How much energy is needed as heat at a pressure of 1 ATM when 78g of liquid ethanol (C2H5-OH) at 298 K is converted to solid enthalpy at 159 K (FP). The molar enthalpy fusion is -277.6 KJ/Mole, and heat capacity of liquid ethanol is 112.3 J/mole k.
I don't get "converted to solid enthalpy"
To calculate the energy needed as heat for this process, we need to consider two steps:
Step 1: Calculate the energy required to cool the liquid ethanol from 298 K to its freezing point (159 K).
Step 2: Calculate the energy required for the phase change (fusion) from liquid to solid ethanol at its freezing point.
Step 1: Energy required to cool the liquid ethanol:
The energy required to cool a substance depends on its heat capacity and the temperature change. In this case, we have the heat capacity of liquid ethanol, which is given as 112.3 J/mol K.
To calculate the energy required to cool the liquid ethanol, we can use the formula:
Q = m × C × ΔT
where
Q = Energy (in joules)
m = mass of the substance (in grams)
C = specific heat capacity (in J/mol K)
ΔT = change in temperature (in K)
Given:
m = 78 g
C = 112.3 J/mol K
ΔT = 159 K - 298 K = -139 K (negative value because we are cooling the substance)
Substituting the values into the formula, we get:
Q1 = 78 g × (1 mol/46.08 g) × 112.3 J/mol K × -139 K
Q1 ≈ -23239 J
Step 2: Energy required for the phase change (fusion):
The energy required for a phase change (fusion) is given by the formula:
Q = n × ΔH
where
Q = Energy (in joules)
n = number of moles
ΔH = enthalpy of fusion (in J/mol)
Given:
n = mass / molar mass
molar mass of ethanol (C2H5-OH) = (2 × 12.01 g/mol) + (6 × 1.01 g/mol) + 16.00 g/mol = 46.08 g/mol
m = 78 g
ΔH = -277.6 kJ/mol = -277600 J/mol (converted from kJ to J)
Substituting the values into the formula, we get:
n = 78 g × (1 mol/46.08 g) ≈ 1.69 mol (rounded)
Q2 = 1.69 mol × (-277600 J/mol)
Q2 ≈ -468824 J
Finally, to find the total energy required as heat, we add Q1 and Q2 together:
Total energy = Q1 + Q2
Total energy = -23239 J + (-468824 J)
Total energy ≈ -492063 J (rounded)
Therefore, approximately -492063 J of energy is needed as heat at a pressure of 1 ATM to convert 78 g of liquid ethanol at 298 K to solid ethanol at its freezing point (159 K) using the given enthalpy of fusion and heat capacity values.