<u>Answer:</u>
<u>For a:</u> The total heat required is 36621.5 J
<u>For b:</u> The total heat required is 58944.5 J
<u>Explanation:</u>
To calculate the heat required at different temperature, we use the equation:
.........(1)
where,
q = heat absorbed
m = mass of substance
= specific heat capacity of substance
= change in temperature
To calculate the amount of heat required at same temperature, we use the equation:
........(2)
where,
q = heat absorbed
m = mass of substance
= enthalpy of the reaction
The processes involved in the given problem are:
![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)](https://tex.z-dn.net/?f=1.%29C_2H_5OH%28l%29%2835%5EoC%29%5Crightarrow%20C_2H_5OH%28l%29%2878%5EoC%29%5C%5C2.%29C_2H_5OH%28l%29%2878%5EoC%29%5Crightarrow%20C_2H_5OH%28g%29%2878%5EoC%29)
We are given:
Change in temperature remains the same.
![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](https://tex.z-dn.net/?f=m%3D42.0g%5C%5Cc_l%3D2.3J%2Fg.K%5C%5CT_2%3D78%5EoC%5C%5CT_1%3D35%5EoC%5C%5C%5CDelta%20T%3D%5BT_2-T_1%5D%3D%5B78-35%5D%5EoC%3D43%5EoC%3D43K)
Putting values in equation 1, we get:
![q_1=42.0g\times 2.3J/g.K\times 43K\\\\q_1=4153.8J](https://tex.z-dn.net/?f=q_1%3D42.0g%5Ctimes%202.3J%2Fg.K%5Ctimes%2043K%5C%5C%5C%5Cq_1%3D4153.8J)
We are given:
Conversion factor: 1 kJ = 1000 J
Molar mass of ethanol = 46 g/mol
![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](https://tex.z-dn.net/?f=m%3D42.0g%5C%5C%5CDelta%20H_%7Bvap%7D%3D38.56kJ%2Fmol%3D%5Cfrac%7B35.56kJ%7D%7B1mol%7D%5Ctimes%20%28%5Cfrac%7B1000J%7D%7B1kJ%7D%29%5Ctimes%20%28%5Cfrac%7B1%7D%7B46g%2Fmol%7D%29%3D773.04J%2Fg)
Putting values in equation 2, we get:
![q_2=42.0g\times 773.04J/g\\\\q_2=32467.7J](https://tex.z-dn.net/?f=q_2%3D42.0g%5Ctimes%20773.04J%2Fg%5C%5C%5C%5Cq_2%3D32467.7J)
Total heat required = ![[q_1+q_2]](https://tex.z-dn.net/?f=%5Bq_1%2Bq_2%5D)
Total heat required = ![[4153.8J+32467.7J]=36621.5J](https://tex.z-dn.net/?f=%5B4153.8J%2B32467.7J%5D%3D36621.5J)
Hence, the total heat required is 36621.5 J
The processes involved in the given problem are:
![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)](https://tex.z-dn.net/?f=1.%29C_2H_5OH%28s%29%28-155%5EoC%29%5Crightarrow%20C_2H_5OH%28s%29%28-144%5EoC%29%5C%5C2.%29C_2H_5OH%28s%29%28-144%5EoC%29%5Crightarrow%20C_2H_5OH%28l%29%28-144%5EoC%29%5C%5C3.%29C_2H_5OH%28l%29%28-144%5EoC%29%5Crightarrow%20C_2H_5OH%28l%29%2878%5EoC%29%5C%5C4.%29C_2H_5OH%28l%29%2878%5EoC%29%5Crightarrow%20C_2H_5OH%28g%29%2878%5EoC%29)
We are given:
Change in temperature remains the same.
![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](https://tex.z-dn.net/?f=m%3D42.0g%5C%5Cc_s%3D0.97J%2Fg.K%5C%5CT_2%3D-144%5EoC%5C%5CT_1%3D-155%5EoC%5C%5C%5CDelta%20T%3D%5BT_2-T_1%5D%3D%5B-144-%28-155%29%5D%5EoC%3D11%5EoC%3D11K)
Putting values in equation 1, we get:
![q_1=42.0g\times 0.97J/g.K\times 11K\\\\q_1=448.14J](https://tex.z-dn.net/?f=q_1%3D42.0g%5Ctimes%200.97J%2Fg.K%5Ctimes%2011K%5C%5C%5C%5Cq_1%3D448.14J)
We are given:
![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](https://tex.z-dn.net/?f=m%3D42.0g%5C%5C%5CDelta%20H_%7Bfusion%7D%3D5.02kJ%2Fmol%3D%5Cfrac%7B5.02kJ%7D%7B1mol%7D%5Ctimes%20%28%5Cfrac%7B1000J%7D%7B1kJ%7D%29%5Ctimes%20%28%5Cfrac%7B1%7D%7B46g%2Fmol%7D%29%3D109.13J%2Fg)
Putting values in equation 2, we get:
![q_2=42.0g\times 109.13J/g\\\\q_2=4583.5J](https://tex.z-dn.net/?f=q_2%3D42.0g%5Ctimes%20109.13J%2Fg%5C%5C%5C%5Cq_2%3D4583.5J)
We are given:
Change in temperature remains the same.
![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](https://tex.z-dn.net/?f=m%3D42.0g%5C%5Cc_l%3D2.3J%2Fg.K%5C%5CT_2%3D78%5EoC%5C%5CT_1%3D-144%5EoC%5C%5C%5CDelta%20T%3D%5BT_2-T_1%5D%3D%5B78-%28-144%29%5D%5EoC%3D222%5EoC%3D222K)
Putting values in equation 1, we get:
![q_3=42.0g\times 2.3J/g.K\times 222K\\\\q_3=21445.2J](https://tex.z-dn.net/?f=q_3%3D42.0g%5Ctimes%202.3J%2Fg.K%5Ctimes%20222K%5C%5C%5C%5Cq_3%3D21445.2J)
We are given:
![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](https://tex.z-dn.net/?f=m%3D42.0g%5C%5C%5CDelta%20H_%7Bvap%7D%3D38.56kJ%2Fmol%3D%5Cfrac%7B38.56kJ%7D%7B1mol%7D%5Ctimes%20%28%5Cfrac%7B1000J%7D%7B1kJ%7D%29%5Ctimes%20%28%5Cfrac%7B1%7D%7B46g%2Fmol%7D%29%3D773.04J%2Fg)
Putting values in equation 2, we get:
![q_4=42.0g\times 773.04J/g\\\\q_4=32467.7J](https://tex.z-dn.net/?f=q_4%3D42.0g%5Ctimes%20773.04J%2Fg%5C%5C%5C%5Cq_4%3D32467.7J)
Total heat required = ![[q_1+q_2+q_3+q_4]](https://tex.z-dn.net/?f=%5Bq_1%2Bq_2%2Bq_3%2Bq_4%5D)
Total heat required = ![[448.14+4583.5+21445.2+32467.7]J=58944.5J](https://tex.z-dn.net/?f=%5B448.14%2B4583.5%2B21445.2%2B32467.7%5DJ%3D58944.5J)
Hence, the total heat required is 58944.5 J