Question

4. Use the following data to sketch a heating curve for 1 mole of methanol. Start the curve at -100°C and end it at 100°C Boiling point: 65 c; Melting point: -94*C; AHvap: 37 kJ/moI; AHsus: 3.18 kJ/mol; Molar heat capacities, liquid: 81.1 J/(mo*C), gas: 43.9 J/(mol*C), solid: 48.7 J/(mol°C)

Answer 1

Answer:

The heating curve is construct with the temperature (ºC) in y-axis and the heat added (Q) in x-axis:

Q=n gas AT Cgas = 43.9 J/mol.°C Temperature (°C) BP Q=n Cliquid AT Cliquid = 81.1 J/mol.°C Qần AHvap AHvap = 37 kJ/mol Q=n AHfus AHfus=3,18 kJ/mol MP -94 -100 Q=n Csolid AT Csolid=48.7J/mol.°C Heat added 292) 3,18 kJ 12,9 kJ 37 kJ 1,5 kJ

• The first stage (blue line) correspond to the heating of solid methanol. In this case, the slope of the curve is equal to molar heat capacity of solid methanol (C_solid) = 47.8 J/mol.ºC. This curve is from -100 ºC until -94 ºC (melting point of methanol). In this range the temperature 292 J are added. This is calculate with the equation:

$Q=n\: C_{solid}\: \Delta T=1\, mol\times 47.8\, J/mol.^{\circ}C\, (-94\, ^{\circ}C-(-100\, ^{\circ}C))$

• The second stage (green line) correspond to the fusion of solid methanol. In this step the temperature does not change. however the system absorbs heat to transform the methanol from solid to liquid. The amount of heat needed is

$Q=n\: \Delta H_{fus}=1\, mol\times 3.18\, kJ/mol=3.18\, kJ/mol$

• The third curve (yellow line) is the heating of liquid methanol. In this case, the slope of the curve is equal to molar heat capacity of liquid methanol (C_liquid) = 81.1 J/mol.ºC. This curve goes from -94 ºC (m.p.) until 65 ºC (boiling point). The amount of heat added to the system in this curve is :

$Q=n\: C_{liquid}\: \Delta T=1\, mol\times 81.1\, J/mol.^{\circ}C\, (65\, ^{\circ}C-(-94\, ^{\circ}C))$

• The fourth stage (purple line) correspond to the vaporization of methanol. In this step the temperature does not change, however the system absorbs heat to transform the methanol from liquid to gas. The amount of heat needed is

$Q=n\: \Delta H_{vap}=1\, mol\times 37\, kJ/mol=37\, kJ/mol$

• The last stage (red line) is the heating of vapor of methanol. In this case, the slope of the curve is equal to molar heat capacity of gas methanol (C_gas) = 43.9 J/mol.ºC. This curve goes from 65 ºC (m.p.) until 100 ºC. The amount of heat added to the system in this curve is :

$Q=n\: C_{gas}\: \Delta T=1\, mol\times 43.9\, J/mol.^{\circ}C\, (100\, ^{\circ}C-65\, ^{\circ}C)$