This document describes using regression analysis to determine whether molecular weight or number of carbon chains is a better predictor of boiling point for alcohols. It uses data on boiling points of alcohols from methanol to octanol to build 2nd and 3rd order regression models with molecular weight and carbon chains as predictors. The models are used to predict boiling points for higher alcohols to calculate percentage errors. The analysis finds that the 2nd order carbon chain model has the lowest percentage errors, indicating number of carbon chains is a better predictor of boiling point than molecular weight.

1. Which model is a better predictor, using molecular weight or number of carbon chain
2 or more independent variable (predictor)
Is boiling point associated with molecular weight and carbon chains.
Molecular weight or number of carbon chains – independent variables (predictor)
Boiling point of alcohol – dependent variable (outcome)
Using Regression and Anova for analysis
Independent variable
Dependent variable
Is molecular weight or number carbon chains a good predictor
Independent variable Dependent
variable
Data for b/p from CRC Handbook. Click here data
IA secondary data based – Regression analysis for boiling point estimation for alcohol
B/point = x1 (molecular weight) + intercept
B/point = x1 (number of carbons) + intercept or
Research Question
Use 5 -12 carbon chains for regression model
Use regression to estimate the b/p for 15, 17,19 carbon chain
Find the % error using expt values with predicted values.
Using molecular weight, 2nd and 3rd order as predictor for b/p.
Using carbon chain 2nd and 3rd order as predictor for b/p.
MF
Number
carbon
Molecular
weight b/p
CH3OH 1 32.04 64.7
C2H5OH 2 46.09 78
C3H7OH 3 60.09 97
C4H9OH 4 74.12 117.7
C5H11OH 5 88.15 138
C6H13OH 6 102.16 157
C7H15OH 7 116.88 175

2. Homologous Series
Class Functional Suffix Example Formula
Alcohol Hydroxyl - ol methanol CnH2n+1OH
• member differ by CH2 gp
• same functional group
• similar chemical properties
• chemical formula CnH2n+1OH
• end with ol
Number
carbon
IUPAC
name
Structure formula b/p
1 Methanol CH3OH 64.7
2 Ethanol CH3CH2OH 78
3 Propanol CH3CH2CH2OH 97
4 Butanol CH3(CH2)2CH2OH 117.7
5 Pentanol CH3(CH2)3CH2OH 138
methanol ethanol propanol butanol
H
‫׀‬
H - C – OH
‫׀‬
H
H H
‫׀‬ ‫׀‬
H - C – C – OH
‫׀‬ ‫׀‬
H H
H H H
‫׀‬ ‫׀‬ ‫׀‬
H - C – C – C – OH
‫׀‬ ‫׀‬ ‫׀‬
H H H
H H H H
‫׀‬ ‫׀‬ ‫׀‬ ‫׀‬
H - C – C – C – C – OH
‫׀‬ ‫׀‬ ‫׀‬ ‫׀‬
H H H H
Hydrocarbon skeleton Functional gp
b/p
increase ↑
Physical properties
• Increase RMM / molecular size
•RMM increase ↑ - Van Der Waals forces stronger ↑
↓
boiling point increases ↑
(Increasing polarisability ↑)
London dispersion forces/temporary dipole ↑
Number
carbon
Molecular
weight b/p
1 32.04 64.7
2 46.09 78
3 60.09 97
4 74.12 117.7
5 88.15 138
6 102.16 157
7 116.88 175
8 130.23 195
9 144.26 214
10 158.28 230
11 172.31 243
12 186.34 260
14 214.39 289
15 228.41 299
17 256.5 308
19 284.5 345
Boiling point for diff alcohol
boiling point increase with increase carbon atoms

3. IA secondary data based –Regression analysis for b/p estimation for alcohol
Molecular weight 2nd, 3rd order as predictor for b/p Carbon chain, 2nd, 3rd order as predictor for b/p
Number
carbon
Molecular
weight b/p
predict
poly fit 3rd
order
predict
poly fit 2nd
order
1 32.04 64.7
2 46.09 78
3 60.09 97
4 74.12 117.7
5 88.15 138
6 102.16 157
7 116.88 175
8 130.23 195
9 144.26 214
10 158.28 230
11 172.31 243
12 186.34 260
14 214.39 289
15 228.41 299
17 256.5 308
19 284.5 345
Number
carbon
Molecular
weight b/p
predict
poly fit 3rd
order
predict
poly fit 2nd
order
1 32.04 64.7
2 46.09 78
3 60.09 97
4 74.12 117.7
5 88.15 138
6 102.16 157
7 116.88 175
8 130.23 195
9 144.26 214
10 158.28 230
11 172.31 243
12 186.34 260
14 214.39 289
15 228.41 299
17 256.5 308
19 284.5 345
Research Question
Use 5 -12 carbon chains for regression model
Use regression to predict b/p for 15, 17, 19 carbon chain
Find the % error using expt values with predicted values.
Using molecular weight, 2nd and 3rd order as predictor for b/p.
Using carbon chain 2nd and 3rd order as predictor for b/p.

4. Predicted b/p for carbon 19 – MW of 284.5
3rd order fit, y = -0.00002x3 + 0.007x2 + 0.6284x + 43.5
b/p= -0.00002(284.5)3 + 0.007(284.5)2 + 0.6284(284.5) + 43.5 = 328
Predicted b/p for carbon 17 – MW of 256.5
3rd order fit, y = -0.00002x3 + 0.007x2 + 0.6284x + 43.5
b/p= -0.00002(256.5)3 + 0.007(256.5)2 + 0.6284(256.5) + 43.5 = 328
Predicted b/p for carbon 19 – MW of 284.5
2nd order fit, y = -0.0021x2 + 1.837x – 8.095
b/p= -0.0021(256.5)2 + 1.837(256.5) – 8.095 = 344
Predicted b/p for carbon 17 – MW of 256.5
2nd order fit, y = -0.0021x2 + 1.837x – 8.095
b/p= -0.0021(256.5)2 + 1.837(256.5) – 8.095 = 324
Predicted b/p for carbon 15 – MW of 228.4
2nd order fit, y = -0.0021x2 + 1.837x – 8.095
b/p= -0.0021(228.4)2 + 1.837(228.4) – 8.095 = 301
Predicted b/p for carbon 15 – MW of 228.4
3rd order fit, y = -0.00002x3 + 0.007x2 + 0.6284x + 43.5
b/p= -0.00002(228.4)3 + 0.007(228.4)2 + 0.6284(228.4) + 43.5 = 313
Research Question
Which model, molecular weight model, 2nd , 3rd order, better predictor for b/p.
Which model, carbon chain model, 2nd, 3rd order, better predictor for b/p.
Molecular weight 3rd order as predictor for b/p
y = -2E-05x3 + 0.007x2 + 0.6284x + 43.501
R² = 0.9991
0
50
100
150
200
250
300
0 50 100 150 200
b/p
molecular weight
molecular weight vs b/p
Molecular weight 2nd order as predictor for b/p
y = -0.0021x2 + 1.8371x - 8.0951
R² = 0.999
0
50
100
150
200
250
300
0 50 100 150 200
b/p
molecular weight
molecular weight vs b/p

5. Predicted b/p for carbon 19
2nd order fit, y = -0.44x2 + 24.96x + 23.44
b/p= -0.44(19)2 + 24.96(19) + 23.44 = 339
Predicted b/p for carbon 17
2nd order fit, y = -0.44x2 + 24.96x + 23.44
b/p= -0.44(17)2 + 24.96(17) + 23.44 = 320
Predicted b/p for carbon 15
2nd order fit, y = -0.44x2 + 24.96x + 23.44
b/p= -0.44(15)2 + 24.96(15) + 23.44 = 298
Predicted b/p for carbon 19
3rd order fit, y = -0.0455x3 + 0.718x2 + 15.53x + 47.78
b/p= -0.0455(19)3 + 0.718(19)2 + 15.53(19) + 47.78 = 290
Predicted b/p for carbon 17
3rd order fit, y = -0.0455x3 + 0.718x2 + 15.53x + 47.78
b/p= -0.0455(17)3 + 0.718(17)2 + 15.53(17) + 47.78 = 296
Predicted b/p for carbon 15
3rd order fit, y = -0.0455x3 + 0.718x2 + 15.53x + 47.78
b/p= -0.0455(15)3 + 0.718(15)2 + 15.53(15) + 47.78 = 289
Research Question
Which model, molecular weight model, 2nd , 3rd order, better predictor for b/p.
Which model, carbon chain model, 2nd, 3rd order, better predictor for b/p.
Carbon chain 3rd order as predictor for b/p
y = -0.0455x3 + 0.7186x2 + 15.532x + 47.781
R² = 0.9993
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14
b/p
carbon chain
carbon chain vs b/p
y = -0.4405x2 + 24.964x + 23.44
R² = 0.9992
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14
b/p
carbon chain
carbon chain vs b/p
Carbon chain 2nd order as predictor for b/p

6. IA secondary data based –Regression analysis for b/p estimation for alcohol
Molecular weight 2nd, 3rd order as predictor for b/p Carbon chain, 2nd, 3rd order as predictor for b/p
Number
carbon
Molecular
weight b/p
predict
poly fit 3rd
order
(% error)
predict
poly fit 2nd
order
(% error)
1 32.04 64.7
2 46.09 78
3 60.09 97
4 74.12 117.7
5 88.15 138
6 102.16 157
7 116.88 175
8 130.23 195
9 144.26 214
10 158.28 230
11 172.31 243
12 186.34 260
14 214.39 289
15 228.41 299 313 (5%) 301 (0.6%)
17 256.5 308 328 (6.5%) 324 (5%)
19 284.5 345 328 (5%) 344 (0.2%)
Number
carbon
Molecular
weight b/p
predict
poly fit 3rd
order
(% error)
predict
poly fit 2nd
order
(% error)
1 32.04 64.7
2 46.09 78
3 60.09 97
4 74.12 117.7
5 88.15 138
6 102.16 157
7 116.88 175
8 130.23 195
9 144.26 214
10 158.28 230
11 172.31 243
12 186.34 260
14 214.39 289
15 228.41 299 289 (3.3%) 298 (0.3%)
17 256.5 308 296 (4%) 320 (4%)
19 284.5 345 290 (16%) 339 (2%)
% error =
(𝑬𝒙𝒑𝒕 𝒗𝒂𝒍𝒖𝒆 −𝑷𝒓𝒆𝒅𝒊𝒄𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆)
𝑬𝒙𝒑𝒕 𝒗𝒂𝒍𝒖𝒆
x 100%
% error =
(𝟐𝟗𝟗 −𝟑𝟏𝟑)
𝟐𝟗𝟗
x 100% = 5%
% error =
(𝑬𝒙𝒑𝒕 𝒗𝒂𝒍𝒖𝒆 −𝑷𝒓𝒆𝒅𝒊𝒄𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆)
𝑬𝒙𝒑𝒕 𝒗𝒂𝒍𝒖𝒆
x 100%
% error =
(𝟐𝟗𝟗 −𝟐𝟖𝟗)
𝟐𝟗𝟗
x 100% = 3.3%
Research Question
Use 5 -12 carbon chains for regression model
Use regression to predict b/p for 15, 17, 19 carbon chain
Find the % error using expt values with predicted values.
Using molecular weight, 2nd and 3rd order as predictor for b/p.
Using carbon chain 2nd and 3rd order as predictor for b/p.

7. carbon chain 2nd order model is a better fit
Research Question
Use regression to predict b/p for carbon 15, 17, 19 based on molecular weight.
Which model, molecular weight model, better predictor for b/p.
Which model, carbon chain model, better predictor for b/p.
molecular weight 2nd order model is a better fit
% error 2nd order, smaller compared to 3rd order model
2nd order fit – % error changes from 0.6% to 5% to 0.2% as
carbon chain changes from 15 to 17 to 19.
% error 2nd order smaller compared to 3rd order model.
2nd order fit – % error changes from 0.3% to 4% to 2% as
carbon chain changes from 15 to 17 to 19.
y = -0.4405x2 + 24.964x + 23.44
R² = 0.9992
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14
b/p
carbon chain
carbon chain vs b/p
y = -0.0021x2 + 1.8371x - 8.0951
R² = 0.999
0
50
100
150
200
250
300
0 50 100 150 200
b/p
molecular weight
molecular weight vs b/p
Number
carbon
Molecular
weight b/p
predict
poly fit 3rd
order
(% error)
predict
poly fit 2nd
order
(% error)
15 228.41 299 313 (5%) 301 (0.6%)
17 256.5 308 328 (6.5%) 324 (5%)
19 284.5 345 328 (5%) 344 (0.2%)
Number
carbon
Molecular
weight b/p
predict
poly fit 3rd
order
(% error)
predict
poly fit 2nd
order
(% error)
15 228.41 299 289 (3.3%) 298 (0.3%)
17 256.5 308 296 (4%) 320 (4%)
19 284.5 345 290 (16%) 339 (2%)
molecular weight 2nd order model is a better fit
carbon chain 2nd order model is a better fit

8. carbon chain 2nd order model is a weaker fit
Research Question
Which model, molecular weight or carbon chain model, a better predictor for b/p.
molecular weight 2nd order model is a better fit
% error 2nd order molecular weight model, smaller
compared to carbon chain model.
2nd order fit – % error changes from 0.6% to 5% to 0.2% as
carbon chain changes from 15 to 17 to 19.
% error 2nd order carbon chain model higher
compared to molecular weight model.
2nd order fit – % error changes from 0.3% to 4% to 2% as
carbon chain changes from 15 to 17 to 19.
y = -0.4405x2 + 24.964x + 23.44
R² = 0.9992
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14
b/p
carbon chain
carbon chain vs b/p
y = -0.0021x2 + 1.8371x - 8.0951
R² = 0.999
0
50
100
150
200
250
300
0 50 100 150 200
b/p
molecular weight
molecular weight vs b/p
Number
carbon
Molecular
weight b/p
predict
poly fit 3rd
order
(% error)
predict
poly fit 2nd
order
(% error)
15 228.41 299 313 (5%) 301 (0.6%)
17 256.5 308 328 (6.5%) 324 (5%)
19 284.5 345 328 (5%) 344 (0.2%)
Number
carbon
Molecular
weight b/p
predict
poly fit 3rd
order
(% error)
predict
poly fit 2nd
order
(% error)
15 228.41 299 289 (3.3%) 298 (0.3%)
17 256.5 308 296 (4%) 320 (4%)
19 284.5 345 290 (16%) 339 (2%)
molecular weight 2nd order model is a better fit
carbon chain 2nd order model is a weaker fit