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Concept explainers
Interpretation:
The partial pressure and total pressure of the given mixtures are to be calculated.
Concept introduction:
The mole fraction of an individual gas for the combination of gases is the ratio of the moles of the individual gas with the total number of moles.
Here,
The mole fraction of an individual gas for the combination of gases can be calculated from the ratio of the partial pressure of the individual gas with the total pressure of the combination.
Here,
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Answer to Problem 101AP
Solution:
(a)The pressure of flask (iii) is
(b)The total pressure after opening the valve is
Explanation of Solution
Given information:
Volume:
Pressure:
a)The pressure in flak (ii) and (iii)
The number of molecules in flask (i) is 9, whereas in flask (ii) the number of molecules is also 9.
The volume of flask (i) is
Now, the temperature and number of moles are constant and the volume of flask (ii) is half of the volume of flask (i), so the pressure of flask (ii) will be:
Substitute
The number of molecules in flask (iii) is
The volume of flask (iii) is
So, the pressure of flask (ii) will be:
Substitute
Hence, the pressure of flask (iii) is
b) The total pressure and the partial pressure of each gas after the valves are opened.
Before opening the valves, flask (i) is considered.
So,
After opening the valves, the total of all flasks is considered.
So,
The combined gas law forms the relationship between pressure, volume, temperature, and number of moles. This can be shown as
For constant temperature:
Rearrange the above equation for final pressure as follows:
Substitute
The number of red color sphere is 15.
The number of blue color sphere is 15.
So, the total number of moles is as follows:
Substitute
Calculate the mole fraction of red color sphere as follows:
Substitute
Calculate the mole fraction of the blue color sphere as follows:
Substitute
Calculate the partial pressure of the red gas as
Substitute
Calculate the partial pressure of the blue gas as follows:
Substitute
Hence, the total pressure after opening the valve is
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