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Lisa...
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I need to calculate q, w, \Delta E, \Delta H and \Delta S for the process of heating a sample of ice weighing 18.02 g (1 mole) from -30.0 °C to 140.0°C at constant pressure of 1 atm.
Given are the temperature independent heat capacities (Cp) for solid, liquid and gaseous water: 37.5 J/K/mol, 75.3 J/K/mol, 36.4 J/K/mol respectively. Also, the enthalpies of fusion and vaporization are 6.01 kJ/mol and 40.7 kJ/mol respectively. Assure ideal gas behavior.
I thought of this process as 5 steps:
I) Solid water of -30°C is heated to 0°C
II) Solid water of 0°C melts to give liquid water at 0°C
III) Liquid water of 0°C is heated to 100°C
IV) Liquid water of 100°C is vaporized to give gaseous water at 100°C
V) Gaseous water of 100°C is heated to 140°C
Then I figured I needed to calculate q, w, \Delta E, \Delta H and \Delta S for each step seperately and sum them to give the values of q, w, \Delta E, \Delta H and \Delta S for the whole process.
=> So q is calculated for I),III) and V) by q=n Cp\Delta T with the Cp values of respectively solid, liquid and gaseous water. For II) and IV) q= n H with values of H of respectively fusion and vaporization enthalpies.
=> Because the process is carried out at constant pressure, all the q's equal the H's.
=> Entropies are calculated for I), III) and V) by \Delta S = n C_p ln \frac{T_2}{T_1} and for II) and IV) with \Delta S =\frac{\Delta H}{T} with T the melting/boiling point and delta H the fusion/ vaporization enthalpy.
=> Now the point at which I got stuck: calculating w and \Delta E
I know that \Delta E = w + q and w = -p \Delta V. For V) I can calculate w with p= 1 atm and by using the ideal gas law to find delta V and with the delta E formula + known q delta E can be obtained...
But what about the work that is done in the other four steps? I don't know the changes in volume. Could somebody please please please explain to me how I'd calculate w and delta E for the first 4 steps?
EDIT: Now I figured delta E = 0 for II and IV therefore w=-q, because \Delta E = n C_v \Delta T thus it only depends on the temperature, which remains constant during II and IV, so \Delta T =0 = \Delta E . Is that a correct way of thinking? And now how would I tackle calculation of delta E & w of step I, III and V?
Given are the temperature independent heat capacities (Cp) for solid, liquid and gaseous water: 37.5 J/K/mol, 75.3 J/K/mol, 36.4 J/K/mol respectively. Also, the enthalpies of fusion and vaporization are 6.01 kJ/mol and 40.7 kJ/mol respectively. Assure ideal gas behavior.
I thought of this process as 5 steps:
I) Solid water of -30°C is heated to 0°C
II) Solid water of 0°C melts to give liquid water at 0°C
III) Liquid water of 0°C is heated to 100°C
IV) Liquid water of 100°C is vaporized to give gaseous water at 100°C
V) Gaseous water of 100°C is heated to 140°C
Then I figured I needed to calculate q, w, \Delta E, \Delta H and \Delta S for each step seperately and sum them to give the values of q, w, \Delta E, \Delta H and \Delta S for the whole process.
=> So q is calculated for I),III) and V) by q=n Cp\Delta T with the Cp values of respectively solid, liquid and gaseous water. For II) and IV) q= n H with values of H of respectively fusion and vaporization enthalpies.
=> Because the process is carried out at constant pressure, all the q's equal the H's.
=> Entropies are calculated for I), III) and V) by \Delta S = n C_p ln \frac{T_2}{T_1} and for II) and IV) with \Delta S =\frac{\Delta H}{T} with T the melting/boiling point and delta H the fusion/ vaporization enthalpy.
=> Now the point at which I got stuck: calculating w and \Delta E
I know that \Delta E = w + q and w = -p \Delta V. For V) I can calculate w with p= 1 atm and by using the ideal gas law to find delta V and with the delta E formula + known q delta E can be obtained...
But what about the work that is done in the other four steps? I don't know the changes in volume. Could somebody please please please explain to me how I'd calculate w and delta E for the first 4 steps?
EDIT: Now I figured delta E = 0 for II and IV therefore w=-q, because \Delta E = n C_v \Delta T thus it only depends on the temperature, which remains constant during II and IV, so \Delta T =0 = \Delta E . Is that a correct way of thinking? And now how would I tackle calculation of delta E & w of step I, III and V?
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