ايووگاڊرو مستقل

ايووگاڊرو مستقل; Avogadro constant
	; اميڊيو ايووگاڊرو, جن جي نالي تي مستقل جو نالو رکيو ويو آهي.
عام علامتون	NA, L
SI اڪائي	mol−1
صحيح قدر
باهمي تناسب مول	1023 × 6.02214076

ايووگاڊرو مستقل (Avogadro's Constant)، عام طور تي N_A يا L جي طور تي ظاهر ڪيو ويندو آهي، اڪائين جي نظام جو وضاحت ڪندڙ هڪ مستقل آهي، هن مستقل جي قدر (10²³ × 6.0221407) mol⁻¹ آهي، جڏهن مول سان باهمي تناسب ۾ ظاهر ڪيو ويندو آهي.^[1] اهو ڪنهن به شي جي نموني ۾ مول جي تعداد مطابق مادي ۾ موجود ذرڙن جي انگ جو تناسب بيان ڪري ٿو، جتي ذرڙا ڪهڙا به نامزد بنيادي وجود، جهڙوڪ ماليڪيول، ايٽم، آئن، آئن جا جوڙا، وغيره ٿي سگهن ٿا. جڏهن مول جي لحاظ کان ظاهر ڪيو ويندو آهي ته هن مستقل جي عددي قدر کي ايووگاڊرو نمبر طور سڃاتو وڃي ٿو، عام طور تي N₀ جي طور تي ظاهر ڪيو ويندو آهي. ايووگاڊرو نمبر هڪ پورو انگ آهي جيڪو ڪنهن به مادي جي هڪ مول ۾ ذرڙن جي تعداد جي برابر آهي (مول جي تعريف سان)، تاريخي طور تي اڪائين جي نظام جي 2019ع جي نظرثاني کان اڳ 12 گرام ڪاربن-12 (₁₂C) ۾ ايٽمن جي تعداد جي تجرباتي تعين مان نڪتل آهي، يعني گرام-کان-ڊالٽن جي ماس جي اڪائي جو تناسب، g/Da. مستقل ۽ نمبر، ٻنهي جو نالو اطالوي طبيعيات دان ۽ ڪيميادان، اميڊيو ايووگاڊرو جي نالي تي رکيو ويو آهي.

ايووگاڊرو مستقل کي هڪ تناسبي عنصر طور استعمال ڪيو ويندو آهي جڏهن ته مادي X جي نموني ۾ مادي n(X) جي مقدار کي بنيادي وجودن N(X) جي لاڳاپيل تعداد سان ڳنڍيو ويندو آهي: $N (X)$ :

n(\mathrm {X} )={\frac {N(\mathrm {X} )}{N_{\mathrm {A} }}}

ايووگاڊرو مستقل N_A اهو عنصر پڻ آهي جيڪو مادي جي هڪ ذرڙي جي سراسري ماس m(X) کي ان جي مولر ماس M(X) ۾ تبديل ڪري ٿو. يعني، M(X) = m(X) ⋅ NA. هن مساوات کي 12C تي لاڳو ڪرڻ سان بلڪل 12 Da جي ايٽمي ماس ۽ 12 g/mol جي مولر ماس سان ايووگاڊرو ڪانسٽنٽ لاءِ هيٺ ڏنل تعلق پيدا ٿئي ٿو (ٻيهر ترتيب ڏيڻ کان پوءِ): NA = (g/Da) mol−1، جيڪو ايووگاڊرو نمبر N0 = g/Da ٺاهيندو آهي. تاريخي طور تي، اهو بلڪل صحيح هو، پر SI جي 2019 جي نظرثاني کان وٺي، تعلق هاڻي صرف تقريبن آهي، جيتوڻيڪ برابري اڃا تائين اعلي درستگي سان فرض ڪري سگهجي ٿي.

مستقل NA هڪ مادي جي مولر حجم (في مول حجم) کي پڻ ڳنڍيندو آهي سراسري مقدار جيڪو ان جي ذرڙن مان هڪ جي نالي سان قبضو ڪيو ويو آهي، جڏهن ٻئي حجم جي ساڳين يونٽن ۾ ظاهر ڪيا ويا آهن. مثال طور، جيئن ته عام حالتن ۾ پاڻي جو مولر حجم تقريباً 18 mL/mol آهي، پاڻي جي هڪ ماليڪيول پاران قبضو ڪيل حجم تقريباً 18/(6.022×1023) mL، يا تقريباً 0.030 nm3 (ڪعبي نانو ميٽر) آهي. هڪ ڪرسٽل مادي لاءِ، N0 هڪ ڪرسٽل جي مقدار کي ورجائيندڙ يونٽ سيلز جي هڪ مول جي مقدار سان، هڪ واحد سيل جي مقدار سان (ٻئي ساڳئي يونٽن ۾) سان لاڳاپيل ڪري ٿو.

هڪ ڪرسٽل مادي لاءِ، N0 هڪ ڪرسٽل جي مقدار کي هڪ مول سان ڳنڍي ٿو. ورجائيندڙ يونٽ انٽيٽي (سيلز) جي قيمت، هڪ واحد انٽيٽي (سيلز) جي مقدار سان (ٻئي ساڳئي يونٽن ۾).

تعريف

ايووگاڊرو ڪانسٽنٽ تاريخي طور تي مول جي پراڻي تعريف مان نڪتل هو جيئن 12 گرام ڪاربان-12 (12C) ۾ مادي جي مقدار. هن پراڻي تعريف موجب، mol−1 (ايووگاڊرو نمبر) ۾ ايووگاڊرو ڪانسٽنٽ جي عددي قدر هڪ جسماني ڪانسٽنٽ هئي جنهن کي تجرباتي طور تي طئي ڪرڻو پوندو هو.

ڪاربان-12، M(12C)، ۽ ان جي ايٽمي ماس، m(12C) جي مولر ماس سان ايووگاڊرو ڪانسٽنٽ جو تاريخي تعلق هيٺ ڏنل مساوات ۾ ظاهر ڪري سگهجي ٿو:

The Avogadro constant was historically derived from the old definition of the mole as the amount of substance in 12 grams of carbon-12 (¹²C). By this old definition, the numerical value of the Avogadro constant in mol⁻¹ (the Avogadro number) was a physical constant that had to be determined experimentally.

The historical relationship of the Avogadro constant to the molar mass of carbon-12, $M (12 C)$ , and its atomic mass, $m (12 C)$ , can be expressed in the following equation: $N_{\text{A}}={\frac {M(^{12}{\text{C}})}{m(^{12}{\text{C}})}}={\frac {12{\text{ g/mol}}}{12{\text{ Da}}}}={\frac {\text{g/mol}}{\text{Da}}}=({\text{g/Da}}){\text{ mol}}^{-1}$ Thus, $N 0$ , the numerical value of $N A$ , was equal to the number of daltons in a gram (g/Da), where the dalton is defined as سانچو:Sfrac of the mass of a ¹²C atom.

The redefinition of the mole in 2019, as being the amount of substance consisting of exactly 6.02214076×10²³ elementary entities, means that the mass of 1 mole of a substance is now exactly the product of the Avogadro number and the average mass of one of the entities involved. The dalton, however, is still defined as سانچو:Sfrac of the mass of a ¹²C atom, which must be determined experimentally and is known only with finite accuracy. Thus, prior experiments that aimed to determine the numerical value of the Avogadro constant when expressed in reciprocal moles—i.e. the Avogadro number (now numerically fixed)—are re-interpreted as measurements of the numerical value in grams of the dalton.

By the old definition of mole, the numerical value of the mass of one mole of a substance expressed in grams (i.e., its molar mass in g/mol or kg/kmol), was precisely equal to the average mass of one particle expressed in daltons. With the new definition, this numerical equivalence is no longer exact, as it is affected by the uncertainty in the value of the gram-to-dalton (g/Da) mass-unit ratio. However, it may still be assumed for all practical purposes. For example, the average mass of one molecule of water is about 18.0153 daltons, and an amount of one mole of water has a corresponding macroscopic mass of about 18.0153 grams. Also, the Avogadro number is the approximate number of nucleons (protons and neutrons) in one gram of ordinary matter.

An amount of substance consisting of just a single elementary entity might be thought of as an "elementary amount", analogous to the elementary charge, $e$ . Letting $n a$ denote this elementary amount, then 1 mol = $N 0 n a$ , with the mole defined such that $N A = N 0$ /mol, which can be rearranged as 1 mol = $N 0 / N A$ . Thus, $n a = 1/ N A$ , the reciprocal of the Avogadro constant. The fundamental definition of the Avogadro constant itself is therefore one per elementary amount ( $N A = 1/ n a$ ), independent of any macroscopic base unit chosen for the physical quantity. (Since there is an aggregate of an Avogadro number of elementary entities in one mole, the Avogadro constant can also be expressed (in terms of the mole) as an Avogadro number per mole—but this is not its "definition".) The Avogadro constant, a well-defined quantity value (with dimension 1/N), independent of the mole, is therefore a bona fide defining constant for the 2019 redefinition of the mole.

Introducing $n a$ in place of $1/ N A$ , means that $n (X) = N (X) n a$ —amount of substance is an aggregate of $N (X)$ elementary entities—which is easier to comprehend than $N (X)$ "reciprocal Avogadro constants". Also the molar mass is then $M (X) = m (X)/ n a$ —the entity mass per entity, which is self-evident.

In older literature, the Avogadro number was also denoted سانچو:Mvar, although that conflicts with the symbol for number of particles in statistical mechanics.

تاريخ

تصور جي ابتداء

ايووگاڊرو مستقل جو نالو اطالوي سائنسدان، اميڊيو ايووگاڊرو (1776-1856)، جي نالي تي رکيو ويو، جيڪو سال 1811ع ۾ پهرين ڀيرو تجويز ڪيو ته،

"هڪ گئس (ڪنهن نوعيت جي گئس) جو حجم (هڪ ڏنل دٻاء ۽ گرميء پد تي)، هن ۾ موجود ايٽمن يا ماليڪيولن جي تعداد سان سڌو تناسب رکي ٿو، گئس جي نوعيت ڪهڙي به هو."

ايووگاڊرو جو مفروضو سندس وفات کان چار سال پوءِ مشهور ٿيو، جڏهن اسٽينسلائو ڪينيزارو 1860ع ۾ ڪارلسروهي ڪانگريس ۾ ايووگاڊرو جي ڪم جي وڪالت ڪئي.^[2]

ايووگاڊرو نمبر 1909ع ۾، فزڪس دان جين پيرين پاران ٺاهيو ويو، جنهن ان کي بلڪل 32 گرام آڪسيجن گئس ۾ ماليڪيولن جي تعداد جي طور تي بيان ڪيو.

هن تعريف جو مقصد هڪ مادي جي هڪ مول جي ماس کي گرام ۾ ڪرڻ هو. عددي طور تي هائيڊروجن ايٽم جي ماس جي نسبت هڪ ماليڪيول جي ماس جي برابر هجي. جيڪو ايٽمي ماس جي قدرتي يونٽ هو، ۽ آڪسيجن جي ايٽمي ماس جي 1/16 جي برابر سمجهيو ويو (مخصوص تناسب جي قانون موجب).

پهريون ماپ

The value of Avogadro's number (not yet known by that name) was first obtained indirectly by Josef Loschmidt in 1865, by estimating the number of particles in a given volume of gas. This value, the number density $n 0$ of particles in an ideal gas, is now called the Loschmidt constant in his honor, and is related to the Avogadro constant, $N A$ , by

n_{0}={\frac {p_{0}N_{\rm {A}}}{R\,T_{0}}},

where $p 0$ is the pressure, $R$ is the gas constant, and $T 0$ is the absolute temperature. Because of this work, the symbol $L$ is sometimes used for the Avogadro constant, and, in German literature, that name may be used for both constants, distinguished only by the units of measurement. (However, $N A$ should not be confused with the entirely different Loschmidt constant in English-language literature.)

Perrin himself determined the Avogadro number, which he called "Avogadro's constant" (constante d'Avogadro), by several different experimental methods. He was awarded the 1926 Nobel Prize in Physics, largely for this work.

The electric charge per mole of electrons is a constant called the Faraday constant and has been known since 1834, when Michael Faraday published his works on electrolysis. In 1910, Robert Millikan with the help of Harvey Fletcher obtained the first measurement of the charge on an electron. Dividing the charge on a mole of electrons by the charge on a single electron provided a more accurate estimate of the Avogadro number.

SI نظام جي 1971ع واري تعريف

In 1971, in its 14th conference, the International Bureau of Weights and Measures (BIPM) decided to regard the amount of substance as an independent dimension of measurement, with the mole as its base unit in the International System of Units (SI). Specifically, the mole was defined as the amount of a substance that contains as many elementary entities as there are atoms in 12 grams (0.012 kilograms) of carbon-12 (¹²C). Thus, in particular, an amount of one mole of carbon 12 had a corresponding mass that was exactly 12 grams of that element.

By this definition, one mole of any substance contained exactly as many elementary entities as one mole of any other substance. However, this number $N 0$ was a physical constant that had to be experimentally determined since it depended on the mass (in grams) of one atom of ¹²C, and therefore, it was known only to a limited number of decimal digits. The common rule of thumb that "one gram of matter contains $N 0$ nucleons" was exact for carbon-12, but slightly inexact for other elements and isotopes.

In the same conference, the BIPM also named $N A$ (the factor that related the amount of a substance to the corresponding number of particles) the "Avogadro constant". However, the term "Avogadro number" continued to be used, especially in introductory works. As a consequence of this definition, $N A$ was not a pure number, but had the quantity dimension of reciprocal of amount of substance (N⁻¹).

2019ع ۾ SI نظام پاران ٻيهر تعريف

اصل مضمون جي لاءِ ڏسو 2019 revision of the SI

In its 26th Conference, the BIPM adopted a different approach: effective 20 May 2019, it defined the Avogadro constant $N A$ as the exact value 6.02214076×10²³ mol-1, thus redefining the mole as exactly 6.02214076×10²³ constituent particles of the substance under consideration. One consequence of this change is that the mass of a mole of ¹²C atoms is no longer exactly 0.012 kg. On the other hand, the dalton, Da (سانچو:Aka unified atomic mass unit, u), remains unchanged as سانچو:Sfrac of the mass of ¹²C. Thus, the molar mass constant remains very close to but no longer exactly equal to 1 g/mol, although the difference (4.5×10⁻¹⁰ in relative terms, as of March 2019) is insignificant for all practical purposes.

ٻين مستقلن سان تعلق

ايوگاڊرو مستقل ( $N A$ )ٻين طبيعي مستقلن ۽ خاصيتن سان لاڳاپيل آهي.

اهو مولر گيس مستقل (R) ۽ بولٽزمان مستقل ( $k B$ ) کي ڳنڍي ٿو، جيڪو SI ۾ بلڪل 1.380649×10−23 جولز في ڪيلون طور بيان ڪيو ويو آهي:
R= kB NA = 8.314462618.. J⋅mol−1⋅K−1
اهو فيراڊي مستقل F ۽ ابتدائي چارج e کي ڳنڍي ٿو، جيڪو SI ۾ بلڪل بيان ڪيو ويو آهي: اهو فيراڊي مستقل F ۽ ابتدائي چارج e سان لاڳاپيل آهي، جيڪو SI ۾ بلڪل 1.602176634×10−19 ڪولمبس طور بيان ڪيو ويو آهي:
1.602176634×10⁻¹⁹ coulombs
F = e N_A = 9.648533212...×10⁴ C⋅mol⁻¹
$F = e N A =$
F = e NA = 9.648533212...×104 C⋅mol−1
1.602176634×10⁻¹⁹ coulombs:
F = e N_A = 9.648533212...×10⁴ C⋅mol
اهو مولر ماس مستقل (M_u ۽ ايٽمي ماس مستقل (m_u) کي ڳنڍي ٿو: هن وقت
1.66053906892(52)×10⁻²⁷ kg:
M_u = m_u N_A = 1.00000000105(31)×10⁻³ kg⋅mol⁻¹

$N A$
$k B$
$R = k B N A =$
1.380649×10⁻²³ J/K:
R = k_B
N_A = 8.314462618... J⋅mol⁻¹⋅K⁻¹
$M u$
$m u$
$M u = m u N A =$
1.66053906892(52)×10⁻²⁷ kg:
m_u N_A = 1.00000000105(31)×10⁻³ ^k kg⋅mol⁻¹

Avogadro constant N_A is related to other physical constants and properties.

It relates the molar gas constant R and the Boltzmann constant k_B, which in the SI is defined to be exactly 1.380649×10⁻²³ J/K:
R = k_B N_A = 8.314462618... J⋅mol⁻¹⋅K⁻¹
It relates the Faraday constant F and the elementary charge e, which in the SI is defined as exactly
It relates the molar mass constant

The Avogadro constant $N A$ is related to other physical constants and properties.

It relates the molar gas constant سانچو:Mvar and the Boltzmann constant $k B$ , which in the SI is defined to be exactly :
$R = k B N A =$
It relates the Faraday constant and the elementary charge , which in the SI is defined as exactly :
$F = e N A =$
It relates the molar mass constant $M u$ and the atomic mass constant $m u$ currently
$M u = m u N A =$

تفصيل

Avogadro constant $N A$ is also the factor that converts the average mass $m (X)$ of one particle of a substance to its molar mass $M (X)$ . That is, $M (X) = m (X) \cdot N A$ . Applying this equation to ¹²C with an atomic mass of exactly 12 Da and a molar mass of 12 g/mol yields (after rearrangement) the following relation for the Avogadro constant: $N A$ = (g/Da) mol⁻¹, making the Avogadro number $N 0$ = g/Da. Historically, this was precisely true, but since the 2019 revision of the SI, the relation is now merely approximate, although equality may still be assumed with high accuracy.

The constant $N A$ also relates the molar volume (the volume per mole) of a substance to the average volume nominally occupied by one of its particles, when both are expressed in the same units of volume. For example, since the molar volume of water in ordinary conditions is about 18 mL/mol, the volume occupied by one molecule of water is about 18/(6.022×10²³) mL, or about 0.030 nm3 (cubic nanometres). For a crystalline substance, $N 0$ relates the volume of a crystal with one mole worth of repeating unit cells, to the volume of a single cell (both in the same units).

پڻ ڏسو

ٻاهريان ڳنڍڻا

1996 definition of the Avogadro constant from the IUPAC Compendium of Chemical Terminology ("Gold Book")
Some Notes on Avogadro's Number, 6.022×10²³ (historical notes)
An Exact Value for Avogadro's Number – American Scientist
Avogadro and molar Planck constants for the redefinition of the kilogram
Murrell, John N. (2001). "Avogadro and His Constant". Helvetica Chimica Acta 84 (6): 1314–1327. doi:10.1002/1522-2675(20010613)84:6<1314::AID-HLCA1314>3.0.CO;2-Q.
Scanned version of "Two hypothesis of Avogadro", 1811 Avogadro's article, on BibNum

حوالا

↑ Newell, David B.; Tiesinga, Eite (2019). The International System of Units (SI). NIST Special Publication 330. Gaithersburg, Maryland: National Institute of Standards and Technology. doi:10.6028/nist.sp.330-2019. https://www.nist.gov/si-redefinition/meet-constants.
↑ "Stanislao Cannizzaro | Science History Institute". Science History Institute. حاصل ڪيل June 2, 2022.

[SI20192-1] Newell, David B.; Tiesinga, Eite (2019). The International System of Units (SI). NIST Special Publication 330. Gaithersburg, Maryland: National Institute of Standards and Technology. doi:10.6028/nist.sp.330-2019. https://www.nist.gov/si-redefinition/meet-constants.

[2] "Stanislao Cannizzaro | Science History Institute". Science History Institute. حاصل ڪيل June 2, 2022.

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