Respuesta :
Answer:
For a: The total heat required is 36621.5 J
For b: The total heat required is 58944.5 J
Explanation:
- For a:
To calculate the heat required at different temperature, we use the equation:
[tex]q=mc\Delta T[/tex] .........(1)
where,
q = heat absorbed
m = mass of substance
[tex]c[/tex] = specific heat capacity of substance
[tex]\Delta T[/tex] = change in temperature
To calculate the amount of heat required at same temperature, we use the equation:
[tex]q=m\times \Delta H[/tex] ........(2)
where,
q = heat absorbed
m = mass of substance
[tex] \Delta H[/tex] = enthalpy of the reaction
The processes involved in the given problem are:
[tex]1.)C_2H_5OH(l)(35^oC)\rightarrow C_2H_5OH(l)(78^oC)\\2.)C_2H_5OH(l)(78^oC)\rightarrow C_2H_5OH(g)(78^oC)[/tex]
- For process 1:
We are given:
Change in temperature remains the same.
[tex]m=42.0g\\c_l=2.3J/g.K\\T_2=78^oC\\T_1=35^oC\\\Delta T=[T_2-T_1]=[78-35]^oC=43^oC=43K[/tex]
Putting values in equation 1, we get:
[tex]q_1=42.0g\times 2.3J/g.K\times 43K\\\\q_1=4153.8J[/tex]
- For process 2:
We are given:
Conversion factor: 1 kJ = 1000 J
Molar mass of ethanol = 46 g/mol
[tex]m=42.0g\\\Delta H_{vap}=38.56kJ/mol=\frac{35.56kJ}{1mol}\times (\frac{1000J}{1kJ})\times (\frac{1}{46g/mol})=773.04J/g[/tex]
Putting values in equation 2, we get:
[tex]q_2=42.0g\times 773.04J/g\\\\q_2=32467.7J[/tex]
Total heat required = [tex][q_1+q_2][/tex]
Total heat required = [tex][4153.8J+32467.7J]=36621.5J[/tex]
Hence, the total heat required is 36621.5 J
- For b:
The processes involved in the given problem are:
[tex]1.)C_2H_5OH(s)(-155^oC)\rightarrow C_2H_5OH(s)(-144^oC)\\2.)C_2H_5OH(s)(-144^oC)\rightarrow C_2H_5OH(l)(-144^oC)\\3.)C_2H_5OH(l)(-144^oC)\rightarrow C_2H_5OH(l)(78^oC)\\4.)C_2H_5OH(l)(78^oC)\rightarrow C_2H_5OH(g)(78^oC)[/tex]
- For process 1:
We are given:
Change in temperature remains the same.
[tex]m=42.0g\\c_s=0.97J/g.K\\T_2=-144^oC\\T_1=-155^oC\\\Delta T=[T_2-T_1]=[-144-(-155)]^oC=11^oC=11K[/tex]
Putting values in equation 1, we get:
[tex]q_1=42.0g\times 0.97J/g.K\times 11K\\\\q_1=448.14J[/tex]
- For process 2:
We are given:
[tex]m=42.0g\\\Delta H_{fusion}=5.02kJ/mol=\frac{5.02kJ}{1mol}\times (\frac{1000J}{1kJ})\times (\frac{1}{46g/mol})=109.13J/g[/tex]
Putting values in equation 2, we get:
[tex]q_2=42.0g\times 109.13J/g\\\\q_2=4583.5J[/tex]
- For process 3:
We are given:
Change in temperature remains the same.
[tex]m=42.0g\\c_l=2.3J/g.K\\T_2=78^oC\\T_1=-144^oC\\\Delta T=[T_2-T_1]=[78-(-144)]^oC=222^oC=222K[/tex]
Putting values in equation 1, we get:
[tex]q_3=42.0g\times 2.3J/g.K\times 222K\\\\q_3=21445.2J[/tex]
- For process 4:
We are given:
[tex]m=42.0g\\\Delta H_{vap}=38.56kJ/mol=\frac{38.56kJ}{1mol}\times (\frac{1000J}{1kJ})\times (\frac{1}{46g/mol})=773.04J/g[/tex]
Putting values in equation 2, we get:
[tex]q_4=42.0g\times 773.04J/g\\\\q_4=32467.7J[/tex]
Total heat required = [tex][q_1+q_2+q_3+q_4][/tex]
Total heat required = [tex][448.14+4583.5+21445.2+32467.7]J=58944.5J[/tex]
Hence, the total heat required is 58944.5 J
The latent heat is the heat required to achieve a change of state.
Note that the heat required to convert 42.0 g of ethanol at 35 °C to the vapor phase at 78 °C if given by;
H = mcθ + mL
m = mass of ethanol
c = specific heat capacity of ethanol
θ = temperature change
L = Latent heat of vaporization of ethanol
Substituting values;
H = (42 × 2.3 × (78 - 35)) + (42/46 × 38.56 × 10^3)
H = 4154 + 35207
H = 39.367 kJ
b) Heat required to convert the same amount of ethanol at - 155 oC to the vapor phase at 78 °C;
H = mLfus + mcθ + mLvap
H = (42/46 × 5.02 × 10^3) + (42 × 2.3 × 78 - (- 155)) + (42/46 × 38.56 × 10^3)
H = 4583 + 22508 + 35207
H = 62.3 kJ
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