Consider the following properties of a particular substance:
melting point: -7.2 degrees C
boiling point: 58.8 degrees C
heat of fusion: 10.571 kJ/mol
specific heat of the solid: 87.4 J/mol degrees C
specific heat of the gas: 40.0 J/mol degrees C
specific heat of the liquid: 151.4 J/mol degrees C
heat of vaporization: 29.96 kJ/mol
A 1.54 mol sample of this substance was heated from -40.0 degrees C to 80.0 degrees C at a constant rate of 623 J/min.
a) How much heat (in kJ) was absorbed in the process?
b) How many minutes does it take to reach room temperature (25 degrees C)?
heat from-40C to -7.2C: =1.54*87.4*32.8 joules
heat to melt at -7.2= 1.54*10.571 *1000 joules
heat from-7.2 to 58.8;= 1.54*151.4 Joules
Heat to boil at 58.8;= 1.54*29.96 *1000 joules
heat from 58.8 to 80= ....
then add the heats.
To answer the given questions, we need to calculate the amount of heat absorbed during the heating process and the time it takes to reach room temperature.
a) To find the amount of heat absorbed (Q) in kJ, we can use the formula:
Q = (n × ΔHfusion) + (m × Cp,solid × ΔTsolid) + (n × ΔHvaporization) + (m × Cp,liquid × ΔTliquid) + (m × Cp,gas × ΔTgas)
where:
n = number of moles of the substance
m = mass of the substance (in grams)
ΔHfusion = heat of fusion (in kJ/mol)
Cp,solid = specific heat of the solid (in J/mol degrees C)
ΔTsolid = change in temperature of the solid (in degrees C)
ΔHvaporization = heat of vaporization (in kJ/mol)
Cp,liquid = specific heat of the liquid (in J/mol degrees C)
ΔTliquid = change in temperature of the liquid (in degrees C)
Cp,gas = specific heat of the gas (in J/mol degrees C)
ΔTgas = change in temperature of the gas (in degrees C)
Given data:
n = 1.54 mol
ΔHfusion = 10.571 kJ/mol
Cp,solid = 87.4 J/mol degrees C
Cp,liquid = 151.4 J/mol degrees C
Cp,gas = 40.0 J/mol degrees C
To calculate the change in temperature for each phase, we can use the respective melting and boiling points:
ΔTsolid = melting point - initial temperature
ΔTliquid = boiling point - melting point
ΔTgas = final temperature - boiling point
Substituting the given values:
ΔTsolid = (-7.2 - (-40.0)) = 32.8 degrees C
ΔTliquid = (58.8 - (-7.2)) = 66 degrees C
ΔTgas = (80.0 - 58.8) = 21.2 degrees C
Now, we can calculate the amount of heat absorbed:
Q = (1.54 × 10.571) + (m × 87.4 × 32.8) + (1.54 × 29.96) + (m × 151.4 × 66) + (m × 40.0 × 21.2)
Since we don't have the mass of the substance provided, we can't calculate the exact value of Q. However, if you have the mass, you can substitute the value and calculate the heat absorbed in kilojoules (kJ).
b) To determine the time it takes to reach room temperature (25 degrees C), we can assume that the rate of heat increase is constant. This means the rate at which heat is absorbed is equal to the rate at which the heat source provides heat.
Given data:
Rate of heat = 623 J/min
We need to calculate the time taken to reach the desired temperature change (from 80.0 degrees C to 25.0 degrees C) using the formula:
ΔQ = Rate of Heat × Δt
where:
ΔQ = amount of heat absorbed (in Joules)
Rate of Heat = 623 J/min
Δt = time taken (in minutes)
Rearranging the formula:
Δt = ΔQ / Rate of Heat
We can use the value of ΔQ obtained from part a) (in Joules) and substitute it into the formula. Since we don't have the value of ΔQ, we can't calculate the exact time taken. However, if you have the value of ΔQ, you can substitute it and find the time taken in minutes.
Keep in mind that the calculated time does not take into account potential variables such as heat loss to the surroundings, so it might not represent the exact time needed to reach room temperature.