日本酒を飲むときは，「やわらぎ水」（チェイサー）を飲むと，非常に健康によい！消化器官でのエタノール濃度が下がって，吸収が減少するからであろう。
エタノールと水は完全混合する。水の水
素結合ネットワーク内にエタノールも参加できるので引力的な相互作用が働くためであろう。
1

ではこの引力的な相互作用をどのように確認したらいいのであろうか？
一番簡単なのはその体積の変化であろう。
100 mLずつ混合すれば，引力的であれば体積は200 mLより減少し，斥力的であれば増加する。
これらを定量的にあらわす指標が部分モル体積である。溶液内のある成分を1 mol増加させると溶液の体積がどれだけ増加するのかという量である。
2

溶液の密度と部分モル体積
実際に部分モル体積を求めるには，ある温度 T での溶液の濃度を変えて，密度をピクノメーター（比重瓶）等で正確に測定すればよい。
化学便覧等にも，濃度c (w/w%)と密度ρ(g cm-3)の表が掲載されている。

3

化学便覧データ

4

25℃ NaCl水溶液
c (w/w％) は 1−26 w/w％の範囲
ρ/g cm = αc + βc + γc + δc + �dρ32= 4αc + 3βc + 2γc + δdc−6−5
α = 0.0, β = 0.339931 × 10 , γ = 1.39329 × 10
−3

4

3

2

δ = 0.699864 × 10−2

, � = 0.997062

14点測定
化学便覧データ5２成分の溶液を考え，成分１を溶媒に，成分２を溶質にする。
溶液内の成分１，２の物質量(mol)をn1, n2とし，それぞれのモル質量(g mol-1) (分子量）をM1, M2とする。
成分２の濃度は質量パーセント濃度c2 (w/w%)で与えられており，c2の関数として溶液の密度ρ(c2)が測定されたとしよう。

100n2 M2c2 =n1 M 1 + n2 M 2

この時，成分１および２の部分モル体積はどのように求めたらいいのであろうか？
6

100n2 M2
c2 =,n1 M 1 + n2 M 2100n1 M1c1 =, c1 + c2 = 100
n1 M 1 + n2 M 2n1 M 1 + n2 M 2
ρ(c2 )V = n1 M1 + n2 M2 , V =ρ(c2 )
�
�
�
�
∂V
M1
n1 M1 + n2 M2 ∂ρ(c2 )
V̄1 =
=
−
∂n1 n2ρρ2∂n1 n2
�
�
�
��
�
�
�
∂ρ(c2 )dρ(c2 )∂c2dρ(c2 )
−100n2 M2==M1
2∂n1 n2dc2∂n1 n2dc2(n1 M1 + n2 M2 )��dρ(c2 )
−c2 M1=
dc2
n1 M 1 + n2 M 2��
M1
n1 M1 + n2 M2 dρ(c2 )−c2 M1
V̄1 =
−
ρ
ρ2
dc2
n1 M 1 + n2 M 2��
M1
c2 dρ(c2 )=1+
ρ(c2 )
ρ(c2 ) dc2
7

�

�

�

�

n1 M1 + n2 M2 ∂ρ(c2 )
M2
V̄2 =
−
=
2
ρ
ρ
∂n2 n1
n1
�
�
�
��
�
�
��
�
∂ρ(c2 )dρ(c2 )∂c2dρ(c2 )
100M2
100n2 M2==−M2
2
∂n2 n1
dc2∂n2 n1
dc2
n1 M1 + n2 M2(n1 M1 + n2 M2 )��dρ(c2 ) 100M2 n1 M1 + 100M2 n2 M2 − 100n2 M22=
dc2(n1 M1 + n2 M2 )2��dρ(c2 )
100M2 n1 M1=
dc2(n1 M1 + n2 M2 )2
��
M2
n1 M1 + n2 M2 dρ(c2 )100M2 n1 M1
V̄2 =
−
ρ
ρ2
dc2
(n1 M1 + n2 M2 )2��
M2
c1 dρ(c2 )=1−
ρ(c2 )
ρ(c2 ) dc2��M2
c2 − 100 dρ(c2 )=1+
ρ(c2 )
ρ(c2 )
dc2
∂V
∂n2

8

�
�
n1 M 1c2 dρ(c2 )n1 V̄1 + n2 V̄2 =1+
ρ(c2 )
ρ(c2 ) dc2
��
n2 M 2c2 − 100 dρ(c2 )+1+
ρ(c2 )
ρ(c2 )
dc2
n1 M 1 + n2 M 2
1 dρ
=
+ 2
(n1 M1 c2 − n2 M2 c1 )ρ(c2 )
ρ dc2
n1 M 1 + n2 M 2
1 dρ
n1 M1 n2 M2 − n2 M2 n1 M1
=
+ 2
100
ρ(c2 )
ρ dc2
n1 M1 + n2 M2
n1 M 1 + n2 M 2n1 M1 + n2 M2===Vρ(c2 )(n1 M1 + n2 M2 )/V
V = n1 V̄1 + n2 V̄2ある濃度の時の成分１，２の物質量と部分モル体
積がわかれば溶液の体積が求められる。
9

NaCl水溶液数値データ
water-NaCl M̲Na=22.990

M̲Cl=35.45

M̲H=1.008

M̲O=15.999

25℃

水密度
=0.997047 g
cm-3

NaCl密度（０℃）=2.168 g cm-3溶液1000cm3n̲1
溶液 1000 gは NaCl g /溶液
溶液1000 cm3に水 何グラbar̲V̲1+n̲2
純水体積ｃｍ 質量モル濃度
純水＋NaCl体
c w/w%
ρ/ g cm-3dρ / dc
bar̲V̲1
bar̲V̲2=> 何cm3
1000 g
NaCl / mol
NaCl / mol dm-3 => 何g？
NaCl g / dm3 NaCl mol
ム？
水 molbar̲V̲2
３
mol kg-1
NaCl体積 cm3 積
1 1.004074913 0.007027526 18.06774456 17.87400015 995.9416247
10 0.171115674
0.171812956 1004.074913 10.04074913 0.171812956 994.0341637 55.17813842 1000.015495 996.9782404 0.172844115 4.631341849 1001.609582
2 1.011117731 0.007058451 18.06595118 18.25691798 989.0045138
20 0.342231348
0.346036184 1011.117731 20.22235462 0.346036184 990.8953764 55.00390655 1000.015444 993.8301569 0.349215662 9.327654345 1003.157811
3 1.018192494 0.007091416 18.06308111 18.62053327 982.1325591
30 0.513347023
0.522686085 1018.192494 30.54577483 0.522686085 987.6467194 54.82357588 1000.015391 990.5718782 0.529223735 14.08937953 1004.661258
4 1.025301242
0.00712642 18.05922448 18.96582004 975.3231139
40 0.684462697
0.701780453 1025.301242 41.01204968 0.701780453 984.2891923
54.6372019 1000.015336 987.2044069 0.712981976 18.91699708 1006.121404
5 1.032446014 0.007163464 18.05446546 19.29370746
968.573646
50 0.855578371
0.883338479 1032.446014 51.62230069 0.883338479 980.8237132 54.44483559 1000.015278 983.7286639 0.900608812 23.81102431 1007.539688
5.52 1.036176209 0.007183533 18.05166043 19.45762863 965.0868175
55.2 0.944558522
0.978729068 1036.176209 57.19692674 0.978729068 978.9792823 54.34245253 1000.015247 981.8787703 0.999744413 26.38234628 1008.261117
5.64 1.037038515 0.007188242
18.0509826 19.49483535 964.2843397
56.4 0.965092402
1.000837992 1037.038515 58.48897226 1.000837992
978.549543
54.318598 1000.015239 981.4477583 1.022777027 26.97830824 1008.426066
6 1.039628849 0.007202547 18.04888257 19.60508206 961.8817335
60 1.026694045
1.067380749 1039.628849 62.37773097 1.067380749 977.2511185 54.24652337 1000.015217 980.1454882 1.092227708 28.77201613 1008.917504
7 1.046851788
0.00724367 18.04254895 19.90078986 955.2450605
70 1.197809719
1.253929247 1046.851788 73.27962519 1.253929247 973.5721632 54.04230715 1000.015155 976.4556367
1.28796744 33.80056512 1010.256202
81.05411687 0.007286833 18.03553262 20.18163832 948.6614134
80 1.368925394
1.443007352
1054.11687 84.32934962 1.443007352 969.7875207 53.83222429
1000.01509
972.659785 1.487962384 38.89730149 1011.557086
9 1.061426135 0.007332035 18.02789672 20.44839819 942.1286771
90 1.540041068
1.634639838 1061.426135 95.52835211 1.634639838 965.8977825 53.61630766 1000.015023 968.7585264 1.692352822 44.06289304 1012.821419
10 1.068781621 0.007379277 18.01969971
20.7018052 935.6448318
100 1.711156742
1.828852876 1068.781621 106.8781621 1.828852876 961.9034589 53.39458556 1000.014954 964.7523727 1.901285269 49.29804525 1014.050418
10.47 1.072255247 0.007402186 18.01566883 20.81649473 932.6137621
104.7 1.791581109
1.921032245 1072.255247 112.2651244 1.921032245 959.9901228 53.28837762 1000.014921 962.8333697 2.001095844 51.78280645 1014.616176
10.87 1.075220081 0.007422037 18.01215407
20.9119548 930.0421541
108.7 1.860027379
1.999938788 1075.220081 116.8764228 1.999938788 958.3436579 53.19698351 1000.014893 961.1820285 2.086870165
53.9097891 1015.091818
11 1.076185369 0.007428559 18.01099567
20.9425617 929.2079494
110 1.882272416
2.025674035 1076.185369 118.3803906 2.025674035 957.8049785 53.16708179 1000.014883 960.6417536 2.114912827
54.6035012 1015.245255
12 1.083639418
0.00747988
18.0018344 21.17133818 922.8161906
120
2.05338809
2.225132276 1083.639418 130.0367302 2.225132276 953.6026882 52.93381561
1000.01481 956.4270171 2.333395557 59.98004161 1016.407059
13 1.091145809
0.00753324 17.99226168 21.38877465 916.4678013
130 2.224503765
2.427257959 1091.145809 141.8489551 2.427257959 949.2968534 52.69480174 1000.014736 952.1084296 2.556900879 65.42848483 1017.536914
14 1.098706579 0.007588641 17.98231945 21.59548202 910.1611104
140 2.395619439
2.632082838 1098.706579 153.8189211 2.632082838
944.887658
52.4500504 1000.014659 947.6861753 2.785603999 70.94968684 1018.635862
14.92
1.10571227
0.00764141 17.97287918 21.77667853 904.3944135
149.2 2.553045859
2.822934132
1105.71227 164.9722707 2.822934132 940.7399994 52.21981679 1000.014587 943.5262324
3.00075912
76.0942208 1019.620453
15
1.10632377
0.00764608 17.97204595 21.79204333 903.8945266
150 2.566735113
2.839640066
1106.32377 165.9485654 2.839640066 940.3752042 52.19956726 1000.014581 943.1603567 3.019688368 76.54454126 1019.704898
15.76 1.112151823 0.007691099 17.96403804 21.93498752 899.1578121
157.6 2.696783025
2.999232158 1112.151823 175.2751273 2.999232158 936.8766958 52.00536751
1000.01452 939.6514866 3.201309384 80.84646094 1020.497948
16
1.11399942
0.00770556 17.96147592 21.97901494 897.6665358
160 2.737850787
3.049964188
1113.99942 178.2399072 3.049964188 935.7595126 51.94335346 1000.014501 938.5309946 3.259346175 82.21397932 1020.744974
17 1.121735569 0.007767079 17.95064072 22.15692765 891.4756985
170 2.908966461
3.263091149 1121.735569 190.6950467 3.263091149 931.0405224 51.68140563 1000.014419 933.7980279 3.504778869
87.9589699 1021.756998
18 1.129534257 0.007830637 17.93956854 22.32628771 885.3206475
180 3.080082136
3.479058287 1129.534257 203.3161663 3.479058287 926.2180909 51.41371584 1000.014335 928.9613137 3.756197726 93.78051951 1022.741833
18.95 1.137002795 0.007892907 17.92885335 22.47969784 879.5053137
189.5 3.242642026
3.686893047 1137.002795 215.4620297 3.686893047 921.5407654 51.15408079 1000.014254 924.2701351 4.000792136 99.38285501
1023.65299
19 1.137397524 0.007896235 17.92828447 22.48757789 879.2000855
190
3.25119781
3.697904338 1137.397524 216.1055295 3.697904338 921.2919941 51.14027167
1000.01425 924.0206271 4.013824456 99.67967227 1023.700299
20 1.145327408 0.007963873
17.9168107 22.64125833 873.1127824
200 3.422313484
3.919669432 1145.327408 229.0654816 3.919669432 916.2619264 50.86105614 1000.014163 918.9756615 4.277891855
105.65751 1024.633171
20.36 1.148198867 0.007988722 17.91263753 22.69480552 870.9292689
203.6 3.483915127
4.000227402 1148.198867 233.7732894 4.000227402 914.4255779 50.75912172 1000.014132 917.1338742 4.374579516
107.829008 1024.962882
21
1.15332595 0.008033551 17.90516663 22.78776751 867.0575739
210 3.593429158
4.144395097
1153.32595 242.1984495 4.144395097 911.1275004 50.57604776 1000.014075 913.8260287 4.548644504
111.715152 1025.541181
22 1.161395189 0.008105267 17.89336899 22.92752302 861.0333585
220 3.764544832
4.372124257 1161.395189 255.5069416 4.372124257 905.8882473
50.2852205 1000.013985 908.5712583 4.826339529 117.8537553 1026.425014
22.61 1.166353012 0.008150016 17.88610317 23.00962814 857.3733594
226.1 3.868925394
4.512532785 1166.353012
263.712416 4.512532785 902.6405959 50.10494565 1000.013929 905.3139881 4.999257518 121.6385683 1026.952556
23 1.169537165 0.008179024 17.88143196 23.06092241 855.0390961
230 3.935660507
4.60290123 1169.537165 268.9935479
4.60290123 900.5436167 49.98854381 1000.013893 903.2107982 5.111247411 124.0745147 1027.285313
24 1.177753917
0.00825482
17.8693673 23.18834392 849.0738056
240 4.106776181
4.836771731 1177.753917
282.66094 4.836771731 895.0929766
49.6859826 1000.013799 897.7440146 5.403652869 130.3786623 1028.122677
24.69
1.18346814 0.008308308 17.86097332 23.27296813 844.9741621
246.9 4.224845996
4.999970633
1183.46814 292.1982838 4.999970633 891.2698562 49.47376388 1000.013734 893.9095712 5.609940242 134.7778062 1028.687377
25 1.186047484 0.008332656
17.8571845 23.31014722 843.1365634
250 4.277891855
5.073782873 1186.047484 296.5118711 5.073782873 889.5356133 49.37749727 1000.013704 892.1701919 5.703855807 136.7674682
1028.93766
25.96 1.194083471 0.008409297
17.8453846 23.42211019
837.462392
259.6 4.442162902
5.304313297 1194.083471 309.9840691 5.304313297
884.099402
49.075737 1000.013612 886.7178799 5.999679771 142.9815817 1029.699462
26 1.194419908 0.008412531 17.84489079 23.42667408
837.226501
260 4.449007529
5.313983162 1194.419908
310.549176 5.313983162 883.8707317 49.06304367 1000.013608 886.4885323 6.012172337 143.2422398 1029.730772
water ethanol
ETOH=46.06844
H2O=18.01528
mitudo98%EtoH
0.7912c w/w%
rho g cm-3
drho / dcbar̲V̲1
bar̲V̲2
1000 g => cm3 EtOH g /1000 EtOH
g
/ mol
EtOH / mol dm-3 1000 cm3 => g EtOH g /dm3 EtOH mol
水 何グラム 水 mol
n1V1+n2V2
純水体積 ｃｍ３質量モル濃度 mol
純EtOH
kg-1 体積 純水＋純EtOH
10.9952-0.0018 18.05410343 54.57941234 1004.823151
10 0.217068344
0.216026416
995.2
9.952 0.216026416
985.248 54.68957463 999.1618315 988.1660544 0.219260954 12.57836198 1000.744416
20.9934-0.0018 18.05392539 54.60932543 1006.643849
20 0.434136689
0.431271387
993.4
19.868 0.431271387
973.53254.0392378 999.1718067 976.4153545 0.442996621 25.11122346 1001.526578
40.9898-0.0016 18.06790549 53.76588454 1010.305112
40 0.868273378
0.859416989
989.8
39.592 0.859416989
950.208 52.74455906 999.1910227 953.0222748 0.904451435 50.04044489
1003.06272
6
0.9866-0.00155 18.07249784 53.58988082 1013.581999
60 1.302410066
1.284957772
986.6
59.196 1.284957772
927.404 51.47874471 999.2102366 930.1507351 1.385542624 74.81799798 1004.968733
80.9835-0.00155 18.07123072 53.63295627 1016.776817
80 1.736546755
1.707893734
983.5
78.68 1.707893734
904.82 50.22514221 999.2295229
907.499847 1.887550821 99.44388271
1006.94373
100.9804-0.00145 18.08831307 53.24414626
1019.99184
100 2.170683444
2.128138049
980.4
98.04 2.128138049
882.36 48.97842276 999.2479379 884.9733262 2.411870493 123.9130435
1008.88637
120.9775-0.001418.0978408 53.06876005 1023.017903
120 2.604820133
2.54621168
977.5
117.3
2.54621168
860.2 47.74835584 999.2664393 862.7476939 2.960022878
148.255814 1011.003508
140.9747-0.00135 18.10913053 52.89403561 1025.956705
140 3.038956822
2.962071214
974.7
136.458 2.962071214
838.242 46.52950162 999.2847187 840.7246599 3.533670723 172.4696663 1013.194326
16
0.972-0.0014 18.09175431 53.12978652 1028.806584
160
3.47309351
3.375846892
972
155.52 3.375846892
816.48 45.32152706
999.303957 818.8982064 4.134635131
196.562184
1015.46039
18
0.9692-0.0014 18.08913036
53.1625712 1031.778787
180 3.907230199
3.786887509
969.2
174.456 3.786887509
794.744 44.11499571
999.322585 797.0978299 4.764914877 220.4954499
1017.59328
20
0.9664-0.00145 18.06689879 53.39215464 1034.768212
200 4.341366888
4.195496961
966.4
193.28 4.195496961
773.12 42.91468131 999.3418266 775.4097851
5.42670861 244.2871587 1019.696944
10
220.9635-0.0015 18.04203183 53.61975674 1037.882719
220 4.775503577
4.601197696
963.5
211.97 4.601197696
751.5341.7162542 999.3610872
753.755841 6.122440483 267.9095046 1021.665346

数値では見にくいのでグラフにしよう

NaCl水溶液：密度NaCl水溶液

密度 / g cm

-3

1.15

1.10

1.05

0

5

10
15
質量パーセント濃度 / %

20

25
11

NaCl水溶液：部分モル体積
23

NaCl

部分モル体積 / mL

22

21

20

19

water

18
0

5

10
15
質量パーセント濃度 / %

20

25

12

NaCl水溶液：溶解による体積変化
1020

120

1000

溶液の体積（溶解後）部分モル体積から求めた

100

NaClの体積（溶解前）80

純水の体積（溶解前）

960

60

940

NaCl(固)の体積 / mL

980

体積�/ mL

140

純水＋NaClの体積（溶解前）

40

920

20

900

0

1

2

3

NaCl 水溶液モル濃度 / mol L

4

5

-1
13

NaCl(固体）はNa+ とCl-に電離する。
それぞれのイオンは水分子をイオンの近くに引きつける（水和する）ため，引力的な相互作用が働き，体積は減少する。

14

水ーエタノール混合溶液数値データ
water
ethanol

M̲EtOH=46.06
844 g mol-1

M̲H2O=18.015
28 g mol-1

ρ 98%EtoH=0.7912 g cm3溶液1000cm3n̲1
溶液 1000 gは EtOH g /溶
EtOH / mol dm- 溶液1000 cm3に水 何グラbar̲V̲1+n̲2
純水体積 ｃ 質量モル濃度
純水＋純c w/w%
ρ / g cm-3 dρ / dcbar̲V̲1
bar̲V̲2=> 何cm3
液 1000 g
EtOH / mol3=> 何g？
EtOH g /dm3 EtOH molム？
水 molbar̲V̲2
ｍ３
mol kg-1
純EtOH 体積 EtOH
1
0.9952-0.0018 18.05410343 54.57941234 1004.823151
10 0.217068344
0.216026416
995.2
9.952 0.216026416
985.248 54.68957463 999.1618315 988.1660544 0.219260954 12.57836198 1000.744416
20.9934-0.0018 18.05392539 54.60932543 1006.643849
20 0.434136689
0.431271387
993.4
19.868 0.431271387
973.53254.0392378 999.1718067 976.4153545 0.442996621 25.11122346 1001.526578
40.9898-0.0016 18.06790549 53.76588454 1010.305112
40 0.868273378
0.859416989
989.8
39.592 0.859416989
950.208 52.74455906 999.1910227 953.0222748 0.904451435 50.04044489
1003.06272
6
0.9866-0.00155 18.07249784 53.58988082 1013.581999
60 1.302410066
1.284957772
986.6
59.196 1.284957772
927.404 51.47874471 999.2102366 930.1507351 1.385542624 74.81799798 1004.968733
80.9835-0.00155 18.07123072 53.63295627 1016.776817
80 1.736546755
1.707893734
983.5
78.68 1.707893734
904.82 50.22514221 999.2295229
907.499847 1.887550821 99.44388271
1006.94373
100.9804-0.00145 18.08831307 53.24414626
1019.99184
100 2.170683444
2.128138049
980.4
98.04 2.128138049
882.36 48.97842276 999.2479379 884.9733262 2.411870493 123.9130435
1008.88637
120.9775-0.001418.0978408 53.06876005 1023.017903
120 2.604820133
2.54621168
977.5
117.3
2.54621168
860.2 47.74835584 999.2664393 862.7476939 2.960022878
148.255814 1011.003508
140.9747-0.00135 18.10913053 52.89403561 1025.956705
140 3.038956822
2.962071214
974.7
136.458 2.962071214
838.242 46.52950162 999.2847187 840.7246599 3.533670723 172.4696663 1013.194326
16
0.972-0.0014 18.09175431 53.12978652 1028.806584
160
3.47309351
3.375846892
972
155.52 3.375846892
816.48 45.32152706
999.303957 818.8982064 4.134635131
196.562184
1015.46039
18
0.9692-0.0014 18.08913036
53.1625712 1031.778787
180 3.907230199
3.786887509
969.2
174.456 3.786887509
794.744 44.11499571
999.322585 797.0978299 4.764914877 220.4954499
1017.59328
20
0.9664-0.00145 18.06689879 53.39215464 1034.768212
200 4.341366888
4.195496961
966.4
193.28 4.195496961
773.12 42.91468131 999.3418266 775.4097851
5.42670861 244.2871587 1019.696944
22
0.9635-0.0015 18.04203183 53.61975674 1037.882719
220 4.775503577
4.601197696
963.5
211.97 4.601197696
751.5341.7162542 999.3610872
753.755841 6.122440483 267.9095046 1021.665346
240.9605-0.0015518.0144332 53.84537091 1041.124414
240 5.209640266
5.003859475
960.5
230.52 5.003859475
729.98 40.52004743 999.3803572 732.1420154 6.854789823 291.3549039 1023.496919
26
0.9574-0.00165 17.95847145 54.25494237 1044.495509
260 5.643776954
5.403352056
957.4
248.924 5.403352056
708.476 39.32639404 999.4004791
710.574326 7.626725614 314.6157735 1025.190099
28
0.9541-0.0017 17.92472584 54.47907795 1048.108165
280 6.077913643
5.798937407
954.1
267.148 5.798937407
686.952 38.13163048 999.4197853 688.9865774 8.441546727 337.6491405 1026.635718
30
0.9507-0.0018 17.85799459 54.87963716 1051.856527
300 6.512050332
6.191006251
950.7
285.21 6.191006251
665.49 36.94030845 999.4400051 667.4610124 9.302929046 360.4777553 1027.938768
32
0.9471-0.00185 17.81742289 55.10247145 1055.854714
320 6.946187021
6.578733727
947.1
303.072 6.578733727
644.028 35.74898642 999.4592961 645.9354474 10.21498091 383.0535895 1028.989037
34
0.9434-0.00195 17.73903017 55.49413142
1059.99576
340
7.38032371
6.962597388
943.4
320.756 6.962597388
622.644 34.56199404 999.4795494 624.4881134 11.18230865 405.4044489 1029.892562
36
0.9395-0.00195 17.72754579 55.54871276 1064.395955
360 7.814460398
7.341685544
939.5
338.22 7.341685544
601.28 33.37611183 999.4977324 603.0608387 12.21009437 427.4772497 1030.538088
380.9356-0.00205 17.63711265 55.92857581 1068.832835
380 8.248597087
7.717387435
935.6
355.528 7.717387435
580.072 32.19888894 999.5179199 581.7900259 13.30418885 449.3528817 1031.142908
400.9315-0.0021 17.58111819 56.14591498 1073.537305
400 8.682733776
8.087966512
931.5
372.6 8.087966512
558.9 31.02366436 999.5369899 560.5553199 14.47122296 470.9302326 1031.485552
420.9273-0.00215 17.52094166 56.36100471 1078.399655
420 9.116870465
8.454073982
927.3
389.466 8.454073982
537.834 29.85432366 999.5559667 539.4269277 15.71874218 492.2472194 1031.674147
44
0.923-0.00215 17.50286702 56.42231958 1083.423619
440 9.551007154
8.815579603
923
406.12 8.815579603
516.88 28.69119991 999.5737065 518.4108673 17.05536992 513.2962588 1031.707126
46
0.9187-0.0022 17.43463396 56.62968929 1088.494612
460 9.985143843
9.173351648
918.7
422.602 9.173351648
496.098 27.53762362 999.5924413 497.5673163 18.49100712
534.127907 1031.695223
48
0.9143-0.002217.4133572 56.69108989
1093.73291
480 10.41928053
9.52634819
914.3
438.8649.52634819
475.436 26.39070833 999.6098924 476.8441207 20.03707794 554.6814965 1031.525617
50
0.9099-0.0023 17.28214609 57.02925119 1099.021871
500 10.85341722
9.875524329
909.9
454.95 9.875524329
454.95 25.25356253 999.6295145 456.2974464 21.70683444
575.012639 1031.310085
52
0.9053-0.00225 17.31326558 56.95823303 1104.606208
520 11.28755391
10.21862255
905.3
470.756 10.21862255
434.544 24.12085741 999.6454948
435.831009 23.51573731 594.9898888 1030.820898
540.9008-0.0023 17.22713814 57.14834754 1110.124334
540
11.7216906
10.55889889
900.8
486.432 10.55889889
414.368 23.00091922 999.6636363 415.5952528 25.48193608 614.8028311 1030.398084
56
0.8962-0.0023 17.19825646 57.20882011 1115.822361
560 12.15582729
10.89405241
896.2
501.872 10.89405241
394.328 21.88853018 999.6804404 395.4958994
27.6268802 634.3174924 1029.813392
58
0.8916-0.0023
17.1678601 57.26750153 1121.579183
580 12.58996398
11.22521188
891.6
517.128 11.22521188
374.472 20.78635469 999.6970679
375.581091
29.9761047 653.5995956 1029.180687
60
0.887-0.00235 17.06727133 57.44143407 1127.395716
600 13.02410066
11.55237729
887
532.2 11.55237729
354.8 19.69439276 999.7146634 355.8508275 32.56025166 672.6491405 1028.499968
62
0.8823-0.00235 17.03223581 57.49875667 1133.401337
620 13.45823735
11.87420282
882.3
547.026 11.87420282
335.274 18.61053506
999.73092 336.2669964 35.41641409 691.3877654 1027.654762
64
0.8776-0.00235 16.99546871 57.55401552 1139.471285
640 13.89237404
12.19194746
877.6
561.664 12.19194746
315.936 17.53711294 999.7469874 316.8717222 38.58992789 709.8887765 1026.760499
66
0.8729-0.00235 16.95692003 57.60713378 1145.606599
660 14.32651073
12.50561122
872.9
576.114 12.50561122
296.786 16.47412641 999.7628625 297.6650048 42.13679627 728.1521739 1025.817179
68
0.8682-0.0024 16.83534649 57.75581966 1151.808339
680 14.76064742
12.81519409
868.2
590.376 12.81519409
277.824 15.42157546
999.779605 278.6468441 46.12702319 746.1779575 1024.824802
70
0.8634-0.0024
16.7912529 57.80651438 1158.211721
700 15.19478411
13.1191766
863.4
604.3813.1191766
259.02 14.37779485 999.7950602 259.7871515 50.64928036 763.8776542 1023.664806
72
0.8586-0.0024
16.7451182 57.85473575 1164.686699
720
15.6289208
13.4189914
858.6
618.192
13.4189914
240.408 13.34467186 999.8103089 241.1200274 55.81757427 781.3346815 1022.454709
74
0.8538-0.00245 16.60552049 57.98254559 1171.234481
740 16.06305749
13.71463848
853.8
631.812 13.71463848
221.988 12.32220648 999.8263032 222.6454721 61.78099033 798.5490394 1021.194512
76
0.8489-0.00245 16.55298832 58.02735492 1177.995052
760 16.49719417
14.00446813
848.9
645.164 14.00446813
203.736 11.30906653
999.841089 204.3394143 68.73830906 815.4246714 1019.764086
78
0.844-0.00245 16.49811325 58.06929915 1184.834123
780 16.93133086
14.29004325
844
658.32 14.29004325
185.68 10.30680622 999.8556525
186.229937 76.96059483 832.0525784 1018.282515
80
0.8391-0.00245 16.44082371 58.10826842 1191.753069
800 17.36546755
14.57136382
839.1
671.28 14.57136382
167.82 9.315425572 999.8699899 168.3170402 86.82733776 848.4327604 1016.749801
820.8342-0.00255 16.16894311 58.26331032 1198.753297
820 17.79960424
14.84842986
834.2
684.044 14.84842986
150.156 8.334924575 999.8855979 150.6007239 98.88669023 864.5652174 1015.165941
84
0.8291-0.0025 16.21136107 58.24510409 1206.127126
840 18.23374093
15.1175946
829.1
696.44415.1175946
132.656 7.363526962 999.8986658 133.0488934 113.9608808 880.2376138 1013.286507
860.8241-0.0026 15.91569795 58.37065309
1213.44497
860 18.66787762
15.38419795
824.1
708.726 15.38419795
115.374 6.404230187 999.9134746 115.7157085
133.341983 895.7608696 1011.476578
880.8189-0.00265 15.72121065 58.44107509 1221.150324
880 19.10201431
15.64263952
818.9
720.632 15.64263952
98.268 5.454702897 999.9272039 98.55904486 159.1834526 910.8088979 1009.367943
90
0.8136-0.0027 15.51609366 58.50204021 1229.105211
900
19.536151
15.89461245
813.6
732.24 15.89461245
81.36 4.516166277 999.9405156 81.60096766
195.36151 925.4802831 1007.081251
92
0.8082-0.00275 15.29974774 58.55291798 1237.317496
920 19.97028769
16.13998651
808.2
743.544 16.13998651
64.656 3.588953377 999.9533874 64.84749465 249.6285961 939.7674419 1004.614937
940.8027-0.0028 15.07153298 58.59302743
1245.79544
940 20.40442437
16.37863144
802.7
754.538 16.37863144
48.162 2.673397249 999.9657964 48.30464361 340.0737396 953.6627907 1001.967434
96
0.7971-0.00295 14.55879747 58.65063565 1254.547736
960 20.83856106
16.61041702
797.1
765.216 16.61041702
31.884 1.769830944
999.978127 31.97843231 520.9640266 967.1587462 999.1371785
98
0.7912 0.008073469
1263.902932
980 21.27269775
16.83095846
791.2
775.376 16.83095846
15.824 0.878365476
15.87086667 1063.634888
980 995.8708667

数値では見にくいのでグラフにしよう
15

水ーエタノール混合溶液：密度
水-エタノール混合溶液

密度 / g cm

-3

0.95

0.90

0.85

0.80
0

20

40
60
質量パーセント濃度 / %

80

100
16

水ーエタノール混合溶液：部分モル体積
エタノール

18.0

水

57

17.0
16.5

56

16.0

55

15.5
54

エタノールの部分モル体積 / mL

水の部分モル体積 / mL

17.5

58

15.0
53
0

20

40
60
質量パーセント濃度 / %

80

100

データが離散的で微分が正確に求められないためグラフがスムーズではない17

水ーエタノール：混合による体積変化
純エタノール（混合前）1030
純水＋純エタノールの体積
（混合前）

600

1010

400

1000

混合溶液の体積（部分モル体積から求めた）

990

純溶媒の体積 / mL

体積 / mL

1020

800

200
純水（混合前）

980
0

20

40
60
質量パーセント濃度 / %

80

100
18

40 w/w％の濃度で体積減少量は最大となる。
この時，純溶媒の体積はほぼ等しい。
（515 mLの水と515 mLのエタノール合わせて1030 mLが1000 mLの混合溶媒になる）
お酒を水で割ったら体積が減少した！損したのか？
（笑）

エタノールは直線的な水素結合であるのに対して，
水は全方位的な水素結合をとるのが原因か？
19