Since the tests for our aquariums just read the total ammonia content in the water, the question has come up how much of that ammonia is actually toxic? This is a complicated question, which really has to do with the ammonia-ammonium equilibrium, ammonia being toxic, ammonium being comparatively much less toxic. Ammonium is not harmless, there is evidence it interferes with the normal salt exchange at the fish gills, but it is not anywhere as dangerous as ammonia.
Also I'd just like to make it clear that any level of ammonia will cause health problems. Ammonia can cause gill damage, that could become permanent, and a very recent article ("Low levels of environmental ammonia increase susceptibility to disease in Chinook salmon smolts " by Ackerman PA, Wicks BJ, Iwama GK, Randall DJ in PHYSIOLOGICAL AND BIOCHEMICAL ZOOLOGY volume 79 JUL-AUG 2006) showed that fish exposed to low levels of ammonia were more susceptible to disease later on in life. But this mini-article is about when emergency action needs to be taken.
The split between the two species (ammonia and ammonium) is determined by equilibrium. The chemistry reaction can be written as:
NH3 + H+ <--> NH4+
(ammonia) + (H+ ions) <--> (ammonium+ ions)
The +'s indicating a charge of +1, and <--> indicating that the reaction can go both ways.
pH is a measure of the concentration of H+ ions. pH really means -log(base 10) of H+. For example, pH of 7.0 means a concentration of 10^-7 H+ ions, a pH of 5.0 means a concentration of 10^-5 H+ ions.
Therefore the lower the pH, the higher the concentration of H+ ions.
Now, with more H+ ions present, the above equilibrium chemical reaction gets pushed towards the right hand side. This is known as Le Chatelier's Principle. But, Le Chatelier's is a general rule, it does not give us the exact splits.
The calculate the splits, we need the equilibrium constant K = [NH3][H+]/[NH4+] where [] stands for the concentration of the species in the []'s. K is a function of temperature, so experimentation needed to be performed, and some high level computations (well beyond the scope of this mini-article) needed to be performed.
Clegg, S. and Whitfield, M did that experiment. (Their paper is "A chemical model of seawater including dissolved ammonia and the stoichiometric dissociation constant of ammonia in estuarine water and seawater from -2 to 40 deg C. Geochimica et Cosmochimia Acta Volume 59, 1995.) They found the equilibrium constant as a function of temperature and salinity.
So with this information, I calculated what % of the total ammonia in the water would be toxic ammonia and ammonium.
How to use the following tables
Know your pH and temperature.
Look up the % toxic ammonia on the following charts for your temp and pH
Know how much ammonia you have in your tank
Multiply your ammonia content by the looked up percentage
If this number is over 0.02 ppm, then immediate action needs to be taken.
Example:
I have a tank at 27 deg with pH 6.6 water and 2.0 ppm of ammonia.
% toxic ammonia (from) the chart is: 0.045%
2.0*(0.00045)=0.008 ppm toxic ammonia, so it is not immediately dangerous, though exposure to any ammonia is unhealthy for the fish.
Note that if the pH of that tank was over 8.0, the level of ammonia would be immediately deadly, so pH does count!
Also, these are only for freshwater, if there is enough demand I might be talked into making up the equivalent charts for saltwater tanks, but not now.
20 deg C or 68.0 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.6835
8.8 ... 6.3363
8.6 ... 4.0937
8.4 ... 2.6225
8.2 ... 1.6709
8.0 ... 1.0608
7.8 ... 0.6719
7.6 ... 0.4250
7.4 ... 0.2686
7.2 ... 0.1696
7.0 ... 0.1071
6.8 ... 0.0676
6.6 ... 0.0427
6.4 ... 0.0269
6.2 ... 0.0170
6.0 ... 0.0107
5.0 ... 0.0011
4.0 ... 0.0001
21 deg C or 69.8 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.7474
8.8 ... 6.3797
8.6 ... 4.1224
8.4 ... 2.6412
8.2 ... 1.6829
8.0 ... 1.0685
7.8 ... 0.6768
7.6 ... 0.4281
7.4 ... 0.2706
7.2 ... 0.1709
7.0 ... 0.1079
6.8 ... 0.0681
6.6 ... 0.0430
6.4 ... 0.0271
6.2 ... 0.0171
6.0 ... 0.0108
5.0 ... 0.0011
4.0 ... 0.0001
22 deg C or 71.6 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.8113
8.8 ... 6.4231
8.6 ... 4.1511
8.4 ... 2.6599
8.2 ... 1.6949
8.0 ... 1.0762
7.8 ... 0.6817
7.6 ... 0.4312
7.4 ... 0.2725
7.2 ... 0.1721
7.0 ... 0.1087
6.8 ... 0.0686
6.6 ... 0.0433
6.4 ... 0.0273
6.2 ... 0.0172
6.0 ... 0.0109
5.0 ... 0.0011
4.0 ... 0.0001
23 deg C or 73.4 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.8751
8.8 ... 6.4664
8.6 ... 4.1798
8.4 ... 2.6786
8.2 ... 1.7069
8.0 ... 1.0838
7.8 ... 0.6866
7.6 ... 0.4343
7.4 ... 0.2745
7.2 ... 0.1734
7.0 ... 0.1095
6.8 ... 0.0691
6.6 ... 0.0436
6.4 ... 0.0275
6.2 ... 0.0174
6.0 ... 0.0110
5.0 ... 0.0011
4.0 ... 0.0001
24 deg C or 75.2 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.9388
8.8 ... 6.5097
8.6 ... 4.2085
8.4 ... 2.6973
8.2 ... 1.7190
8.0 ... 1.0915
7.8 ... 0.6915
7.6 ... 0.4374
7.4 ... 0.2764
7.2 ... 0.1746
7.0 ... 0.1102
6.8 ... 0.0696
6.6 ... 0.0439
6.4 ... 0.0277
6.2 ... 0.0175
6.0 ... 0.0110
5.0 ... 0.0011
4.0 ... 0.0001
25 deg C or 77.0 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.0025
8.8 ... 6.5530
8.6 ... 4.2372
8.4 ... 2.7159
8.2 ... 1.7310
8.0 ... 1.0992
7.8 ... 0.6964
7.6 ... 0.4405
7.4 ... 0.2784
7.2 ... 0.1758
7.0 ... 0.1110
6.8 ... 0.0701
6.6 ... 0.0442
6.4 ... 0.0279
6.2 ... 0.0176
6.0 ... 0.0111
5.0 ... 0.0011
4.0 ... 0.0001
26 deg C or 78.8 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.0661
8.8 ... 6.5963
8.6 ... 4.2658
8.4 ... 2.7346
8.2 ... 1.7430
8.0 ... 1.1069
7.8 ... 0.7013
7.6 ... 0.4436
7.4 ... 0.2804
7.2 ... 0.1771
7.0 ... 0.1118
6.8 ... 0.0706
6.6 ... 0.0445
6.4 ... 0.0281
6.2 ... 0.0177
6.0 ... 0.0112
5.0 ... 0.0011
4.0 ... 0.0001
27 deg C or 80.6 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.1296
8.8 ... 6.6396
8.6 ... 4.2945
8.4 ... 2.7533
8.2 ... 1.7550
8.0 ... 1.1146
7.8 ... 0.7062
7.6 ... 0.4467
7.4 ... 0.2823
7.2 ... 0.1783
7.0 ... 0.1126
6.8 ... 0.0711
6.6 ... 0.0449
6.4 ... 0.0283
6.2 ... 0.0179
6.0 ... 0.0113
5.0 ... 0.0011
4.0 ... 0.0001
28 deg C or 82.4 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.1931
8.8 ... 6.6828
8.6 ... 4.3232
8.4 ... 2.7720
8.2 ... 1.7671
8.0 ... 1.1223
7.8 ... 0.7110
7.6 ... 0.4498
7.4 ... 0.2843
7.2 ... 0.1796
7.0 ... 0.1134
6.8 ... 0.0716
6.6 ... 0.0452
6.4 ... 0.0285
6.2 ... 0.0180
6.0 ... 0.0113
5.0 ... 0.0011
4.0 ... 0.0001
29 deg C or 84.2 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.2565
8.8 ... 6.7260
8.6 ... 4.3518
8.4 ... 2.7906
8.2 ... 1.7791
8.0 ... 1.1300
7.8 ... 0.7159
7.6 ... 0.4529
7.4 ... 0.2863
7.2 ... 0.1808
7.0 ... 0.1142
6.8 ... 0.0721
6.6 ... 0.0455
6.4 ... 0.0287
6.2 ... 0.0181
6.0 ... 0.0114
5.0 ... 0.0011
4.0 ... 0.0001
30 deg C or 86.0 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.3198
8.8 ... 6.7692
8.6 ... 4.3805
8.4 ... 2.8093
8.2 ... 1.7911
8.0 ... 1.1376
7.8 ... 0.7208
7.6 ... 0.4560
7.4 ... 0.2882
7.2 ... 0.1820
7.0 ... 0.1149
6.8 ... 0.0726
6.6 ... 0.0458
6.4 ... 0.0289
6.2 ... 0.0182
6.0 ... 0.0115
5.0 ... 0.0012
4.0 ... 0.0001
31 deg C or 87.8 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.3831
8.8 ... 6.8123
8.6 ... 4.4091
8.4 ... 2.8280
8.2 ... 1.8032
8.0 ... 1.1453
7.8 ... 0.7257
7.6 ... 0.4591
7.4 ... 0.2902
7.2 ... 0.1833
7.0 ... 0.1157
6.8 ... 0.0730
6.6 ... 0.0461
6.4 ... 0.0291
6.2 ... 0.0184
6.0 ... 0.0116
5.0 ... 0.0012
4.0 ... 0.0001
32 deg C or 89.6 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.4463
8.8 ... 6.8554
8.6 ... 4.4378
8.4 ... 2.8467
8.2 ... 1.8152
8.0 ... 1.1530
7.8 ... 0.7306
7.6 ... 0.4622
7.4 ... 0.2922
7.2 ... 0.1845
7.0 ... 0.1165
6.8 ... 0.0735
6.6 ... 0.0464
6.4 ... 0.0293
6.2 ... 0.0185
6.0 ... 0.0117
5.0 ... 0.0012
4.0 ... 0.0001
33 deg C or 91.4 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.5094
8.8 ... 6.8985
8.6 ... 4.4664
8.4 ... 2.8653
8.2 ... 1.8272
8.0 ... 1.1607
7.8 ... 0.7355
7.6 ... 0.4653
7.4 ... 0.2941
7.2 ... 0.1858
7.0 ... 0.1173
6.8 ... 0.0740
6.6 ... 0.0467
6.4 ... 0.0295
6.2 ... 0.0186
6.0 ... 0.0117
5.0 ... 0.0012
4.0 ... 0.0001
34 deg C or 93.2 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.5724
8.8 ... 6.9416
8.6 ... 4.4950
8.4 ... 2.8840
8.2 ... 1.8392
8.0 ... 1.1684
7.8 ... 0.7404
7.6 ... 0.4684
7.4 ... 0.2961
7.2 ... 0.1870
7.0 ... 0.1181
6.8 ... 0.0745
6.6 ... 0.0470
6.4 ... 0.0297
6.2 ... 0.0187
6.0 ... 0.0118
5.0 ... 0.0012
4.0 ... 0.0001
35 deg C or 95.0 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.6353
8.8 ... 6.9846
8.6 ... 4.5236
8.4 ... 2.9026
8.2 ... 1.8513
8.0 ... 1.1761
7.8 ... 0.7453
7.6 ... 0.4716
7.4 ... 0.2980
7.2 ... 0.1883
7.0 ... 0.1189
6.8 ... 0.0750
6.6 ... 0.0474
6.4 ... 0.0299
6.2 ... 0.0189
6.0 ... 0.0119
5.0 ... 0.0012
4.0 ... 0.0001
Also I'd just like to make it clear that any level of ammonia will cause health problems. Ammonia can cause gill damage, that could become permanent, and a very recent article ("Low levels of environmental ammonia increase susceptibility to disease in Chinook salmon smolts " by Ackerman PA, Wicks BJ, Iwama GK, Randall DJ in PHYSIOLOGICAL AND BIOCHEMICAL ZOOLOGY volume 79 JUL-AUG 2006) showed that fish exposed to low levels of ammonia were more susceptible to disease later on in life. But this mini-article is about when emergency action needs to be taken.
The split between the two species (ammonia and ammonium) is determined by equilibrium. The chemistry reaction can be written as:
NH3 + H+ <--> NH4+
(ammonia) + (H+ ions) <--> (ammonium+ ions)
The +'s indicating a charge of +1, and <--> indicating that the reaction can go both ways.
pH is a measure of the concentration of H+ ions. pH really means -log(base 10) of H+. For example, pH of 7.0 means a concentration of 10^-7 H+ ions, a pH of 5.0 means a concentration of 10^-5 H+ ions.
Therefore the lower the pH, the higher the concentration of H+ ions.
Now, with more H+ ions present, the above equilibrium chemical reaction gets pushed towards the right hand side. This is known as Le Chatelier's Principle. But, Le Chatelier's is a general rule, it does not give us the exact splits.
The calculate the splits, we need the equilibrium constant K = [NH3][H+]/[NH4+] where [] stands for the concentration of the species in the []'s. K is a function of temperature, so experimentation needed to be performed, and some high level computations (well beyond the scope of this mini-article) needed to be performed.
Clegg, S. and Whitfield, M did that experiment. (Their paper is "A chemical model of seawater including dissolved ammonia and the stoichiometric dissociation constant of ammonia in estuarine water and seawater from -2 to 40 deg C. Geochimica et Cosmochimia Acta Volume 59, 1995.) They found the equilibrium constant as a function of temperature and salinity.
So with this information, I calculated what % of the total ammonia in the water would be toxic ammonia and ammonium.
How to use the following tables
Know your pH and temperature.
Look up the % toxic ammonia on the following charts for your temp and pH
Know how much ammonia you have in your tank
Multiply your ammonia content by the looked up percentage
If this number is over 0.02 ppm, then immediate action needs to be taken.
Example:
I have a tank at 27 deg with pH 6.6 water and 2.0 ppm of ammonia.
% toxic ammonia (from) the chart is: 0.045%
2.0*(0.00045)=0.008 ppm toxic ammonia, so it is not immediately dangerous, though exposure to any ammonia is unhealthy for the fish.
Note that if the pH of that tank was over 8.0, the level of ammonia would be immediately deadly, so pH does count!
Also, these are only for freshwater, if there is enough demand I might be talked into making up the equivalent charts for saltwater tanks, but not now.
20 deg C or 68.0 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.6835
8.8 ... 6.3363
8.6 ... 4.0937
8.4 ... 2.6225
8.2 ... 1.6709
8.0 ... 1.0608
7.8 ... 0.6719
7.6 ... 0.4250
7.4 ... 0.2686
7.2 ... 0.1696
7.0 ... 0.1071
6.8 ... 0.0676
6.6 ... 0.0427
6.4 ... 0.0269
6.2 ... 0.0170
6.0 ... 0.0107
5.0 ... 0.0011
4.0 ... 0.0001
21 deg C or 69.8 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.7474
8.8 ... 6.3797
8.6 ... 4.1224
8.4 ... 2.6412
8.2 ... 1.6829
8.0 ... 1.0685
7.8 ... 0.6768
7.6 ... 0.4281
7.4 ... 0.2706
7.2 ... 0.1709
7.0 ... 0.1079
6.8 ... 0.0681
6.6 ... 0.0430
6.4 ... 0.0271
6.2 ... 0.0171
6.0 ... 0.0108
5.0 ... 0.0011
4.0 ... 0.0001
22 deg C or 71.6 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.8113
8.8 ... 6.4231
8.6 ... 4.1511
8.4 ... 2.6599
8.2 ... 1.6949
8.0 ... 1.0762
7.8 ... 0.6817
7.6 ... 0.4312
7.4 ... 0.2725
7.2 ... 0.1721
7.0 ... 0.1087
6.8 ... 0.0686
6.6 ... 0.0433
6.4 ... 0.0273
6.2 ... 0.0172
6.0 ... 0.0109
5.0 ... 0.0011
4.0 ... 0.0001
23 deg C or 73.4 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.8751
8.8 ... 6.4664
8.6 ... 4.1798
8.4 ... 2.6786
8.2 ... 1.7069
8.0 ... 1.0838
7.8 ... 0.6866
7.6 ... 0.4343
7.4 ... 0.2745
7.2 ... 0.1734
7.0 ... 0.1095
6.8 ... 0.0691
6.6 ... 0.0436
6.4 ... 0.0275
6.2 ... 0.0174
6.0 ... 0.0110
5.0 ... 0.0011
4.0 ... 0.0001
24 deg C or 75.2 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 9.9388
8.8 ... 6.5097
8.6 ... 4.2085
8.4 ... 2.6973
8.2 ... 1.7190
8.0 ... 1.0915
7.8 ... 0.6915
7.6 ... 0.4374
7.4 ... 0.2764
7.2 ... 0.1746
7.0 ... 0.1102
6.8 ... 0.0696
6.6 ... 0.0439
6.4 ... 0.0277
6.2 ... 0.0175
6.0 ... 0.0110
5.0 ... 0.0011
4.0 ... 0.0001
25 deg C or 77.0 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.0025
8.8 ... 6.5530
8.6 ... 4.2372
8.4 ... 2.7159
8.2 ... 1.7310
8.0 ... 1.0992
7.8 ... 0.6964
7.6 ... 0.4405
7.4 ... 0.2784
7.2 ... 0.1758
7.0 ... 0.1110
6.8 ... 0.0701
6.6 ... 0.0442
6.4 ... 0.0279
6.2 ... 0.0176
6.0 ... 0.0111
5.0 ... 0.0011
4.0 ... 0.0001
26 deg C or 78.8 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.0661
8.8 ... 6.5963
8.6 ... 4.2658
8.4 ... 2.7346
8.2 ... 1.7430
8.0 ... 1.1069
7.8 ... 0.7013
7.6 ... 0.4436
7.4 ... 0.2804
7.2 ... 0.1771
7.0 ... 0.1118
6.8 ... 0.0706
6.6 ... 0.0445
6.4 ... 0.0281
6.2 ... 0.0177
6.0 ... 0.0112
5.0 ... 0.0011
4.0 ... 0.0001
27 deg C or 80.6 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.1296
8.8 ... 6.6396
8.6 ... 4.2945
8.4 ... 2.7533
8.2 ... 1.7550
8.0 ... 1.1146
7.8 ... 0.7062
7.6 ... 0.4467
7.4 ... 0.2823
7.2 ... 0.1783
7.0 ... 0.1126
6.8 ... 0.0711
6.6 ... 0.0449
6.4 ... 0.0283
6.2 ... 0.0179
6.0 ... 0.0113
5.0 ... 0.0011
4.0 ... 0.0001
28 deg C or 82.4 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.1931
8.8 ... 6.6828
8.6 ... 4.3232
8.4 ... 2.7720
8.2 ... 1.7671
8.0 ... 1.1223
7.8 ... 0.7110
7.6 ... 0.4498
7.4 ... 0.2843
7.2 ... 0.1796
7.0 ... 0.1134
6.8 ... 0.0716
6.6 ... 0.0452
6.4 ... 0.0285
6.2 ... 0.0180
6.0 ... 0.0113
5.0 ... 0.0011
4.0 ... 0.0001
29 deg C or 84.2 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.2565
8.8 ... 6.7260
8.6 ... 4.3518
8.4 ... 2.7906
8.2 ... 1.7791
8.0 ... 1.1300
7.8 ... 0.7159
7.6 ... 0.4529
7.4 ... 0.2863
7.2 ... 0.1808
7.0 ... 0.1142
6.8 ... 0.0721
6.6 ... 0.0455
6.4 ... 0.0287
6.2 ... 0.0181
6.0 ... 0.0114
5.0 ... 0.0011
4.0 ... 0.0001
30 deg C or 86.0 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.3198
8.8 ... 6.7692
8.6 ... 4.3805
8.4 ... 2.8093
8.2 ... 1.7911
8.0 ... 1.1376
7.8 ... 0.7208
7.6 ... 0.4560
7.4 ... 0.2882
7.2 ... 0.1820
7.0 ... 0.1149
6.8 ... 0.0726
6.6 ... 0.0458
6.4 ... 0.0289
6.2 ... 0.0182
6.0 ... 0.0115
5.0 ... 0.0012
4.0 ... 0.0001
31 deg C or 87.8 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.3831
8.8 ... 6.8123
8.6 ... 4.4091
8.4 ... 2.8280
8.2 ... 1.8032
8.0 ... 1.1453
7.8 ... 0.7257
7.6 ... 0.4591
7.4 ... 0.2902
7.2 ... 0.1833
7.0 ... 0.1157
6.8 ... 0.0730
6.6 ... 0.0461
6.4 ... 0.0291
6.2 ... 0.0184
6.0 ... 0.0116
5.0 ... 0.0012
4.0 ... 0.0001
32 deg C or 89.6 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.4463
8.8 ... 6.8554
8.6 ... 4.4378
8.4 ... 2.8467
8.2 ... 1.8152
8.0 ... 1.1530
7.8 ... 0.7306
7.6 ... 0.4622
7.4 ... 0.2922
7.2 ... 0.1845
7.0 ... 0.1165
6.8 ... 0.0735
6.6 ... 0.0464
6.4 ... 0.0293
6.2 ... 0.0185
6.0 ... 0.0117
5.0 ... 0.0012
4.0 ... 0.0001
33 deg C or 91.4 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.5094
8.8 ... 6.8985
8.6 ... 4.4664
8.4 ... 2.8653
8.2 ... 1.8272
8.0 ... 1.1607
7.8 ... 0.7355
7.6 ... 0.4653
7.4 ... 0.2941
7.2 ... 0.1858
7.0 ... 0.1173
6.8 ... 0.0740
6.6 ... 0.0467
6.4 ... 0.0295
6.2 ... 0.0186
6.0 ... 0.0117
5.0 ... 0.0012
4.0 ... 0.0001
34 deg C or 93.2 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.5724
8.8 ... 6.9416
8.6 ... 4.4950
8.4 ... 2.8840
8.2 ... 1.8392
8.0 ... 1.1684
7.8 ... 0.7404
7.6 ... 0.4684
7.4 ... 0.2961
7.2 ... 0.1870
7.0 ... 0.1181
6.8 ... 0.0745
6.6 ... 0.0470
6.4 ... 0.0297
6.2 ... 0.0187
6.0 ... 0.0118
5.0 ... 0.0012
4.0 ... 0.0001
35 deg C or 95.0 deg F
=============
pH ... % toxic ammonia
=============
9.0 ... 10.6353
8.8 ... 6.9846
8.6 ... 4.5236
8.4 ... 2.9026
8.2 ... 1.8513
8.0 ... 1.1761
7.8 ... 0.7453
7.6 ... 0.4716
7.4 ... 0.2980
7.2 ... 0.1883
7.0 ... 0.1189
6.8 ... 0.0750
6.6 ... 0.0474
6.4 ... 0.0299
6.2 ... 0.0189
6.0 ... 0.0119
5.0 ... 0.0012
4.0 ... 0.0001