Ethanol Rocket: Difference between revisions
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The molecular weight of ethanol is <math>46.069</math> g/mol, and the molar weight of oxygen is 32 g/mol. The oxygen--ethanol fuel ratio is <math>3\times 32 / 46 = 2.1</math>. We need <math>2.1 </math> kg of oxygen to <math>1</math> kg of ethanol. The air consists of 23.2 mass-% of oxygen, thus the air--ethanol ratio is <math>2.1/0.232 = 9</math>. | The molecular weight of ethanol is <math>46.069</math> g/mol, and the molar weight of oxygen is 32 g/mol. The oxygen--ethanol fuel ratio is <math>3\times 32 / 46 = 2.1</math>. We need <math>2.1 </math> kg of oxygen to <math>1</math> kg of ethanol. The air consists of 23.2 mass-% of oxygen, thus the air--ethanol ratio is <math>2.1/0.232 = 9</math>. | ||
The volume-% of oxygen in air is 20.9%. The volume of the bottle is <math>V = 500 </math> ml which gives the amount of oxygen to be <math>0.209 V = 0.209 \times 500 = 104.5</math> ml <math>=0.1045\times1.429 = 0.149 </math> g of oxygen, which gives the amount of ethanol <math>0.126 / 2.1 = 0.072 </math> g <math>=0.072/0.789= 0.091</math> ml. '''OR''' directly using air--ethanol ratio we have <math>\rho V/9 = 1.2041 \times 0.5 /9 = 0.066</math> gram. That amount equals to <math>V/\rho_\textrm{Ethanol} = 0.066g/(789g/l) = 0.084 </math> ml. Almost the same result. See the attached spreadsheet for detailed calculations (and mistakes). | The volume-% of oxygen in air is 20.9%. The volume of the bottle is <math>V = 500 </math> ml which gives the amount of oxygen to be <math>0.209 V = 0.209 \times 500 = 104.5</math> ml <math>=0.1045\times1.429 = 0.149 </math> g of oxygen, which gives the amount of ethanol <math>0.126 / 2.1 = 0.072 </math> g <math>=0.072/0.789= 0.091</math> ml. '''OR''' directly using air--ethanol ratio we have <math>\rho V/9 = 1.2041 \times 0.5 /9 = 0.066</math> gram. That amount equals to <math>V/\rho_\textrm{Ethanol} = 0.066g/(789g/l) = 0.084 </math> ml. Almost the same result. See the attached spreadsheet for detailed calculations (and mistakes). The small difference in amounts is due to the density of oxygen, which is at STP (0 degrees). | ||
[[File:Ethanol oxygen combustion.ods|thumb|Ethanol oxygen combustion spreadsheet]] | [[File:Ethanol oxygen combustion.ods|thumb|Ethanol oxygen combustion spreadsheet]] | ||
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|- | |- | ||
| Oxygen (g)|| 1.429 g/l ||STP | | Oxygen (g)|| 1.429 g/l ||STP | ||
|- | |||
| Oxygen (g)|| 1.314 g/l || 20 °C | |||
|- | |- | ||
| Ethanol (l) ||789.45 g/l|| 20 °C | | Ethanol (l) ||789.45 g/l|| 20 °C | ||
Revision as of 20:21, 29 May 2021
Introduction
Theory
Ethanol 3d model
| -1.1712 | 0.2997 | 0.0000 | O |
| -0.0463 | -0.5665 | 0.0000 | C |
| 1.2175 | 0.2668 | 0.0000 | C |
| -0.0958 | -1.2120 | 0.8819 | H |
| -0.0952 | -1.1938 | -0.8946 | H |
| 2.1050 | -0.3720 | -0.0177 | H |
| 1.2426 | 0.9307 | -0.8704 | H |
| 1.2616 | 0.9052 | 0.8886 | H |
| -1.1291 | 0.8364 | 0.8099 | H |
HCH bonds are assumed to be undistorded tetraherdal angle 109.5 degrees. Actually the electrons repeal each other. The HOC bond is 104.5 deg because. . .
Valence shell electron-pair repulsion theory (VSEPR theory). . .
| Atom | Radius | |
|---|---|---|
| C | 170 pm | 1.42 |
| H | 120 pm | 1.00 |
| O | 152 pm | 1.27 |
Use CPK coloring convention, white (hydrogen), black (carbon) and red (oxygen).
Ethanol reaction with Oxygen and Air
Ethanol reaction with oxygen
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textrm{C}_2 \textrm H_6 \textrm O + 3\textrm O_2 \to 2 \textrm{CO}_2 + 3 \textrm H_2\textrm O }
The molecular weight of ethanol is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 46.069} g/mol, and the molar weight of oxygen is 32 g/mol. The oxygen--ethanol fuel ratio is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3\times 32 / 46 = 2.1} . We need Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2.1 } kg of oxygen to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1} kg of ethanol. The air consists of 23.2 mass-% of oxygen, thus the air--ethanol ratio is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2.1/0.232 = 9} .
The volume-% of oxygen in air is 20.9%. The volume of the bottle is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V = 500 } ml which gives the amount of oxygen to be Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0.209 V = 0.209 \times 500 = 104.5} ml Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle =0.1045\times1.429 = 0.149 } g of oxygen, which gives the amount of ethanol Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0.126 / 2.1 = 0.072 } g ml. OR directly using air--ethanol ratio we have Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho V/9 = 1.2041 \times 0.5 /9 = 0.066} gram. That amount equals to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V/\rho_\textrm{Ethanol} = 0.066g/(789g/l) = 0.084 } ml. Almost the same result. See the attached spreadsheet for detailed calculations (and mistakes). The small difference in amounts is due to the density of oxygen, which is at STP (0 degrees).
File:Ethanol oxygen combustion.ods
The density of oxygen
| Density Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho} | At | |
|---|---|---|
| Oxygen (g) | 1.429 g/l | STP |
| Oxygen (g) | 1.314 g/l | 20 °C |
| Ethanol (l) | 789.45 g/l | 20 °C |
| Air (l) | 1.2041 g/l | 20 °C |
References
https://nptel.ac.in/content/storage2/courses/123106002/MODULE%20-%20I/Lecture%201.pdf
