Judul: Pembuatan Biodiesel Karet dan Biodiesel Sawit dengan Instrumen Ultrasonik serta Karakteristik Campurannya
Abstrak: Biodiesel is one of known alternative fuel, obtained by oil processing, for example from rubberseed oil and palm oil. Conventionally, biodiesel obtained by reacted oil with methanol for 1 hour at temperature of 65 oC with mechanical stirring, using homogenous catalyst such as NaOH. Homogeneous catalysts dissolve fully in the glycerol layer and partially in the biodiesel layer during the triglyceride transesterification process. Heterogeneous (solid) catalysts, such as CaO, can prevent contamination, making product separation much easier. Moreover, the reaction time of conventional methods can be shortened by applying ultrasonic energy. This research consists of several stages, aimed to obtain biodiesel yield from transesterification using homogenous and heterogenous catalyst, to produce rubberseed biodiesel and palm biodiesel by applying ultrasonic energy, and then obtain the characteristics of palm biodiesel, rubberseed biodiesel, and mix of both. The result showed that the transesterification process using heterogenous catalyst need longer time and give the lower biodiesel yield than the transesterification using homogenous catalyst. Ultrasonic transesterification of palm oil gives a greater yield then the conventional stirring methods, which ultrasonic transesterification yield range between 96.52% to 98.03% and the acid number range from 0.50 mg KOH/g sample to 0.63 mg KOH/g sample. Ultrasonic esterification succeeded in reducing acid value of rubber seed oil in a shorter time, which is smaller than acid value by 30 minute conventional esterification. Ultrasonic transesterification only succeeded to form biodiesel from rubberseed oil that has gone through the 30 minutes ultrasonic esterification (78.84% yield) and through an 1 hour conventional esterification (91.55% yield). Rubberseed biodiesel, palm methyl ester, and a blended of both meets the SNI-04-7182-2006 on the characteristics of acid value, density, viscosity, and cloud point. The iodine number of rubberseed biodiesel was still above the standard, but blending palm methyl ester to rubberseed biodiesel can reduce the iodine number of blended biodiesel to meet the standards. Production cost analysis at biodiesel blended (25% palm methyl ester ini rubberseed biodiesel) resulted : ultrasonic methods still more expensive than conventional methods.
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Judul: Biodiesel Production from Used Cooking Oil Using KOH Catalyst by Ultrasonic Wave Method
Abstrak: Kebijakan penggantian BBM menjadi bahan bakar nabati telah dikeluarkan untuk mengurangi tekanan impor dan ancaman ketahanan energi, salah satunya melalui pembuatan biodiesel dari minyak jelantah. Teknologi pembuatan biodiesel secara konvensional membutuhkan waktu yang lama serta energi yang cukup besar. Metode ultrasonik dapat menjadi alternatif karena dapat mempersingkat waktu serta membutuhkan input energi yang lebih kecil. Penelitian ini bertujuan melihat pengaruh waktu paparan gelombang ultrasonik (5, 10, dan 15 menit) dan konsentrasi katalis KOH (1,0%, 1,5%, dan 2,0% b/b) dan membandingkannya dengan nilai SNI. Mutu yang diuji dan dianalisis pada hasil biodiesel yaitu yield, viskositas kinematik, densitas, dan bilangan asam. Rancangan percobaan pada penelitian menggunakan rancangan acak lengkap dengan dua faktor, dan dianalisis dengan ANOVA (α = 0,05) dan uji lanjut Duncan. Hasil perlakuan terbaik yang diperoleh yaitu perlakuan konsentrasi katalis KOH 2,0% dengan waktu transesterifikasi selama 15 menit. Perlakuan tersebut menghasilkan yield sebesar 78,61%, viskositas kinematik sebesar 4,505 cSt, densitas sebesar 850,2761 kg/m3, dan bilangan asam sebesar 0,468 mg KOH/g. Seluruh mutu pada perlakuan ini telah memenuhi standar SNI 7182:2015., The policy of subtituting fossil fuel into biofuels has been issued to reduce import pressure and the threat of energy security, one of which is by making biodiesel from used cooking oil. Conventional biodiesel production technology requires a long time and considerable energy. The ultrasonic method can be an alternative because it can shorten the time and requires less input energy. This research aims to analyze the effect of exposure time to ultrasonic waves (5, 10, and 15 minutes) and KOH catalyst concentration (1,0%, 1,5%, and 2,0% w/w) and compare them with the SNI. The parameters tested and analyzed on the biodiesel were yield, kinematic viscosity, density, and acid number. The experimental design in this research used a complete randomized design with two factors, and was analyzed by ANOVA (α = 0,05) and Duncan's post hoc test. The best treatment result obtained is the treatment of 2,0% KOH catalyst concentration with a transesterification time of 15 minutes. The treatment resulted a yield 78,61%, kinematic viscosity 4,505 cSt, density 850,2761 kg/m3 and the acid value 0,468 mg KOH/g. All quality in this treatment has met the SNI 7182:2015.
Keyword: biodiesel, transesterification, ultrasonic, used cooking oil

Judul: Closed Knight’s Tour pada Papan Catur Berbentuk Persegi Panjang dengan Ukuran Maksimal 8 × 8
Abstrak: Closed Knight’s Tour merupakan langkah kuda yang mengunjungi setiap kotak pada papan catur tepat satu kali dengan langkah kuda berawal dan berakhir pada kotak yang sama. Graf yang terbentuk dari closed knight’s tour dinotasikan sebagai graf G(m,n), dengan m adalah banyaknya baris dan n adalah banyaknya kolom. Graf tersebut memuat Hamiltonian cycle. Sebuah graf terhubung G adalah graf bipartite jika dan hanya jika graf tersebut tidak memiliki cycle dengan panjang ganjil. Papan catur yang memenuhi syarat cukup untuk memiliki closed knight’s tour adalah papan catur berukuran 5 × 6, 5 × 8, 6 × 6, 6 × 7, 6 × 8, 7 × 8, dan 8 × 8.
Keyword: bipartite, closed knight’s tour, hamiltonian cycle, knight’s tour, teori graf