Ethanol (C2H5OH) boils at a temperature of 78.3oC.
What amount of energy, in joules, is necessary to heat to boiling and then completely vaporize a 13.1 g sample of ethanol initially at a temperature of 11.1oC.
The specific heat of ethanol is approximately constant at 2.44 JK-1g-1
The heat of vaporization of ethanol is 38.56 kJ mol-1.
q1 = heat to raise T from 11.1 to 78.3 C.
q1 = mass x specific heat x (Tfinal-Tinitial).
q2 = heat to vaporize ethanol.
q2 = mass x deltaHvap.
Total = sum q1 + q2
516.01
To calculate the amount of energy required to heat and vaporize the ethanol sample, we need to consider the following steps:
1. Calculate the energy required to heat the ethanol sample from 11.1°C to its boiling point at 78.3°C.
2. Calculate the energy required to vaporize the heated ethanol sample.
3. Add the two calculated energies to get the total energy required.
Step 1: Calculate the energy required to heat the ethanol sample.
The equation to calculate the energy using the specific heat formula is:
Q = m × c × ΔT
Where:
Q = Energy (in joules)
m = Mass of the ethanol sample (in grams)
c = Specific heat of ethanol (in J K^(-1) g^(-1))
ΔT = Change in temperature (in °C)
Substituting the given values:
m = 13.1 g
c = 2.44 J K^(-1) g^(-1)
ΔT = 78.3°C - 11.1°C
Q1 = 13.1 g × 2.44 J K^(-1) g^(-1) × (78.3°C - 11.1°C)
Step 2: Calculate the energy required to vaporize the heated ethanol sample.
The heat of vaporization (ΔHvap) is given in kJ mol^(-1). We need to convert it to J g^(-1) since we have the mass.
The molar mass of ethanol (C2H5OH) is:
(2 × 12.01 g/mol) + (6 × 1.01 g/mol) + 16.00 g/mol
= 46.08 g/mol
The heat of vaporization can be converted as follows:
38.56 kJ/mol × (1 mol / 46.08 g)
Now, we can calculate the energy using the following formula:
Q2 = m × ΔHvap
Substituting the given values:
m = 13.1 g
ΔHvap = 38.56 kJ/mol × (1 mol / 46.08 g)
Q2 = 13.1 g × [38.56 kJ/mol × (1 mol / 46.08 g)]
Step 3: Calculate the total energy required.
To obtain the total energy required, simply sum up Q1 and Q2.
Total Energy = Q1 + Q2
Now you can substitute the calculated values and solve for the total energy in joules.