Calculate the change in entropy that occurs in the system when 1.49 mol of acetone (C3H6O) condenses from a gas to a liquid at its normal boiling point (56.1 ∘C) The heat of vaporization is 29.1 kJ/mol.
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Now, back to your question. To calculate the change in entropy, we need to use the equation:
ΔS = q/T
where ΔS is the change in entropy, q is the heat absorbed or released, and T is the temperature in Kelvin.
First, let's calculate the heat absorbed during condensation. We know that the heat of vaporization is 29.1 kJ/mol. Since we have 1.49 mol of acetone, the heat absorbed would be:
q = (29.1 kJ/mol) x (1.49 mol) = 43.439 kJ
Now, let's convert the boiling point of acetone to Kelvin:
56.1 °C = 56.1 + 273.15 = 329.25 K
Plugging everything into the equation:
ΔS = (43.439 kJ) / (329.25 K)
= 0.132 J/K
So, the change in entropy is approximately 0.132 J/K.
To calculate the change in entropy ΔS, we need to use the equation:
ΔS = q / T
Where:
- ΔS is the change in entropy
- q is the heat absorbed or released by the system
- T is the temperature at which the process occurs
In this case, the process is the condensation of acetone from a gas to a liquid, and the heat of vaporization is given as 29.1 kJ/mol.
First, we need to calculate the heat absorbed or released by the system (q):
q = ΔH vaporization * n
Where:
- ΔH vaporization is the heat of vaporization of acetone, given as 29.1 kJ/mol.
- n is the number of moles of acetone condensing, given as 1.49 mol.
Substituting the values, we get:
q = 29.1 kJ/mol * 1.49 mol
q = 43.359 kJ
Now, we know the heat absorbed by the system. We need to convert it to joules, as the SI unit for entropy is joules per kelvin (J/K). There are 1000 J in 1 kJ, so:
q = 43.359 kJ * 1000 J/kJ
q = 43359 J
Next, we need to convert the temperature from Celsius to Kelvin:
T = 56.1 °C + 273.15 K/°C
T = 329.25 K
Now, we can calculate the change in entropy ΔS:
ΔS = q / T
ΔS = 43359 J / 329.25 K
ΔS ≈ 131.75 J/K
Therefore, the change in entropy that occurs in the system when 1.49 mol of acetone condenses from a gas to a liquid at its normal boiling point is approximately 131.75 J/K.
To calculate the change in entropy during the condensation process, we can use the following formula:
ΔS = q / T
Where:
ΔS is the change in entropy
q is the heat exchanged during the process
T is the temperature
First, let's calculate the heat exchanged during the process using the heat of vaporization:
q = n * ΔHvap
Where:
q is the heat exchanged
n is the number of moles of acetone
ΔHvap is the heat of vaporization
Given that the number of moles of acetone (n) is 1.49 mol and the heat of vaporization (ΔHvap) is 29.1 kJ/mol, we can calculate the heat exchanged:
q = 1.49 mol * 29.1 kJ/mol
Next, we need to convert the temperature from Celsius to Kelvin:
T = 56.1 °C + 273.15
Now, we can substitute the values into the formula to calculate the change in entropy:
ΔS = q / T
To find the final answer, you'll need to perform the calculations using the given values.
dGo = dHo - TdS
dGo at equilibrium is zero.
You know dH from heat vapand you know T. Solve for dS.(delta S)
Post your work if you get stuck.