}$ or continuing with the line they were taught ("1 mole of any gas under STP occupies $22.4~\mathrm{L}$") without realizing it didn't hold under the new conditions.

Just as a "proof" of this working for the old definition.

$$V=\frac{nRT}{P}=\frac{1 \mathrm{mol}{\times}8.2057338{\times}{10}^{-2}\frac{\mathrm{L}{\cdot}\mathrm{atm}}{\mathrm{K}{\cdot}\mathrm{mol}}{\times}273.15\mathrm{K}}{1~\mathrm{atm}}=22.41396~\mathrm{L}{\approx}22.4~\mathrm{L}$$

Included the "one mole" term as well...so that the units cancel out in the equation, leaving behind Liter.
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paracetamol
paracetamol
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clarification
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Tyberius ♦
Tyberius ♦
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Tyberius ♦
Tyberius ♦
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