Concept explainers
(a)
Interpretation:
The pressure of the vapors of methyl alcohol is to be calculated under the given conditions.
Concept Introduction :
The ideal gas equation is the expression that relates different measurable properties of a gas. The expression is given as:
where,
P = Pressure of the gas
V = Volume of the container in which the gas is occupied
R = Ideal gas constant = 0.0821 L atm/ mol K
n = number of moles of the gas = Mass of gas / Molecular mass of gas
T = Absolute temperature of the gas i.e., temperature on Kelvin scale
(a)
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Answer to Problem 1QAP
The pressure of the vapor at 35 0C is 237 mm Hg and at 45 0C is 245 mm Hg.
Explanation of Solution
Given:
P1 = 254 mm Hg
T1 = 57 0C = (57+273) K = 330 K
T2 = 35 0C = (35+273) K = 308 K and T2 = 45 0C = (45+273) K = 318 K
Considering the ideal gas equation for two different conditions of temperature and pressure,
Since, volume is constant so, the pressure of the vapor under second condition can be calculated as
For T2 = 35 0C = (35+273) K = 308 K:
For T2 = 45 0C = (45+273) K = 318 K:
Therefore, the pressure of the vapor at 35 0C is 237 mm Hg and at 45 0C is 245 mm Hg.
(b)
Interpretation:
The pressures calculated in part (a) are to be compared with the equilibrium pressures of methyl alcohol.
Concept Introduction :
If the pressure of vapor is more than the equilibrium pressure, it indicates that the liquid has undergone condensation.
(b)
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Answer to Problem 1QAP
At 35 0C, the vapor pressure is more than the equilibrium pressure and at45 0C, the vapor pressure is less than the equilibrium pressure.
Explanation of Solution
Given:
Equilibrium vapor pressure of methyl alcohol at
35 0C = 203 mm Hg
45 0C = 325 mm Hg
The calculated pressure of methyl alcohol at
35 0C = 237 mm Hg
45 0C = 245 mm Hg
Thus, at 35 0C, the equilibrium vapor pressure of methyl alcohol is more than the calculated pressure, which implies that some of the vapors condense. The vapor pressure at 45 0C is less than the equilibrium vapor pressure, which implies the equilibrium stage has still not reached and the liquid vaporizes.
(c)
Interpretation:
The pressure of methyl alcohol vapors inside the flask is to be calculated at 35 0C and 45 0C.
Concept Introduction : When a liquid is present in a closed container, it starts form vapors above the liquid surface. A stage is reached when the liquid and vapors are present in equilibrium with each other.
(c)
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Answer to Problem 1QAP
Pressure of methyl alcohol vapors
At 35 0C = 203 mm Hg
At 45 0C = 325 mm Hg
Explanation of Solution
Once equilibrium between a liquid and its vapors is reached in a closed container, the liquid keeps on changing to vapors and vapors keep on changing to liquid. No further increase in pressure exerted by the vapors is observed.
Since, at 35 0C, the equilibrium pressure of methyl alcohol vapors is less than the calculated pressure, the pressure that can actually be achieved is the equilibrium pressure,i.e. 203 mm Hg.
At 45 0C, the equilibrium pressure of methyl alcohol vapors is less than the calculated pressure, thus the liquids are still getting converted to reach equilibrium. The system will reach equilibrium to exert a pressure of 325 mm Hg.
(d)
Interpretation:
The physical state of methyl alcohol present in the flask at two different temperatures, 35 oC and 45 oC is to be calculated.
Concept Introduction:
Vaporization results in the formation of vapors from liquid and condensation results in the formation of liquids from vapors.
(d)
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Answer to Problem 1QAP
At 35 0C, the flask mainly contains liquid and at 45 0C, the flask mainly contains vapors.
Explanation of Solution
As shown in the above parts, at 35 0C, condensation is taking place and thus vapors are getting converted to liquid. Thus, the flask mainly contains liquid.
At 45 0C, vaporization is taking place and thus more liquid molecules are getting converted to vapors and thus the flask mainly contains vapor state.
Therefore, at 35 0C, the flask contains mainly liquid state and at 45 0C, the flask mainly contains vapor state.
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Chapter 9 Solutions
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