Ethanol (C2H5OH) melts at -114 oC and boils at 78 oC. The enthalpy of fusion of ethanol is 5.02 kJ/mol, and its enthalpy of vaporization is 38.56 kJ/mol. The specific heat capacity of solid and liquid ethanol are 0.97 and 2.3 J/g-K, respectively.
How much heat is required to convert 42.0 g of ethanol at 35 oC to the vapor phase at 78 oC?
How much heat is required to convert 42.0 g of ethanol at -155 oC to the vapor phase at 78 oC?
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To determine the amount of heat required to convert the given mass of ethanol from the liquid phase at the given initial temperature to the vapor phase at the final temperature, we will need to consider the different phase changes involved and calculate the heat for each step.
Step 1: Heating the liquid ethanol from the initial temperature to its boiling point at 78 °C.
First, calculate the heat required to raise the temperature of the liquid ethanol from 35 °C to its boiling point at 78 °C. We will use the specific heat capacity of liquid ethanol, which is 2.3 J/g-K.
Heat = mass × specific heat capacity × change in temperature
Heat = 42.0 g × 2.3 J/g-K × (78 °C - 35 °C)
Step 2: Vaporizing the liquid ethanol at its boiling point.
Next, calculate the heat required to vaporize the liquid ethanol. To do this, we will use the enthalpy of vaporization of ethanol, which is 38.56 kJ/mol.
To convert grams to moles of ethanol, we need to know its molar mass:
Molar mass of ethanol (C2H5OH):
C = 12.01 g/mol
H = 1.01 g/mol
O = 16.00 g/mol
Total molar mass = (2 × C) + (6 × H) + O
Total molar mass = (2 × 12.01) + (6 × 1.01) + 16.00 g/mol
First, convert grams of ethanol to moles:
Moles of ethanol = 42.0 g / Total molar mass
Then, multiply the moles of ethanol by the enthalpy of vaporization to calculate the heat required:
Heat = Moles of ethanol × Enthalpy of vaporization
Heat = Moles of ethanol × 38.56 kJ/mol
Step 3: Calculate the total heat required.
To find the total heat required, add the heat from Step 1 and Step 2.
Total Heat = Heat from Step 1 + Heat from Step 2
To convert from kJ to J, multiply the value by 1000.
For the case when the initial temperature is -155 °C, the calculations are similar. However, in Step 1, since the initial temperature is below the melting point of ethanol, we must also consider the heat required for the solid-to-liquid phase change.
Step 1: Heating the solid ethanol from the initial temperature to its melting point at -114 °C.
Calculate the heat required to raise the temperature of the solid ethanol from -155 °C to its melting point at -114 °C using the specific heat capacity of the solid ethanol, which is 0.97 J/g-K.
Heat = mass × specific heat capacity × change in temperature
Heat = 42.0 g × 0.97 J/g-K × (-114 °C - (-155 °C))
Step 2: Melting the solid ethanol at its melting point.
Calculate the heat required to melt the solid ethanol. This is given by the enthalpy of fusion, which is 5.02 kJ/mol.
To convert grams to moles of ethanol, use the molar mass calculated earlier.
Heat = Moles of ethanol × Enthalpy of fusion
Heat = Moles of ethanol × 5.02 kJ/mol
Step 3: Heating the liquid ethanol from its melting point to its boiling point.
Calculate the heat required to raise the temperature of the liquid ethanol from -114 °C to its boiling point at 78 °C.
Heat = mass × specific heat capacity × change in temperature
Heat = 42.0 g × 2.3 J/g-K × (78 °C - (-114 °C))
Step 4: Vaporizing the liquid ethanol at its boiling point.
Calculate the heat required to vaporize the liquid ethanol using the enthalpy of vaporization of ethanol.
Heat = Moles of ethanol × Enthalpy of vaporization
Heat = Moles of ethanol × 38.56 kJ/mol
Step 5: Calculate the total heat required.
To find the total heat required, add the heat from Steps 1, 2, 3, and 4.
Total Heat = Heat from Step 1 + Heat from Step 2 + Heat from Step 3 + Heat from Step 4
To calculate the amount of heat required to convert a substance from one phase to another, we need to consider the heat energy required for each phase change and for changing the temperature within each phase.
Let's break down the calculations step by step:
1. Determining the energy required to heat the solid ethanol from its initial temperature to its melting point:
First, we calculate the temperature difference: ΔT = T_final - T_initial = (melting point) - (initial temperature)
ΔT = (-114 oC) - (35 oC) = -149 oC
Next, we use the specific heat capacity of solid ethanol to calculate the energy required:
Energy = mass * specific heat capacity * ΔT
Energy = 42.0 g * 0.97 J/g-K * (-149 oC)
2. Determining the energy required to melt the solid ethanol at its melting point:
Energy = enthalpy of fusion * moles of ethanol
First, we need to determine the number of moles of ethanol in 42.0 g:
Moles = mass / molar mass
The molar mass of ethanol (C2H5OH) is 46.07 g/mol
Moles = 42.0 g / 46.07 g/mol
Finally, we calculate the energy required:
Energy = 5.02 kJ/mol * (moles of ethanol)
3. Determining the energy required to heat the liquid ethanol from its melting point to its boiling point:
ΔT = T_final - T_initial = (boiling point) - (melting point)
ΔT = 78 oC - (-114 oC)
Energy = mass * specific heat capacity * ΔT
4. Determining the energy required to vaporize the liquid ethanol at its boiling point:
Energy = enthalpy of vaporization * moles of ethanol
5. Determining the energy required to heat the vaporized ethanol from its boiling point to the final temperature:
ΔT = T_final - T_initial = (final temperature) - (boiling point)
ΔT = 78 oC - (78 oC)
Energy = mass * specific heat capacity * ΔT
To find the total energy required, we add the energy calculated in each step together.
Now let's calculate the energy required for each case:
Case 1: Ethanol at 35 oC to the vapor phase at 78 oC:
- Follow the steps outlined above for each phase change and add the energies calculated in each step to obtain the total energy required.
Case 2: Ethanol at -155 oC to the vapor phase at 78 oC:
- Follow the same steps as in Case 1, but note that the temperature difference for the solid ethanol will be different since it is now starting at a lower temperature: (-114 oC) - (-155 oC) = 41 oC.
By following these calculations, you should be able to determine the amount of heat required for each scenario.