Respuesta :
Answer:
The answer to the question above is
The energy required to heat 87.1 g acetone from a solid at -154.0°C to a liquid at -42.0°C = 29.36 kJ
Explanation:
The given variables are
ΔHfus = 7.27 kJ/mol
Cliq = 2.16 J/g°C
Cgas = 1.29 J/g°C
Csol = 1.65 J/g°C
Tmelting = -95.0°C.
Initial temperature = -154.0°C
Final temperature = -42.0°C?
Mass of acetone = 87.1 g
Molar mass of acetone = 58.08 g/mol
Solution
Heat required to raise the temperature of solid acetone from -154 °C to -95 °C or 59 °C is given by
H = mCsolT = 87.1 g* 1.65 J/g°C* 59 °C = 8479.185 J
Heat required to melt the acetone at -95 °C = ΔHfus*number of moles =
But number of moles = mass÷(molar mass) = 87.1÷58.08 = 1.5
Heat required to melt the acetone at -95 °C =1.5 moles*7.27 kJ/mol = 10.905 kJ
The heat required to raise the temperature to -42 degrees is
H = m*Cliq*T = 87.1 g* 2.16 J/g°C * 53 °C = 9971.21 J
Total heat = 9971.21 J + 10.905 kJ + 8479.185 J = 29355.393 J = 29.36 kJ
The energy required to heat 87.1 g acetone from a solid at -154.0°C to a liquid at -42.0°C is 29.36 kJ
Taking into account the definition of calorimetry, sensible heat and latent heat, the amount of total heat required is 29,355.393 J.
Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.
Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state (phase change).
Latent heat is defined as the energy required by a quantity of substance to change state.
When this change consists of changing from a solid to a liquid phase, it is called heat of fusion and when the change occurs from a liquid to a gaseous state, it is called heat of vaporization.
- -154 °C to -95 °C
In firts place, you know that the melting point is -95°C. So, first of all you must increase the temperature from -154 ° C (in solid state) to -95 ° C, in order to supply heat without changing state (sensible heat).
The amount of heat a body receives or transmits is determined by:
Q = c× m× ΔT
where Q is the heat exchanged by a body of mass m, made up of a specific heat substance c and where ΔT is the temperature variation.
In this case, you know:
- c(solid)= 1.65 [tex]\frac{J}{gC}[/tex]
- m= 87.1 g
- ΔT= Tfinal - Tinitial= -95 °C - (-154) °C= 59 °C
Replacing:
Q1= 1.65 [tex]\frac{J}{gC}[/tex]× 87.1 g× 59 °C
Solving:
Q1=8,479.185 J
- Change of state
The heat Q that is necessary to provide for a mass m of a certain substance to change phase is equal to
Q = m×L
where L is called the latent heat of the substance and depends on the type of phase change.
In this case, you know:
- n= 87.1 grams×[tex]\frac{1 mole}{58.08 grams}[/tex]= 1.5 moles, where 58.08 [tex]\frac{g}{mole}[/tex] is the molar mass of Cr, that is, the amount of mass that a substance contains in one mole.
- ΔHfus= 7.27 [tex]\frac{kJ}{mol}[/tex]= 7,270 [tex]\frac{J}{mol}[/tex]
Replacing:
Q2= 1.5 moles×7,270 [tex]\frac{J}{mol}[/tex]
Solving:
Q2= 10,905 J
- -95 °C to -42 °C
Similar to sensible heat previously calculated, you know:
- c(liquid)= 2.16 [tex]\frac{J}{gC}[/tex]
- m= 87.1 g
- ΔT= Tfinal - Tinitial= -42 °C - (-95) °C= 53 °C
Replacing:
Q3= 2.16[tex]\frac{J}{gC}[/tex] × 87.1 g× 53 °C
Solving:
Q3= 9,971.208 J
- Total heat required
The total heat required is calculated as:
Total heat required= Q1 + Q2 + Q3
Total heat required= 8,479.185 J + 10,905 J + 9,971.208 J
Total heat required= 29,355.393 J
In summary, the amount of total heat required is 29,355.393 J.
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