BROWN ON VAPOUR-DENSITY DETERMINATIONS. X.-Tables for the Calculation of Vapour-densityDeterminations. By JAJ. T.BROWN. IFunder the head of vapours we include gases there are several tables which may he used for lessening the labour of calculating a vapour-density. There is one by Gerhardt * giving approxi- mately the values of the expression 760 (1 + 0-00367 T)for every integral value of T frorri 0 to 30. There is another by Bunsen t indicating the vaIues of I + 0-00366T and log. (1 + 0.00366 'T') €or every T = 0.1 from -2 to + 40. mere is also a table calculated by Mr. Greville Williams giving the values of the 1 formula 1+ 0-00367 T for every T = 1 from 0 to 150; and lastly Gerhardtt gives the values of log. (1 + 0-00367 T) for every integral value of T from 0 to 299.But 1 found that by substituting the weight of a cubic centirnetre of air for that of a cubic centimetre of nitrogen in the formula with which I headed a table for the calculation of direct nitrogen determinations I obtained an expression which occurs three times in the formula €or the determination of a vapour-density according to the method of Dumas. For in this formula which is generally written-P' -P + p -p' D= 1+ k (T-t))-v'] 1 H 1 + 0.00367 'I"r60 but which written without any abbreviation and modified becomes * Gerhardt Trait6 de Chimie Organique rol 1 page 50. t Bunsen's Gasomtry translated by Roscoe page 268. Cerhardt vol 1 page 115. BROWN ON VAPOUR-DENSITY DETERMINATIONS. 0*0012932 From we see the repetition of the expression 760(1 + 0-0036Z T)' this expression I have calculated a table of its values for every T = 0.5 from -20 to + 50 and for every T = 1 from 51 to 350.I have also added a column of differences for calculating the fractional values of the expression. In order to find the weight in grarnmes of a given volume of air at any pressure and tempe- rature up to 350' C, multiply the number in the table headed 0*0012932 '760 (1 + 0.00367 T.) corresponding to the temperature by the volume expressed in cubic centimetres and also by the pressure expressed in millimetres. 0.00367 -(T -t)] for 1-k 0.00367T In substituting ['I -t 1+0.00367 t 1 +0*00367t' I have made no actual alteration as the two expressions are equal; but as I have given a table indicating the values of the quantity 0.00367 for every t = 0.5 from -20 to + 50 the 1 + 0.00367 t expression is reduced to the simple form of 1 + k (T -t).In calculating by this table it is only necessary to use it to the fifth decimal place unless the value of v is very large. In calculating the table for correcting for the expansion of the glass viz. that headed 1 + k (T -t) I have adopted the values of k as given by Regnault * taking the average value of t at 30. Gerhardt gives a table for the same purpose headed log. [l + k (T -t)] for every T -t = 10 from 100 to 290 and takes the value of k at 0.000027. The three following examples win illustrate more fully the use of the tables. Ex. 1.-To find the weight of 90 C.C.of air at a temperature of 15" C. and at a pressure of 746 mm. 0~00000161279x 90 x 746 = 0.108282 gramme. Ex.2.-To find the density of a vapour from the following data (Dumas). * Regnault's Elements of Clwmirtry translated by Betton vol 2 page 420. -/-Gerhardt vol 1 page 117. BROWN ON VAPOUR-DENSITY DETERMINATIONS. T = 350' C. T -t = 335 t = 15" c. P' = 28.3920 grammes. P = 28.2093 , v = 90 c. c. v = 0.5 C. C. K = 746 mm. 28.3920 -28.2093 + (0~0000016127x 90 x 746) -(0~000001612x 0.5 x 746) D= [90(1'0104) -0*6(1 + 0*00347x 335)] x 0.000000'744S x 746 28.3920 -28 2093 + 0'1082 -0.0006 0.2903 -=-0.0499 = 5'51 0.0499 Ex. &-To find the density of a vapour from the following data (Gay-Lussac)-D= 0*0012932 + '760 (1 + 0.00367 T) Ht P = 0.1069.v = 43 c. c. H = 761 mm.; H' = 680.5. Diff. of level = 80.5 mm. T = 96. - T 0'0012932 ~___ t 60(1 -!-0.00367T) Diff. -20 0*00000183636 -19.5 0-00000183273 -19 0*00000182912 -18.5 0~00000182552 -18 0~00000182193 -17.5 0~00000181836 0*00,500181480 -17 16.5 0-00000181125 -16 0~00000180772 -15.5 0'0C000180421 -15 0.00000180070 -14.5 0-0000 0179'121 -14 0~00000179374 -13.5 0~00000179027 -13 0-00000178682 -12.5 0'000001 78339 -12 0*00000177996 -11.5 0*00000177655 363 -20 36 1 -19.5 360 -19 359 -18.5 357 -18 356 -17.5 355 -17 353 -16.5 351 -16 351 -195 349 -15 347 -14.5 347 -14 345 -13.5 343 -13 343 -12.5 341 -12 330 -11.5 0.00367 1 + 0.00367t Diff.0*00396071 783 0*00395288 779 0+00304509 777 0'00333732 774 0 00392958 770 0.00392 188 768 0'00391.120 764 0.00390656 762 0.00389694 758 0-00389136 756 0'00388380 753 0.00387627 750 0'00386577 747 0*00386730 744 0'00355386 741 0'00384645 '138 0'00383907 736 0.00353171 '732 BROWN ON VAPOUR-DENSITY DETERMINATIOXS. T --. -11 -10.5 -10 -9-5 -8.5 -a -7.5 -P -6-5 -6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -1.5 -1 -0-5 0 4-0-5 1 1-5 2 2-5 3 3-5 4 4.5 5 8-5 6 6.5 7 7-5 8 8-5 9 9.5 10 10.5 It 11.5 12 12.5 13 13.5 14 145 15 3.5'5 16 16.5 0'0012932 760(l i 0 003671 O.OO000177316 0~00000176977 0'00000176640 0-000001 76304 0*00000175970 0-00000175636 O*OOOOO175304 0*00000 17497 4 0*00000174644 0~00000174316 0-00000173989 0'000001 73663 0.00000173338 0-00000173015 O*OOOOOl72693 @00000172372 0-00000172052 0'00000171733 0~00000171416 0'00000 171099 0*00000170784 0-00000170470 0-000CO 170157 Oa00000169846 0*00000169535 0*00000169226 0'00000168918 0-00000168610 0.00000168304 0-00000167999 C.00000 167696 0*00000167393 0-000001 67091 0~00000166791 0-00000166491 0*00000166193 0.00000165896 0~0000016 5599 0*00000165304 OOG000165010 0~00000164717 0'000001 64425 0'00000164134 V00000163844 0'00000163555 0.0000016 3 267 0~00000162980 0*00000162694 0'00000162409 0'00000162125 0'000001 61E42 0'00000 161560 0-00000161279 0-00000160999 0~00000160320 0~00000160442 0-00367 DiK DifX t 1 't 0~0036'ii 339 -11 040382439 730 337 -10'5 0-00381709 727 336 0-00380ga2 725 334 -10 9.5 0*00380257 721 334 -9 0.00379536 719 332 -8-5 0-00378817 716 330 -8 0'00378101 714 330 -7-5 0-00377387 711 328 -7 0.00376676 708 327 -6-5 0-00375968 '105 '326 -6 0.00375263 703 325 -5.5 o'OC374560 700 323 -5 0-00373ri60 698 322 -4-5 0 003'73162 695 321 -4 0.00372467 692 320 -3.5 090371775 690 319 -3 0-00371085 687 317 -2.5 0-00370398 685 317 -2 0*00369713 682 315 -1.5 0.00369031 680 314 -1 0-00368351 677 313 -0.5 0.00367674 674 311 0 0-003ci7000 673 311 + 0.5 0.00366327 669 309 1 0-00365658 668 308 1.5 O.GO3 649 9 0 665 308 2 0.00364325 662 306 2.5 0.00363663 660 305 3 0.00363003 658 303 3-5 0-00362345 655 303 4 0.0036 16 90 653 302 4.5 0'00361037 651 300 5 0'00360386 648 300 5.5 0-00359738 646 298 6 0-00359092 643 297 6 *5 0-00358449 642 297 7 0'00357807 639 2!)5 7-5 0'00357168 636 29 4 8 0.00356532 685 293 8.5 0.00355897 632 292 9 0.00355265 630 291 9-5 0.003 54 63 5 628 290 10 0'00354007 625 289 10-5 6.00353382 623 288 11 0.00352759 621 28; 11.5 0.0G35213 8 619 286 12 0.003515 19 617 285 12.5 0.00350902 615 284 13 0.003 50287 0 12 ' 283 13.5 0.00349675 610 282 14 0.00349065 605 281 14-5 0-003&3456 606 280 15 0.00347850 604 279 15.5 0.00347246 601 278 16 0.003466 45 600 277 16.6 0 00346045 598 BROWN ON VAPOUR-DENSITY DETERMINATIONS.-~ T 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22-5 23 23'5 24 24.6 25 25.5 26 26-5 27 27.5 28 28.5 29 295 30 30.5 31 31.5 32 32-5 33 33'5 34 34.5 35 35'5 36 36*5 37 37-5 38 38'5 89 39'5 49 40.5 41 41.5 42 42.5 43 43-5 44 44'5 0'0012932 760(1 + 0.00367T; 0 00000160165 0-OCOOO159889 0~00000159613 0.00000159339 0~00000159066 0~00000158793 0-00000158522 0~00000158251 0.00000 157982 0*00000157713 0.00000 157445 0-00000157178 0-0000 0186912 0~00000156647 0*00000156383 0~00000156120 0.00000155857 0-00000155596 0-000001 55 3 35 0-00000155075 0*00000154817 0-00000154559 0*00000154301 0*00000154045 0*00000153790 0*00000153535 O*OOOC0153281 0.00000 153028 0*00000152776 040000152525 0~00000152274 0-00000152025 0*00000151776 0-00000 I51 528 0~00000151281 0'00000151034 0*00000150789 0~00000150544 0'000001 50300 0~0000016005~ 0~00000l49814 0.00 00I) 149572 o.oooao I 49332 0 00000149091 0 -00000 14 88 52 0-0000014561 4 0*00000148876 0-00000118139 0.00nooi 47 902 0-00000147667 0'000001 47 432 0*000001 47 198 0.00000146965 9-00000146732 0-0000014 6500 0.00000146269 Diff.t 0-0036 7 1+ 0.00367t DiE - ~~ 276 17 0.00345447 596 276 17.5 0.00344851 593 274 18 0-30344258 592 273 18.5 0.00343666 589 273 19 0.00343077 588 271 19-5 0.00342489 585 271 20 0*00341904 584. 269 20-5 0-00341320 581 269 21 0-00340739 580 268 21.5 0.00340259 577 267 22 0.00339582 677 266 22.5 0.00339C0.5 573 26 5 23 0*09338432 571 264 23.5 0 00337861 570 263 24 0-00837291 56a 263 261 24?5 25 0'0033(i'123 0'00336 157 566 564 26 I 25.5 0.00335593 562 260 26 OrOO335031 560 258 26.5 0-00334471 559 258 27 0'00333912 556 258 275 0'00333356 555 256 28 0-00332801 553 256 28.5 0.00332248 551 255 29 0'00331697 549 254 29.5 0'00331 148 648 253 30 O.OO33O6 00 545 252 30.5 OW330055 544 251 31 0'00329511 542 251 31-5 0*0@328969 540 249 32 0'0 03284 2 9 539 249 32-5 0-00327890 536 248 33 0.00327354 535 24 7 33.5 090326819 533 2 4'7 34 0.00326286 532 245 34.5 0'00325754 530 245 35 0-00325224 538 244 35.5 0'00334696 526 243 36 0'00384170 524 243 365 0-00323646 523 542 37 oawm23 622 240 37'5 0'00322601 519 241 38 0'00322082 518 239 38.5 0 00321564 516 238 39 0'00321048 515 238 39-5 0 00320533 513 287 40 0'00320020 511 237 40.5 0'00319509 509 235 41 0'00319000 508 235 41.5 0'00318492 507 234 42 0-00317985 505 233 42.5 0'003 17480 503 233 43 0.00310977 501 232 43.5 0.00316476 500 231 44 0-003159% 499 230 44.5 0'0031 5477 497 BROWN ON VAPOUR-DENSITY DETERMINATIONS.T 0-0012032 760(1 + 0.00367T) Diff. t 0.0 0 3 67 1 + 0.00367t -__- 45 0*00000146 039 230 45 0-00314980 45.5 0-0000014 5809 229 45.5 0-00314485 46 0*00000145880 228 46 0'00313991 46.5 0-00000145352 227 46.5 0.00313499 47 0-00000145125 227 47 0.00313009 47.5 0*00000144898 226 47.5 0-003125 19 48 0'00000144672 2 25 48 0*00312032 48'5 0'0000 014 4447 225 48 5 0-00311546 49 0*00000144222 2 24 49 0*00311061 49.5 0'00000143998 223 49.5 0-00310578 50 0~00000143775 60 0.0 0310097 ~-(YO012932 0.0012932 T 'SO(1 + 0+00367T) D8. T T60(1 + 0.00367T) 51 C =00000143330 442 88 0-00000128619 52 0.00000142888 48 9 89 0-00000128263 53 0*00000142449 436 90 0~00000127909 54 0~00000142013 434 91 O*OOOOO127557 55 0.000001415 79 431 92 0'00000 127207 56 0'00000141148 428 93 0*00000126859 57 0*00000140720 426 94 0~00000126513 58 0.00000140294 423 95 0*00000126169 59 0-00003139871 421 96 0.00000125826 60 0~00000139450 418 97 0*00000125486 61 0.00000139032 416 98 0~00000125147 62 0'000001 386 16 413 99 0.0000012 481 0 63 000000138203 410 100 0*00000124475 64 0.OO 000 13 77 93 4 09 101 0-00000124 142 65 0'0000013 7384 406 102 0*O0000I238 10 66 0.00000136978 403 103 0-00000123480 67 0*00000136575 401 104 O*OOOOO123152 68 0*00000136174 399 105 0-00000122826 69 040000135775 396 106 0~G0000122502 70 0~00000136379 395 107 0'000001221'79 71 0'00000134984 391 108 0*00000121858 72 0'00000134593 390 109 0'00000 121 538 73 0*00000134203 387 110 0~00000121220 '74 0*00000133816 385 111 0*00000120904 '75 O*OOOOO133431 383 112 0~00000120590 76 0*00000133048 381 113 0*00000120277 77 0'0 000013 26 67 3i9 114 0~000GOllY966 78 0~00000132288 S76 115 0~00000119656 '79 0~00000131912 374 116 0'00000119348 80 0~00000131538 3'12 117 0~00000119042 81 0~00000131166 3'70 118 0*00000118737 82 0'00000130796 368 119 000000118434 83 OOOUO0130428 366 120 O*OOOOO118 132 84 0~00000130062 364 121 0'00000 11'1832 85 0.00000129698 362 122 0-000001 17633 86 0 00000129336 360 123 0~00000117236 87 0~00000128976 357 124 O'OUOC0116940 DiR.495 494 49 2 490 490 487 486 485 483 481 Diff. 356 354 352 350 348 346 344 343 340 339 337 335 333 332 330 328 326 324 323 321 320 318 316 314 313 311 310 308 306 305 303 302 300 299 297 296 294 BROWN ON VAPOUR-DENSITY DETERMINATIONS.T 0.0012932 %0(1 -f-0.00367T) I)iE - 125 0.00000116646 293 126 0-00300116353 291 127 0'00000116062 290 128 0'000001 157;s 288 129 0~03000115484 287 130 0~00000115197 286 131 0-000001149 11 284 132 0'000001 14627 283 133 0'00000114344 281 134 0'000001 14063 280 135 0'000001 13783 278 135 0'00000 113 50 5 278 137 0'0000011 3227 275 138 0'0000011 2952 275 130 0'00000112677 273 140 0.00000112404 272 141 0'000001121 32 270 142 0'00000111862 270 143 0'00000111592 268 144 0 00000111324 266 145 0'0000 01110 5 8 266 146 0'00000 1 1 07 92 264 147 0'000001 10528 263 148 0'00000110265 261 149 0'00000110004 26 1 150 0'00000109743 259 151 0'00000109484 258 152 0'00000109226 256 153 0'0 0000108970 256 154 0'00000108714 254 155 0'00000108460 253 156 0*00000108207 252 157 0~00000107955 251 158 0~00000107704 250 159 0'00000107454 248 160 0~00000107206 247 161 0'00000106959 247 162 0'000001 06712 245 163 0*00000106467 244 164 0'00000106223 242 165 0'00000105981 242 166 0~00000105739 240 167 0'00000105499 240 168 0'00000105259 239 169 0'00000105020 237 170 0'00000104783 236 171 0'00000 104547 236 172 0'0000010431 1 234 173 0~00000104077 233 174 0-00000103844 232 1'75 0'00000103612 231 176 000000103381 230 177 0-00000103151 229 178 0-00000102922 228 179 0.00 0001026 94 227 T 0.0012932 760(1 + 0.00367T) Diff._I- 180 0~0000U102467 226 181 0~00000102241 225 182 0~00000102016 224 183 0.00000 10179 2 223 184 0~00000101569 222 185 0~00000101347 221 186 0-00000101126 220 I87 0~00000100906 219 188 0~00000100687 218 189 0~00000100469 217 190 0*00000100252 217 191 0~00000100035 215 192 000000099820 215 193 0.0 0000099605 213 194 0*00000099392 213 195 0~00000099179 211 196 0*00000098968 211 197 0.0000009S757 210 198 0.00000098547 209 199 0-00000098388 208 200 0~00000098130 207 201 0.00000097923 207 202 0*00000097716 205 203 0*00000097511 205 204 0*00000097306 204 205 0~00000097102 203 206 0-00000096 8 9 9 202 207 0-00000096 6 97 201 208 0-00000096496 201 209 0-00000096295 199 210 0*00000096096 199 211 0~00000095897 198 212 0.00000095699 197 213 0-00000095502 196 214 0-00000095306 196 215 000000095110 194 216 0~00000091916 194 217 0*00000094722 193 218 0*00000094529 193 219 0-000Q0094336 191 220 0~00000094145 191 221 0*00000093954 190 222 0.00000093764 190 223 0'00000093574 188 224 0*00000093386 188 225 0'00000093198 187 2 26 0'00000093011 186 227 0*00000092825 185 228 0*00000092640 185 229 0*00000092455 184 230 0~00000092271 183 231 0-000000920 8 8 183 332 0-00000091905 182 233 0*00000091723 181 234 0~00000091542 180 BROWN ON VAPOUK-DEKSITY DE'l'EGMINL4TIONS.II T 0.0012932 jO(1 + 0-OO367T) DifE T 0.0012932 60(1 + 0.00367T) DiE - ~~ 235 0~00000091362 180 290 0*00000082428 146 236 0~00000091182 179 291 0.00000082282 146 237 0~00000091003 178 292 0~00000082136 145 238 0'00000090825 178 293 0'00000081991 145 239 0~00000090647 176 294 o-ooooooai846 144 240 0~00000090471 177 295 0'00000081702 144 241 0-00000 0 9029.4 175 296 0~00000081558 143 24 2 0~00000090119 175 297 0~00000081415 143 243 0'00000089944 1'74 298 0~00000081272 142 244 0~00000089770 174 299 0.00000081130 141 245 0*00000089596 1'72 300 0~00000080989 142 246 0*00000089424 173 301 0*00000080847 140 247 0'00000089251 171 302 0~00000080707 141 248 0*00000089080 171 303 0~00000080566 139 249 0*00000088909 170 304 0~00000080427 140 250 0*00000088'739 170 305 0.O 000008 0287 138 251 0*00000088569 169 306 0~00000080149 139 252 0'00000088400 168 307 0 ~00000080010 138 253 0~00000088232 167 308 0*00000079872 137 254 0~00000088065 167 309 0*00000079735 137 255 0.00000087898 167 310 000000079598 136 256 0~00000087731 165 311 0.0000007946 2 136 257 0~00000087566 165 312 0*00000079326 136 258 0-00000087401 165 313 0~00000079190 135 259 0~00000087236 164 314 0-00000059055 134 260 0'00000087052 163 315 0~00000078921 134 261 0'0 000 0 OS6 909 162 316 0-00000078787 134 262 0~00000086747 162 317 0~00000078653 133 263 0*00000086585 162 318 0*00000078520 133 264 0*00000086423 161 319 0-00000078387 132 265 0'000 000862 6 2 160 320 0*00000078255 132 266 0'00000086102 159 321 0~000000~8123 132 267 0~00000085943 159 322 0-0000007i99 1 131 268 0*00000085784 159 323 0~00000077860 130 269 @00000085635 158 324 0*00000077730 130 270 0~00000085467 157 325 0~00000077600 130 271 0'00000085310 157 326 0~00000077170 129 272 0-00000085153 156 327 0~00000077311 129 273 0*00000084997 155 328 0*00000077212 128 274 0*00000084842 155 329 0~000000'77084 128 275 0~00000084687 155 330 0*00000076956 128 276 0-00000084532 153 331 0.00000076828 127 277 0'00000084379 154 332 0~00000076~01 127 278 0*00000084225 152 333 0~00000076574 126 279 0.0000008~0~3 153 334 0*00000076448 126 280 0'00000083920 151 335 0.00000076322 125 281 0-00000083769 151 336 0*00000076197 125 282 0-00000083618 151 337 0*00000076072 125 283 0*00000083467 150 338 0*00000075947 124 284 O~OOOOOOS3317 149 339 0*00000075823 124 285 0.0 0000083168 149 340 0*00000075699 123 286 0~00000083019 149 341 0-00000075576 123 287 0~00000082870 148 342 0.00000075453 123 288 0~00000082722 147 313 0~00000075330 122 280 0~00000082575 147 344 0-00000075208 122 80 LAWES AND GILBXRT ON THE COMPOSITION VALUE 0.0012932 1 1 0*0012932 76O(l + 0.00367T)’ 1760(1 + 0.003671’) g:: 347 I 0~00000075086 0*000000’74965 I :ii .3;; I 0*000000’14723 1 0-000000’74603 120 0*00000074844 121 350 0-00000074483 - 7 T-t 1+k (T-t) T-t 1+:k (T-t) r-t 1+k (T-t) ll-1 1+ k (T -t) - -.35 1*00096 115 1-00326 195 1-00581 275 1*00841 40 1~00110 120 1-00340 200 1*00596 280 1-00866 45 1.00124 125 1*00355 205 1.00610 285 1.00892 50 1*00138 130 1.00369 210 1.00625 290 1-00907 55 1-00151 135 1.00392 215 1-00640 295 1-00923 60 1.00165 140 1*00407 220 1.00655 300 1*00939 65 1.00179 145 1*00421 225 1*006’70 305 1-00954 70 1*00193 150 1.00436 230 1.00685 310 1*00970 75 1.00207 155 1*00451 235 1-00719 315 1.00985 80 1.00220 160 1.00465 240 1-00’734 320 1*01001 85 1.00241 165 1.00480 245 1*00’749 325 1~0101’7 90 1 -00255 170 1*00494 250 1*00765 330 1.01032 95 1*00269 175 1-00509 255 1.00’180 335 1-01048 100 1.00284 180 1*00523 260 1-00795 340 1-01064 105 1*00298 185 1-00551 265 1.00810 345 1*01079 110 - 1-00312 190 1*00566 270 - 1*00826 350- 1*01095