Respuesta :
The energy released by burning 0.15 g of ethanol is[tex]\boxed{{\text{d}}{\text{. 15}}{\text{.2 kJ}}}[/tex].
Further explanation:
Enthalpy is defined as a state function and therefore its value depends upon the initial and final state of the system but not upon the path. This is the reason that the overall reaction can be simply obtained by adding or subtracting the enthalpy change of the individual steps utilized to get the final reaction. Enthalpy change is the amount of energy released or absorbed during a chemical reaction. It is denoted by [tex]\Delta{\text{H}}[/tex].
Combustion reactions are those reactions in which a compound is burned in presence of air to form water and carbon dioxide.
Example of combustion reactions are as follows:
(a) [tex]{\text{C}}{{\text{H}}_4}+{{\text{O}}_2}\to{\text{C}}{{\text{O}}_2} + {{\text{H}}_2}{\text{O}}[/tex]
(b) [tex]{{\text{C}}_{10}}{{\text{H}}_{14}}+12{{\text{O}}_2}\to10{\text{C}}{{\text{O}}_2}+4{{\text{H}}_2}{\text{O}}[/tex]
Enthalpy change of combustion reaction is the amount of energy released when 1 mole of compound is burned in excess of oxygen at standard temperature and pressure to form carbon dioxide and water.
The balanced chemical reaction is written as follows:
[tex]{{\text{C}}_2}{{\text{H}}_5}{\text{OH}}+{\text{3}}{{\text{O}}_2}\to{\text{2C}}{{\text{O}}_2}+3{{\text{H}}_2}{\text{O}}[/tex]
According to the stoichiometric of reaction, 1 mole of ethanol reacts with 3 moles of oxygen molecule to form 2 moles of carbon dioxide and 3 moles of water.
The expression to calculate the number of moles is as follows:
[tex]{\text{number of moles}}=\frac{{{\text{mass of }}{{\text{C}}_2}{{\text{H}}_5}{\text{OH}}}}{{{\text{molar mass of }}{{\text{C}}_2}{{\text{H}}_5}{\text{OH}}}}[/tex] …… (1)
Given mass of [tex]{{\text{C}}_2}{{\text{H}}_5}{\text{OH}}[/tex] is 0.15 g.
Molar mass of [tex]{{\text{C}}_2}{{\text{H}}_5}{\text{OH}}[/tex] is 46.07 g.
Substitute these value in the equation (1).
[tex]\begin{aligned}{\text{number of moles}}&=\frac{{0.51{\text{ g}}}}{{46.07{\text{ g/mol}}}}\\&=0.011{\text{ mol}}\\\end{aligned}[/tex]
The enthalpy of combustion of ethanol at [tex]{\mathbf{25}}\;{\mathbf{^\circ C}}[/tex] is[tex]{\mathbf{1386 kJ/mol}}[/tex].
The formula to calculate amount of energy released is as follows:
[tex]{\text{Amount of energy}}={\text{number of moles}}\times{\text{enthalpy }}[/tex] …… (2)
Substitute 0.011 mol for number of moles and [tex]{\text{1386 kJ/mol}}[/tex]for enthalpy change in equation (2)
[tex]\begin{aligned}{\text{Amount of energy}}&=0.011{\text{ mol}}\times{\text{1386 kJ/mol}}\\&=15.246{\text{ kJ}}\\&\approx15.2{\text{ kJ}}\\\end{aligned}[/tex]
Therefore, the amount of energy released is [tex]{\mathbf{15}}{\mathbf{.2 kJ}}[/tex].
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Answer details:
Grade: Senior school
Subject: Chemistry
Chapter: Thermodynamics
Keywords: Energy, number of moles, enthalpy, enthalpy change, combustion reaction, released, absorbed, standard, temperature, pressure, chemical reaction, 15.2 kj, 0.011 mol and 1386 kj.
0.51 g of ethanol is burned in a defective calorimeter leading to an increase of 10 °C in 200 mL of water. The energy released is 15.2 kJ (d).
0.51 g of ethanol is burned in a calorimeter leading to an increase of 10 °C in 200 mL of water.
First, we will calculate the mass of 200 mL of water using its density (1 g/mL).
[tex]200 mL \times \frac{1g}{mL} = 200g[/tex]
Then, we can calculate the heat absorbed by the water using the following expression.
[tex]Q=c \times m \times \Delta T = \frac{4.184J}{g\° C } \times 200g \times 10 \° C \times \frac{1kJ}{1000J} = 8.37 kJ[/tex]
where,
- c: specific heat capacity of water
- m: mass of water
- ΔT: change in the temperature
Since the calorimeter is not perfect, part of the heat released by the combustion of ethanol was lost. So we can assume the heat released was at least 8.37 kJ.
We can calculate the heat released by the combustion of 0.51 g of ethanol considering:
- The enthalpy of combustion of ethanol is -1386 kJ/mol.
- The molar mass of ethanol is 46.07 g/mol.
[tex]0.51 g \times \frac{1mol}{46.07g} \times \frac{(-1386kJ)}{1mol} \approx -15.2 kJ[/tex]
0.51 g of ethanol is burned in a defective calorimeter leading to an increase of 10 °C in 200 mL of water. The energy released is 15.2 kJ.
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