Formulae you may require
N
x - xi
z= i
s
t calc =
known value- x i
s
n
€
€
µ= x ±
t calc =
ts
N
€
xi − x j
N1 • N 2
N1 + N 2
sp
2
N1
€
i
i
set 2
j
−xj
€
)
N1 +N 2 -2
di
N
sd
i
i=1
N
n
2
∑ (d − d )
i
€
sd =
Q calc =
€
 tsr  2
N= 

 x −µ
€
G calc =
N −1
Gap
Range
ΔG = –RTlnK
s
€
I=
€
1 N
2
CiZ i
∑
2 i=1
K a1K a2 [HA - ] + K a1K w
−b± b 2 − 4ac
+
x=
[H 3O ] =
2a
€
[HA-] + K a1
[A ]
+ log
−
[HA]
€ i2 I
0.51z
at 25 C&1atm : -log γ i =
α I 
1+  i 
 305 

[MY ]€
=
[M ][EDTA]
2
N∑ x i y i − ∑ y i ∑ x i
€
m=
2
N∑ x i 2 − ∑ x i
(
∑ y ∑ x −∑ x ∑ x y
b=
N ∑ x − (∑ x )
i
)
€
€
€
c = νλ
Am =€εX b[ X] + εYb[ Y] + …
A = εbc
€
Chem. 2410, Fall 2010
€
i
i
i
2
2
i
(n−4 )
n+
2
€
ΔG = ΔH – TΔS
€
questionable value- x i
e 3 = e1 + e 2
€
K f ' = K fα Y 4−
2
i
i
2
s2o = s2a + s2s
€
pH =pK a
xi =
N −1
t calc =
y = mx + b
€
)
N
2
N2
set1
i
s=
€
∑( x − x ) + ∑( x
sp =
∑(
xi − xi
∑x
€
E = hν =
[H 3O + ]
α0 =€
[H 3O + ] + K a
i
hc
= hcν˜
λ
α1 =
Ka
[H 3O + ] + K a
€
1
i
Values of Q for rejection of data
Q (90% Conf. level)
0.94
0.76
0.64
0.56
0.51
0.47
0.44
0.41
# of Observations
3
4
5
6
7
8
9
10
Critical values of G for rejection of outlier
G (95% Conf. level)
1.463
1.672
1.822
1.938
2.032
2.110
2.176
# of Observations
4
5
6
7
8
9
10
Student’s t values
Confidence Level (%)
Degrees
of
Freedom
1
2
3
4
5
6
7
8
9
10
15
20
25
30
40
60
120
∞
50
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.691
0.687
0.684
0.683
0.681
0.679
0.677
0.674
Chem. 2410, Fall 2010
90
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.753
1.725
1.708
1.697
1.684
1.671
1.658
1.645
95
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.131
2.086
2.068
2.042
2.021
2.000
1.980
1.960
98
31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.602
2.528
2.485
2.457
2.423
3.390
2.358
2.326
99
63.657
9.925
5.841
4.604
4.032
3.707
3.500
3.355
3.250
3.169
2.947
2.845
2.787
2.750
2.704
2.660
2.617
2.576
99.5
127.32
14.089
7.453
5.598
4.773
4.317
4.029
3.832
3.690
3.581
3.252
3.153
3.078
3.030
2.971
2.915
2.860
2.807
99.9
636.619
31.598
12.924
8.610
6.869
5.959
5.408
5.041
4.781
4.587
4.073
3.850
3.725
3.646
3.551
3.460
3.373
3.291
2