Van der Waals yarıçapı
| Element | yarıçap (Å) |
|---|---|
| Hidrojen | 1.2 (1.09) |
| Karbon | 1.7 |
| Azot | 1.55 |
| Oksijen | 1.52 |
| flor | 1.47 |
| Fosfor | 1.8 |
| Kükürt | 1.8 |
| Klor | 1.75 |
| Bakır | 1.4 |
| Bondi'nin derlemesinden alınan Van der Waals yarıçapı (1964).
| |
Bir atomun van der Waals yarıçapı, rw, başka bir atom için en yakın yaklaşımın mesafesini temsil eden hayali bir sert kürenin yarıçapıdır. 1910 Nobel Fizik Ödülü'nü kazanan Johannes Diderik van der Waals'ın adını aldı, çünkü atomların sadece noktalar olmadığını tanıyan ve boyutlarının fiziksel sonuçlarını van der Waals durum denklemi ile gösteren ilk kişi oldu.
Van der Waals hacmi
Atomik hacim veya moleküler hacim olarak da adlandırılan van der Waals hacmi, Vw, van der Waals yarıçapıyla en doğrudan ilişkili olan atomik özelliktir. Tek bir atom (veya molekül) tarafından "işgal edilen" hacimdir. Van der Waals hacmi, van der Waals yarıçapları (ve moleküller için atomlar arası mesafeler ve açılar) biliniyorsa hesaplanabilir. Tek bir atom için, yarıçapı atomun van der Waals yarıçapı olan bir kürenin hacmidir:
- .
![{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}}](data:image/svg+xml; charset=utf-8; profile="https://www.mediawiki.org/wiki/Specs/SVG/1.0.0";base64,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)
Bir molekül için, van der Waals yüzeyi tarafından çevrelenen hacimdir. Bir molekülün van der Waals hacmi her zaman kurucu atomların van der Waals hacimlerinin toplamından daha küçüktür: atomların kimyasal bağlar oluşturduklarında "üst üste geldiği" söylenebilir.
Bir atomun veya molekülün van der Waals hacmi ayrıca gazlar üzerinde deneysel ölçümlerle, özellikle van der Waals sabiti b, polarizasyon a veya molar refraktivite A'dan belirlenebilir. Her üç durumda da, makroskopik örneklerde ölçümler yapılır ve sonuçların molar miktar olarak ifade edilmesi normaldir. Tek bir atomun veya molekülün van der Waals hacmini bulmak için Avogadro sabiti NA'ya bölünmek gerekir.
Molar van der Waals hacmi, maddenin molar hacmi ile karıştırılmamalıdır. Genel olarak, normal laboratuvar sıcaklıklarında ve basınçlarında, bir gazın atomları veya molekülleri, gaz hacminin yaklaşık 1⁄1000'ini işgal eder, geri kalanı boş alandır. Bu nedenle, sadece atomlar veya moleküller tarafından işgal edilen hacmi sayan molar van der Waals hacmi, standart sıcaklık ve basınçta bir gaz için molar hacminden yaklaşık 1000 kat daha küçüktür.
Van der Waals yarıçapı
Aşağıdaki tabloda elementler için Van der Waals yarıçapları gösterilmektedir. Aksi belirtilmedikçe, veriler Wolfram Research, Inc.'den Mathematica'nın ElementData işlevi tarafından verilir. Değerler picometredir (pm veya 1×10−12 m). Yarıçap arttıkça kutunun gölgesi kırmızıdan sarıya değişir; gri veri eksikliğini gösterir.
| Grub (kolon) |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |
| Periyot (satır ) |
|||||||||||||||||||
| 1 | H 110[1] or 120 |
He 140 | |||||||||||||||||
| 2 | Li 182 |
Be 153[2] |
B 192[2] |
C 170 |
N 155 |
O 152 |
F 147 |
Ne 154 | |||||||||||
| 3 | Na 227 |
Mg 173 |
Al 184[2] |
Si 210 |
P 180 |
S 180 |
Cl 175 |
Ar 188 | |||||||||||
| 4 | K 275 |
Ca 231[2] |
Sc |
Ti |
V |
Cr |
Mn |
Fe |
Co |
Ni 163 |
Cu 140 |
Zn 139 |
Ga 187 |
Ge 211[2] |
As 185 |
Se 190 |
Br 185 |
Kr 202 | |
| 5 | Rb 303[2] |
Sr 249[2] |
Y |
Zr |
Nb |
Mo |
Tc |
Ru |
Rh |
Pd 163 |
Ag 172 |
Cd 158 |
In 193 |
Sn 217 |
Sb 206[2] |
Te 206 |
I 198 |
Xe 216 | |
| 6 | Cs 343[2] |
Ba 268[2] |
* |
Hf |
Ta |
W |
Re |
Os |
Ir |
Pt 175 |
Au 166 |
Hg 155 |
Tl 196 |
Pb 202 |
Bi 207[2] |
Po 197[2] |
At 202[2] |
Rn 220[2] | |
| 7 | Fr 348[2] |
Ra 283[2] |
** |
Rf |
Db |
Sg |
Bh |
Hs |
Mt |
Ds |
Rg |
Cn |
Nh |
Fl |
Mc |
Lv |
Ts |
Og | |
| Lantanitler | * |
La |
Ce |
Pr |
Nd |
Pm |
Sm |
Eu |
Gd |
Tb |
Dy |
Ho |
Er |
Tm |
Yb |
Lu | |||
| Aktinit | ** |
Ac |
Th |
Pa |
U 186 |
Np |
Pu |
Am |
Cm |
Bk |
Cf |
Es |
Fm |
Md |
No |
Lr | |||
Belirleme yöntemleri
Van der Waals yarıçapları, gazların mekanik özelliklerinden (orijinal yöntem), kritik noktadan, kristallerdeki bağlanmamış atom çiftleri arasındaki atomik mesafe ölçümlerinden veya elektriksel veya optik özelliklerin ölçümlerinden (polarizasyon ve molar kırılma) belirlenebilir. Bu çeşitli yöntemler, van der Waals yarıçapı için benzer (1–2 Å, 100–200 pm) ancak aynı olmayan değerler verir. Van der Waals yarıçaplarının tablo değerleri, farklı deneysel değerlerin ağırlıklarını ortalaması alınarak elde edilir ve bu nedenle farklı tablolar, aynı atomun van der Waals yarıçapı için genellikle farklı değerlere sahip olacaktır. Gerçekten de, van der Waals yarıçapının her durumda atomun sabit bir özelliği olduğunu varsaymak için bir neden yoktur: aksine, herhangi bir durumda atomun belirli kimyasal ortamına göre değişme eğilimi gösterir.
Van der Waals durum denklemi
Van der Waals durum denklemi, gerçek gazların davranışını açıklamak için ideal gaz yasasının en basit ve en iyi bilinen modifikasyonudur:
- ,
![{\displaystyle \left(p+a\left({\frac {n}{\tilde {V}}}\right)^{2}\right)({\tilde {V}}-nb)=nRT}](data:image/svg+xml; charset=utf-8; profile="https://www.mediawiki.org/wiki/Specs/SVG/1.0.0";base64,<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="33.129ex" height="7.509ex" style="vertical-align: -3.171ex;" viewBox="0 -1867.7 14264 3233.2" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title">
<title id="MathJax-SVG-1-Title">{\displaystyle \left(p+a\left({\frac {n}{\tilde {V}}}\right)^{2}\right)({\tilde {V}}-nb)=nRT}</title>
<defs aria-hidden="true">
<path stroke-width="1" id="E1-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path>
<path stroke-width="1" id="E1-MJMATHI-70" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path>
<path stroke-width="1" id="E1-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path>
<path stroke-width="1" id="E1-MJMATHI-61" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path>
<path stroke-width="1" id="E1-MJMATHI-6E" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path>
<path stroke-width="1" id="E1-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path>
<path stroke-width="1" id="E1-MJMAIN-7E" d="M179 251Q164 251 151 245T131 234T111 215L97 227L83 238Q83 239 95 253T121 283T142 304Q165 318 187 318T253 300T320 282Q335 282 348 288T368 299T388 318L402 306L416 295Q375 236 344 222Q330 215 313 215Q292 215 248 233T179 251Z"></path>
<path stroke-width="1" id="E1-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path>
<path stroke-width="1" id="E1-MJSZ3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path>
<path stroke-width="1" id="E1-MJSZ3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path>
<path stroke-width="1" id="E1-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path>
<path stroke-width="1" id="E1-MJSZ4-28" d="M758 -1237T758 -1240T752 -1249H736Q718 -1249 717 -1248Q711 -1245 672 -1199Q237 -706 237 251T672 1700Q697 1730 716 1749Q718 1750 735 1750H752Q758 1744 758 1741Q758 1737 740 1713T689 1644T619 1537T540 1380T463 1176Q348 802 348 251Q348 -242 441 -599T744 -1218Q758 -1237 758 -1240Z"></path>
<path stroke-width="1" id="E1-MJSZ4-29" d="M33 1741Q33 1750 51 1750H60H65Q73 1750 81 1743T119 1700Q554 1207 554 251Q554 -707 119 -1199Q76 -1250 66 -1250Q65 -1250 62 -1250T56 -1249Q55 -1249 53 -1249T49 -1250Q33 -1250 33 -1239Q33 -1236 50 -1214T98 -1150T163 -1052T238 -910T311 -727Q443 -335 443 251Q443 402 436 532T405 831T339 1142T224 1438T50 1716Q33 1737 33 1741Z"></path>
<path stroke-width="1" id="E1-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path>
<path stroke-width="1" id="E1-MJMATHI-62" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path>
<path stroke-width="1" id="E1-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path>
<path stroke-width="1" id="E1-MJMATHI-52" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path>
<path stroke-width="1" id="E1-MJMATHI-54" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z"></path>
</defs>
<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true">
 <use xlink:href="#E1-MJSZ4-28"></use>
<g transform="translate(792,0)">
 <use xlink:href="#E1-MJMATHI-70" x="0" y="0"></use>
 <use xlink:href="#E1-MJMAIN-2B" x="725" y="0"></use>
 <use xlink:href="#E1-MJMATHI-61" x="1726" y="0"></use>
<g transform="translate(2255,0)">
 <use xlink:href="#E1-MJSZ3-28"></use>
<g transform="translate(736,0)">
<g transform="translate(120,0)">
<rect stroke="none" width="889" height="60" x="0" y="220"></rect>
 <use xlink:href="#E1-MJMATHI-6E" x="144" y="676"></use>
<g transform="translate(60,-917)">
 <use xlink:href="#E1-MJMATHI-56" x="0" y="0"></use>
 <use xlink:href="#E1-MJMAIN-7E" x="255" y="577"></use>
</g>
</g>
</g>
 <use xlink:href="#E1-MJSZ3-29" x="1866" y="-1"></use>
 <use transform="scale(0.707)" xlink:href="#E1-MJMAIN-32" x="3680" y="1665"></use>
</g>
</g>
 <use xlink:href="#E1-MJSZ4-29" x="6104" y="0"></use>
 <use xlink:href="#E1-MJMAIN-28" x="7064" y="0"></use>
<g transform="translate(7453,0)">
 <use xlink:href="#E1-MJMATHI-56" x="0" y="0"></use>
 <use xlink:href="#E1-MJMAIN-7E" x="255" y="577"></use>
</g>
 <use xlink:href="#E1-MJMAIN-2212" x="8445" y="0"></use>
 <use xlink:href="#E1-MJMATHI-6E" x="9445" y="0"></use>
 <use xlink:href="#E1-MJMATHI-62" x="10046" y="0"></use>
 <use xlink:href="#E1-MJMAIN-29" x="10475" y="0"></use>
 <use xlink:href="#E1-MJMAIN-3D" x="11143" y="0"></use>
 <use xlink:href="#E1-MJMATHI-6E" x="12199" y="0"></use>
 <use xlink:href="#E1-MJMATHI-52" x="12800" y="0"></use>
 <use xlink:href="#E1-MJMATHI-54" x="13559" y="0"></use>
</g>
</svg>)
burada p basınçtır, n söz konusu gazın mol sayısıdır ve a ve b belirli gaza bağlıdır, V hacimdir, R birim mol bazında spesifik gaz sabiti ve T mutlak sıcaklıktır; a moleküller arası kuvvetler için bir düzeltme ve b sonlu atomik veya moleküler boyutlar için düzeltme; b değeri gazın her bir molü başına Van der Waals hacmine eşittir. Değerleri gazdan gaza değişir.
Van der Waals denkleminin mikroskopik bir yorumu da vardır: moleküller birbirleriyle etkileşime girer. Etkileşim çok kısa mesafede kuvvetli iticidir, orta mesafeden hafifçe çekici hale gelir ve uzun mesafeden kaybolur. Çekici ve itici güçler düşünüldüğünde ideal gaz yasası düzeltilmelidir. Örneğin, moleküller arasındaki karşılıklı itme, komşuları her molekülün etrafındaki belirli bir alandan hariç tutma etkisine sahiptir. Böylece, toplam boşluğun bir kısmı rastgele hareket yürüttüğü için her molekül için kullanılamaz hale gelir. Durum denkleminde, bu dışlama hacmi (nb) kabın (V) hacminden çıkarılmalıdır, bu nedenle: (V - nb).
Van der Waals denkleminde tanıtılan diğer terim, , moleküller arasında (van der Waals kuvveti olarak bilinir) zayıf bir çekici kuvveti tanımlar, bu da n arttığında veya V azaldığında ve moleküller birlikte daha kalabalık hale gelir.
![{\displaystyle a\left({\frac {n}{\tilde {V}}}\right)^{2}}](data:image/svg+xml; charset=utf-8; profile="https://www.mediawiki.org/wiki/Specs/SVG/1.0.0";base64,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)
Van der Waals sabit b hacmi, bir atomun veya molekülün van der Waals hacmini gazlar üzerindeki ölçümlerden elde edilen deneysel verilerle hesaplamak için kullanılabilir.
Helyum için, b = 23.7 cm3/mol. Helyum monatomik bir gazdır ve her helyum molü 6.022×1023 atom içerir (Avogadro sabiti, NA)):
![{\displaystyle V_{\rm {w}}={b \over {N_{\rm {A}}}}}](data:image/svg+xml; charset=utf-8; profile="https://www.mediawiki.org/wiki/Specs/SVG/1.0.0";base64,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)
Bu nedenle, rw = 2.11 Å 'ye (≈ 200 pikometre) karşılık gelen tek bir atom Vw = 39.36 Å3'ün van der Waals hacmi. Bu yöntem, çapın 2rw olduğu ve internükleer mesafenin d olduğu yuvarlak uçlu bir çubuk olarak moleküle yaklaşılarak diatomik gazlara genişletilebilir. Cebir daha karmaşıktır, ancak ilişki
![{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}+\pi r_{\rm {w}}^{2}d}](data:image/svg+xml; charset=utf-8; profile="https://www.mediawiki.org/wiki/Specs/SVG/1.0.0";base64,<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="19.526ex" height="5.176ex" style="vertical-align: -1.838ex;" viewBox="0 -1437.2 8407.2 2228.5" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title">
<title id="MathJax-SVG-1-Title">{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}+\pi r_{\rm {w}}^{2}d}</title>
<defs aria-hidden="true">
<path stroke-width="1" id="E1-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path>
<path stroke-width="1" id="E1-MJMAIN-77" d="M90 368Q84 378 76 380T40 385H18V431H24L43 430Q62 430 84 429T116 428Q206 428 221 431H229V385H215Q177 383 177 368Q177 367 221 239L265 113L339 328L333 345Q323 374 316 379Q308 384 278 385H258V431H264Q270 428 348 428Q439 428 454 431H461V385H452Q404 385 404 369Q404 366 418 324T449 234T481 143L496 100L537 219Q579 341 579 347Q579 363 564 373T530 385H522V431H529Q541 428 624 428Q692 428 698 431H703V385H697Q696 385 691 385T682 384Q635 377 619 334L559 161Q546 124 528 71Q508 12 503 1T487 -11H479Q460 -11 456 -4Q455 -3 407 133L361 267Q359 263 266 -4Q261 -11 243 -11H238Q225 -11 220 -3L90 368Z"></path>
<path stroke-width="1" id="E1-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path>
<path stroke-width="1" id="E1-MJMAIN-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path>
<path stroke-width="1" id="E1-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path>
<path stroke-width="1" id="E1-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path>
<path stroke-width="1" id="E1-MJMATHI-72" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path>
<path stroke-width="1" id="E1-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path>
<path stroke-width="1" id="E1-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path>
<path stroke-width="1" id="E1-MJMATHI-64" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path>
</defs>
<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true">
 <use xlink:href="#E1-MJMATHI-56" x="0" y="0"></use>
 <use transform="scale(0.707)" xlink:href="#E1-MJMAIN-77" x="825" y="-213"></use>
 <use xlink:href="#E1-MJMAIN-3D" x="1472" y="0"></use>
<g transform="translate(2528,0)">
<g transform="translate(120,0)">
<rect stroke="none" width="620" height="60" x="0" y="220"></rect>
 <use xlink:href="#E1-MJMAIN-34" x="60" y="676"></use>
 <use xlink:href="#E1-MJMAIN-33" x="60" y="-686"></use>
</g>
</g>
 <use xlink:href="#E1-MJMATHI-3C0" x="3388" y="0"></use>
<g transform="translate(3962,0)">
 <use xlink:href="#E1-MJMATHI-72" x="0" y="0"></use>
 <use transform="scale(0.707)" xlink:href="#E1-MJMAIN-33" x="638" y="510"></use>
 <use transform="scale(0.707)" xlink:href="#E1-MJMAIN-77" x="638" y="-200"></use>
</g>
 <use xlink:href="#E1-MJMAIN-2B" x="5247" y="0"></use>
 <use xlink:href="#E1-MJMATHI-3C0" x="6247" y="0"></use>
<g transform="translate(6821,0)">
 <use xlink:href="#E1-MJMATHI-72" x="0" y="0"></use>
 <use transform="scale(0.707)" xlink:href="#E1-MJMAIN-32" x="638" y="488"></use>
 <use transform="scale(0.707)" xlink:href="#E1-MJMAIN-77" x="638" y="-200"></use>
</g>
 <use xlink:href="#E1-MJMATHI-64" x="7883" y="0"></use>
</g>
</svg>)
kübik fonksiyonlar için normal yöntemlerle çözülebilir.
Kaynak
- ↑ Rowland RS, Taylor R (1996). "Intermolecular nonbonded contact distances in organic crystal structures: comparison with distances expected from van der Waals radii". J. Phys. Chem. 100 (18): 7384–7391. doi:10.1021/jp953141+.
- ↑ 2,00 2,01 2,02 2,03 2,04 2,05 2,06 2,07 2,08 2,09 2,10 2,11 2,12 2,13 2,14 2,15 Mantina, Manjeera; Chamberlin, Adam C.; Valero, Rosendo; Cramer, Christopher J.; Truhlar, Donald G. (2009). "Consistent van der Waals Radii for the Whole Main Group.". The Journal of Physical Chemistry A. 113 (19): 5806–5812. doi:10.1021/jp8111556.