Answer :
the quantity of heat required to convert ethanol from a liquid at 23.0°C to a vapor at its boiling point of 78.3°C, The total = q₁ + q₂
we need to consider two steps: raising the temperature from 23.0°C to the boiling point, and then converting it from a liquid to a vapor.
Step 1: Calculating the heat required to raise the temperature:
To raise the temperature of a substance, we use the equation:
q = m * C * ΔT
where:
q = quantity of heat
m = mass of the substance
C = specific heat capacity of the substance
ΔT = change in temperature
Given that the mass of ethanol is 40.0 g and the specific heat capacity is 2.46 J/g⋅°C, we can substitute these values into the equation:
q₁ = 40.0 g * 2.46 J/g⋅°C * (78.3°C - 23.0°C)
Simplifying the equation gives us:
q₁ = 40.0 g * 2.46 J/g⋅°C * 55.3°C
Now we can calculate the value of q₁.
Step 2: Calculating the heat required for vaporization:
To convert a substance from a liquid to a vapor, we use the equation:
q = n * ΔHvap
where:
q = quantity of heat
n = number of moles of the substance
ΔHvap = enthalpy of vaporization
To calculate the number of moles, we need to use the molar mass of ethanol (C₂H₅OH). The molar mass of ethanol is 46.07 g/mol. We can use this information to determine the number of moles:
moles = mass / molar mass
= 40.0 g / 46.07 g/mol
Now we can substitute the values into the equation:
q₂ = (40.0 g / 46.07 g/mol) * 39.3 kJ/mol
Calculating the value of q₂ gives us:
q₂ = (40.0 g / 46.07 g/mol) * 39.3 kJ/mol
Finally, we can add the values of q₁and q₂to find the total quantity of heat required:
q_total = q₁+ q₂
Substituting the calculated values of q₁ and q₂, we can find the answer in kJ.
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