Respuesta :
Answer :
(a) The value of [tex]\frac{dP}{dT}[/tex] is [tex]5.56\times 10^3Pa/K[/tex]
(b) The percentage error will be 2.5 %
Explanation :
(a) First we have to calculate the [tex]V_{vap}[/tex].
[tex]V_{vap}=V_2-V_1[/tex]
[tex]V_1[/tex] = volume of liquid = [tex]115cm^3mol^{1-}=115\times 10^{-6}m^3mol^{1-}[/tex]
[tex]V_1[/tex] = volume of vapor = [tex]14.5dm^3mol^{1-}=14.5\times 10^{-3}m^3mol^{1-}[/tex]
[tex]V_{vap}=V_2-V_1[/tex]
[tex]V_{vap}=(14.5\times 10^{-3}m^3mol^{1-})-(115\times 10^{-6}m^3mol^{1-})[/tex]
[tex]V_{vap}=1.44\times 10^{-2}m^3mol^{1-}[/tex]
Now we have to calculate the value of [tex]\frac{dP}{dT}[/tex]
The Clausius- Clapeyron equation is :
[tex]\frac{dP}{dT}=\frac{\Delta H_{vap}}{T\Delta V_{vap}}[/tex]
where,
T = temperature = 180 K
[tex]\Delta H_{vap}[/tex] = heat of vaporization = 14.4 kJ/mole = 14400 J/mole
[tex]V_{vap}=1.44\times 10^{-2}m^3mol^{1-}[/tex]
Now put all the given values in the above formula, we get:
[tex]\frac{dP}{dT}=\frac{(14400J/mole)}{(180K)\times (1.44\times 10^{-2}m^3mol^{1-})}\times \frac{1Pa}{1J/m^3}[/tex]
[tex]\frac{dP}{dT}=5.56\times 10^3Pa/K[/tex]
(b) Now we have to calculate the percentage error.
Now we have to calculate the value of [tex]\frac{dP}{dT}[/tex] at normal boiling point.
The Clausius- Clapeyron equation is :
[tex]\frac{dP}{dT}=\frac{\Delta H_{vap}}{T\Delta V_{vap}}[/tex]
As we know that : PV = nRT
So,
[tex]\frac{dP}{dT}=\frac{P\Delta H_{vap}}{RT^2}[/tex]
where,
R = gas constant = 8.314 J/K.mol
T = temperature = 180 K
[tex]\Delta H_{vap}[/tex] = heat of vaporization = 14.4 kJ/mole = 14400 J/mole
P = pressure at normal boiling point = 101325 Pa
Now put all the given values in the above formula, we get:
[tex]\frac{dP}{dT}=\frac{(101325Pa}\times (14400J/mole)}{(8.314J/K.mol)\times (180K)^2}[/tex]
[tex]\frac{dP}{dT}=5.42\times 10^3Pa/K[/tex]
Now we have to determine percentage error.
[tex]\%\text{ error}=\frac{(5.56\times 10^3Pa/K)-(5.42\times 10^3Pa/K)}{5.56\times 10^3Pa/K}\times 100[/tex]
[tex]\%\text{ error}=2.5\%[/tex]
Therefore, the percentage error will be 2.5 %
