### Topic: Heating Curve for 1 Mole of Octane#### Objective:To sketch a heating curve for 1 mole of octane, starting at -57°C and ending at 150°C. Demonstrate the calculations for each step of the process.#### Data Table:| Property | Value ||-------------------------------|---------------------|| Boiling Point | 125.7°C || Melting Point | -56.8°C || ΔHvap (Heat of Vaporization) | 41.5 kJ/mol || ΔHfus (Heat of Fusion) | 20.7 kJ/mol || Molar Heat Capacity (liquid) | 254.6 J/(mol*°C) || Molar Heat Capacity (gas) | 316.9 J/(mol*°C) |**Additional Information:**- Molar heat capacity for the solid (not given in the table): 255.7 J/(K*mol).#### Explanation of Heating Curve:1. **Starting Point (-57°C):** - Begin with octane in its solid state.2. **Melting Phase (-56.8°C):** - Use ΔHfus to calculate energy needed for the phase transition from solid to liquid.3. **Heating Liquid (up to 125.7°C):** - Calculate energy required to raise the temperature of the liquid octane using the molar heat capacity of the liquid.4. **Boiling Phase (125.7°C):** - Use ΔHvap to calculate energy needed for the phase transition from liquid to gas.5. **Heating Gas (up to 150°C):** - Calculate energy needed to raise the temperature of gaseous octane using the molar heat capacity of the gas.**Calculation Notes:**- For each phase (solid, liquid, gas), calculate the heat (q) using the formula: \[ q = m \cdot c \cdot \Delta T \] where \( m \) is the number of moles, \( c \) is the molar heat capacity, and \( \Delta T \) is the temperature change.- For phase transitions, use: - \( q

A heating curve is a graphically representation of the phase transition of a substance. The heat given to the substance is plotted on the horizontal axis and the temperature of substance on the vertical axis. To plot the heating curve, find the heat given to 1 mole of the substance in order to change its temperature – 57oC to 150oC.Let Q1 be the heat given to the substance to change the octane in solid state from – 57oC to – 56.8oC (Melting point) then Q1 is given by, Q1=MoleMolar Heat capacity of solid octaneChange in temperatureQ1=1255.7−56.8+57Q1=51.14 JQ1=0.05114 KJLet Q2 be the heat given to the substance to change the octane in solid state at – 56.8oC to liquid state at – 56.8oC then Q2 is given by, Q2=MoleMolar Heat of fusionQ2=1 mol20.7 KJ/molQ2=20.7 KJLet Q3 be the heat given to the substance to change the octane in liquid state from – 56.8oC to 125.7oC (boiling point) then Q3 is given by, Q3=MoleMolar Heat capacity of liquid octaneChange in temperatureQ3=1 mol254.6 J/moloC125.7oC−−56.8oCQ3=46.4645 JQ3=46.464 KJLet Q4 be the heat given to the substance to change the octane in liquid state at – 125.7oC to gas state at – 125.7oC then Q4 is given by, Q4=MoleMolar Heat of vaporizationQ4=1 mol41.5 KJ/molQ4=41.5 KJLet Q5 be the heat given to the substance to change the octane in gas state from 125.7oC to 150oC then Q5 is given by, Q5=MoleMolar Heat capacity of gas octaneChange in temperatureQ5=1 mol316.9 J/moloC150oC−125.7oCQ5=7700.67 JQ5=7.701 KJNow add up the heat to get the total heat added at a temperature. At T=–57oCIn solid state⇒Q=0At T=–56.7oCIn solid state⇒Q=Q1⇒Q=0.05114 KJAt T=–56.7oCIn liquied state⇒Q=Q1+Q2⇒Q=0.05114 KJ+20.7 KJ⇒ Q=20.75114 KJAt T=125.7oCIn liquid state⇒Q=Q1+Q2+Q3⇒Q=0.05114 KJ+20.7 KJ+46.464 KJ⇒ Q=67.21514 KJAt T=125.7oCIn gas state⇒Q=Q1+Q2+Q3+Q4⇒Q=0.05114 KJ+20.7 KJ+46.464 KJ+41.5 KJ⇒ Q=108.71514 KJAt T=150oCIn gas state⇒Q=Q1+Q2+Q3+Q4+Q5⇒Q=0.05114 KJ+20.7 KJ+46.464 KJ+41.5 KJ+7.701 KJ⇒ Q=116.41614 KJNow sketch the heat curve using above info.

Science

Chemistry

9-10. Use the following data to sketch a heating curve for 1 mole of octane. Start the curve at 57 °C and end it at 150 °C. Show the calculations for each step. You will need the molar heat capacity for the solid, which is not given in the table. It is 255.7 J/K mol. 125.7°C Boiling Point Melting Point AHvap -56.8°C 41.5 kJ/mol AHfus 20.7 kJ/mol Molar Heat capacity (1) Molar Heat capacity (g) 254.6 J/(mol*°C) 316.9 J/(mol* °C) mole nonvxo n to sanm dqn 0001)

9-10. Use the following data to sketch a heating curve for 1 mole of octane. Start the curve at 57 °C and end it at 150 °C. Show the calculations for each step. You will need the molar heat capacity for the solid, which is not given in the table. It is 255.7 J/K mol. 125.7°C Boiling Point Melting Point AHvap -56.8°C 41.5 kJ/mol AHfus 20.7 kJ/mol Molar Heat capacity (1) Molar Heat capacity (g) 254.6 J/(mol°C) 316.9 J/(mol °C) mole nonvxo n to sanm dqn 0001)

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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### Topic: Heating Curve for 1 Mole of Octane

#### Objective:
To sketch a heating curve for 1 mole of octane, starting at -57°C and ending at 150°C. Demonstrate the calculations for each step of the process.

#### Data Table:

| Property | Value |
|-------------------------------|---------------------|
| Boiling Point | 125.7°C |
| Melting Point | -56.8°C |
| ΔH<sub>vap</sub> (Heat of Vaporization) | 41.5 kJ/mol |
| ΔH<sub>fus</sub> (Heat of Fusion) | 20.7 kJ/mol |
| Molar Heat Capacity (liquid) | 254.6 J/(mol*°C) |
| Molar Heat Capacity (gas) | 316.9 J/(mol*°C) |

**Additional Information:**
- Molar heat capacity for the solid (not given in the table): 255.7 J/(K*mol).

#### Explanation of Heating Curve:

1. **Starting Point (-57°C):**
- Begin with octane in its solid state.

2. **Melting Phase (-56.8°C):**
- Use ΔH<sub>fus</sub> to calculate energy needed for the phase transition from solid to liquid.

3. **Heating Liquid (up to 125.7°C):**
- Calculate energy required to raise the temperature of the liquid octane using the molar heat capacity of the liquid.

4. **Boiling Phase (125.7°C):**
- Use ΔH<sub>vap</sub> to calculate energy needed for the phase transition from liquid to gas.

5. **Heating Gas (up to 150°C):**
- Calculate energy needed to raise the temperature of gaseous octane using the molar heat capacity of the gas.

**Calculation Notes:**
- For each phase (solid, liquid, gas), calculate the heat (q) using the formula:
\[
q = m \cdot c \cdot \Delta T
\]
where \( m \) is the number of moles, \( c \) is the molar heat capacity, and \( \Delta T \) is the temperature change.
- For phase transitions, use:
- \( q

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