Respuesta :
Answer:
The final temperature is 10.2 °C
Explanation:
Step 1: Data given
Mass of C3H8O = 1.15 grams
Mass of an aluminium block = 65.0 grams
Initial temperature = 25.0 °C
Molar mass of C3H8O = 60.1 g/mol
Heat of vaporization of the alcohol at 25 °C is 45.4 kJ/mol
Specific heat of aluminium at 25°C = 0.900 J/g°C
Step 2: Calculate moles of C3H8O
Moles C3H8O = mass C3H8O / molar mass C3H8O
Moles C3H8O = 1.15 grams / 60.1 g/mol
Moles C3H8O = 0.0191 moles
Step 3: Calculate heat
Q = 45.4 kJ/mol * 0.0191 moles = 0.867 kJ = 867 Joules
Step 4: Calculate ΔT
Q = m*c*ΔT
⇒ Q = the heat transfer = 867 J
⇒ m = the mass of aluminium = 65.0 grams
⇒ c = the specific heat of aluminium = 0.900 J/g°C
⇒ ΔT = The change of temperature = TO BE DETERMINED
867 J =65.0 g *0.900 J/g°C * ΔT
ΔT = 867 / (0.900*65.0)
ΔT = 14.8
Step 5: Calculate the final temperature
ΔT = T2 - T1
14.8 = 25.0 - T1
T1 = 25.0 - 14.8
T1 = 10.2 °C
The final temperature is 10.2 °C
The final temperature of the block after the evaporation of the alcohol is T₂ = 10.18°C
The relation used in determining the number of moles of a substance is the substance mass divided by its molar mass.
Mathematically, we have:
[tex]\mathbf{number \ of \ moles = \dfrac{mass}{molar \ mass}}[/tex]
Given that:
- The mass of propanol C₃H₈O = 1.15 grams
- The molar mass of the propanol = 60.1 g/mol
- The mass of the aluminium block = 65.0 g
- The initial temperature = 25°C
[tex]\mathbf{number \ of \ moles = \dfrac{1.15 \ g}{60.1 \ g/mol}}[/tex]
number of moles = 0.0191 moles
- The heat of vapourization coming from the aluminum block = 45.4 kJ/mol
- Specific heat of aluminum at 25°C = 0.900 J/g°C
Using the formula for the heat capacity;
Q = mCΔT
(45.4 J/moles × 0.0191 moles) = 65.0 g × 0.900 J/g° C × ΔT
867 J = 58.5 J × ΔT
ΔT = 867 J /58.5 J
ΔT = 14.82
We know that ΔT is the change in temperature;
ΔT = T₁ - T₂
14.82 = 25 - T₂
T₂ = 25 - 14.82
T₂ = 10.18°C
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