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Tuesday, October 9, 2012

Use a Melting Point Apparatus to Figure Out Eutectic Point

Melting point apparatus  is an instrument used to measure melting point of substance. In this experiment, we were going to measure the melting points of different components, and figure out the eutectic point by using polynomial fitting.




Fisher-Johns apparatus

Observing through the lens


Melting point apparatus




Experimental record

Component
Melting range ()
Average ()
100% Benzoic acid
122.0~124.0
123.0
99% Benzoic acid +
1%  2-naphthol
118.0~120.0
119.0
80% Benzoic acid +
20%  2-naphthol
90.4~113.6
102.0
50% Benzoic acid +
50%  2-naphthol
90.2~106.5
98.4
20% Benzoic acid +
80%  2-naphthol
88.3~105.8
97.1
100% 2-naphthol
120.0~122.0
121.0




Data processing



Model
Polynomial


Adj. R-Square
0.91129
0.99865
0.98503


Value
Standard Error
Poly. fitting of Max.
Intercept
122.42316
1.75243
Poly. fitting of Max.
B1
-70.83259
42.35292
Poly. fitting of Max.
B2
179.32579
205.90115
Poly. fitting of Max.
B3
-294.68184
325.2792
Poly. fitting of Max.
B4
185.78141
161.53845
Poly. fitting of Min.
Intercept
121.58944
0.45627
Poly. fitting of Min.
B1
-325.07157
11.02727
Poly. fitting of Min.
B2
1139.85131
53.6097
Poly. fitting of Min.
B3
-1644.22212
84.69171
Poly. fitting of Min.
B4
827.85708
42.05916
Poly. of average
Intercept
122.00714
1.10342
Poly. of average
B1
-198.13952
26.66762
Poly. of average
B2
660.78879
129.64618
Poly. of average
B3
-970.95412
204.81286
Poly. of average
B4
507.30774
101.71309

Analysis

Poly. of average
F(x) = y = 122.00714-198.13952*x+660.78879*x^2
-970.95412*x^3+507.30774*x^4
First order derivative of F(x)
y’ = -198.13952+1321.57758*x
-2912.86236*x^2+2029.23096*x^3
Eutectic point (Benzoic acid / Total)
0.717
Eutectic temperature ()
95.8






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