Respuesta :
Answer:
The slope is 4661.4K
(B), the intercept is 18.156
The vapor pressure of chlorobenzene is 731.4mmHg
The percentage of chlorobenzene originally in the vapor that condenses is = 99.7%
Explanation:
Two sets of conditions (a and b) are observed for L1 and L2 at two different temperatures.
[tex]T_{a}[/tex] = 58.3°C
[tex]L1_{a}[/tex] = 747mmHg
[tex]L2_{a}[/tex] = 52mmHg
[tex]T_{b}[/tex] = 110°C
[tex]L1_{a}[/tex] = 577mmHg
[tex]L2_{b}[/tex] = 222mmHg
We need to convert the temperatures from Celsius to Kelvin (K)
[tex]T_{a}[/tex] = 58.3°C + 273.2
[tex]T_{a}[/tex] = 331.5k
[tex]T_{b}[/tex] = 110°C + 273.2
[tex]T_{b}[/tex] = 383.2k
We then calculate the vapor pressures of the chlorobenzene at each set of conditions by measuring the difference in the mercury levels.
[tex]P^{0}[/tex] = [tex]P_{atm} - (P_1 -P_2)[/tex]
The vapor pressure under the first set of conditions is:
[tex]P^{a}[/tex] = 755mmHg - (747mmHg - 52mmHg)
[tex]P^{a}[/tex] = 60mmHg
The vapor pressure under the second set of conditions is:
[tex]P^{b}[/tex] = 755mmHg - (577mmHg = 222mmHg)
[tex]P^{b}[/tex] = 400mmHg
First question say we should find ΔH(slope) and B(intercept) in the Clausius- Clapeyron equation:
Using the Formula :
[tex]In_p^{0} = \frac{- (delta) H}{RT} + B[/tex]
where (delta) H = ΔH
The slope of the [tex]In_p^{0} = \frac{T_1T_2 In (P_2/P_1)}{T_1-T_2}[/tex]
Calculating the slope; we have:
[tex]\frac{- (delta) H}{R} = \frac{T_1T_2 In (P_2/P_1)}{T_1-T_2}[/tex]
[tex]\frac{- (delta) H}{R}[/tex] = [tex]\frac{331.5 * 383.2 * In (400/60)}{(331.5-383.2)}[/tex]
[tex]\frac{- (delta) H}{R}[/tex] = -4661.4k
[tex]\frac{ (delta) H}{R}[/tex] = 4661.4k
The intercept can be derived from the Clausius-Clayperon Equation by making B the subject of the formula. To calculate the intercept using the first set of condition above; we have:
B = [tex]In_p_{1} + \frac{ (delta) H}{RT}[/tex]
B = [tex]In 60 + \frac{4661.4}{331.5}[/tex]
B = 18.156
Thus the Clausius-Clayperon equation for chlorobenzene can be expressed as:
In P = [tex]\frac{-4661.4k}{T} + 18.156[/tex]
In question (b), the air saturated with chlorobenzeneis 130°C, converting he temperature of 130°C to absolute units of kelvin(k) we have;
T = 130°C + 273.2
T = 403.2k
Calculating the vapor pressure using Clausius-Clapyeron equation: we have;
[tex]In_p_{0}[/tex] = [tex]In_p_{0} = \frac{-4661.4}{403.2} + 18.156[/tex]
[tex]In_p_{0}[/tex] = 6.595
[tex]p_{0}[/tex] = [tex]e^{6.595}[/tex]
[tex]p_{0}[/tex] = 731.mmHg
The vapor pressure of chlorobenzene is 731.4mmHg
The diagram of the flowchart with the seperate vapor and liquid stream can be found in the attached document below.
Afterwards, both the inlet and outlet conditions contain saturated liquid.
From the flowchart, the vapor pressure of chlorobenzene at the inlet and outlet temperatures are known:
[tex]P_1(130^{0}C)[/tex] = 731.44mmHg
[tex]P_1(58.3^{0}C)[/tex] = 60mmHg
To calculate the percentage of the chlorobenzene originally in the vapor pressure that condenses; we must first calculate the mole fractions of chlorobenzene for the vapor inlet and outlet using Raoult's Law:
[tex]y_1 = \frac{P^0 (T)}{P}[/tex]
At inlet conditions, the mole fraction of chlorobenzene is:
[tex]y_1 = \frac{731.44}{101.3}*\frac{101.3}{760}[/tex]
[tex]y_1 = \frac{0.962 mol cholorobenzene}{mol saturated air}[/tex]
At outlet conditions , the mole fraction of chlorobenzene is:
[tex]y_2 = \frac{60}{101.3}*\frac{101.3}{760}[/tex]
[tex]y_2 = \frac{0.0789 mol cholorobenzene}{mol saturated air}[/tex]
Since there is no reaction, the total balance around the condensation is :
[tex]n_1 = n_2 + n_3[/tex]
Let assume, that 100 moles of liquid chlorobenzene (CB) is condensed, therefore the equation becomes:
[tex]n_1 = n_2[/tex] + 100mol
The chlorobenzene balance using the mole fractions calculated above is :
[tex]\frac{0.962mol CB}{mol(air)} * n_1 mol(air) = \frac{0.0789molCB}{mol(air)}*n_2mol(air) + 100CB[/tex]
substituting equation (1) into equation above; we have:
[tex]\frac{0.962mol CB}{mol(air)} * n_1 mol(air) = \frac{0.0789molCB}{mol(air)}*(n_2-100)mol(air) + 100CB[/tex]
[tex]0.962_n_1 mol = 0.0789_n_1mol + 100mol[/tex]
we can solve for n1, i.e ;
n1 = 104.3mol total air
Therefore the moles of chlorobenzene that will produce 100 moles of CB liquid is:
[tex]n_C_B = 104.3 (moles) air * \frac{0.962 mol (CB)}{mol air}[/tex]
[tex]n_C_B[/tex] = 100.34mol CB
Now, calculating the percentage of chlorobenzene that condenses: we have;
% CB Condensation = [tex]\frac{100mol}{100.34mol}*100%[/tex]
% CB Condensation = 99.7%
The percentage of chlorobenzene originally in the vapor that condenses is 99.7%
