Concept explainers
Determine the identity of the gas.
Assuming the
ovide values for each of the following variables. In addition, explain what is happening for each variable, incorporating the kinetic molecular theory into your explanation.
m>Temperature of gas mixture = ?K
m>Total moles of gas mixture = ?mol
m>Total pressure of gas mixture = ?atm
m>Volume of balloon = ?L
Now assuming the
ovide values for each of the following variables. In addition, explain what is happening for each variable, incorporating the kinetic molecular theory into your explanation.
m>Temperature of gas mixture = ?K
m>Total moles of gas mixture = ?mol
m>Total pressure of gas mixture = ?atm
m>Volume of rigid container = ? L
(a)
Interpretation:
To determine the identity of the gas based on the pressure, volume and temperature given.
Concept Introduction:
The ideal gas equation is:
Where,
P = Pressure of the gas
V = Volume of the gas
n = moles of the gas
R = Universal gas constant
T = Temperature of the gas.
Answer to Problem 118AP
The monatomic gas is Argon.
Explanation of Solution
The ideal gas equation is
Where,
P = Pressure of the gas = 1.00 atm
V = Volume of the gas = 2.50 L
n = moles of the gas = ?
R = Universal gas constant = 0.0821 L.atm/mol.K
T = Temperature of the gas = -48 ° C = 225 K
Substituting the values in the given equation, we get,
Thus, the moles of the gas = 0.135 mol
From the moles of the gas, one can find the molar mass of the gas thereby identity of the gas.
The monatomic gas with this molecular weight is Argon.
(b)
Interpretation:
To determine the values of different variables when another gas is added to the elastic balloon which already has a monatomic gas in it.
Concept Introduction:
The ideal gas equation is:
Where,
P = Pressure of the gas
V = Volume of the gas
n = moles of the gas
R = Universal gas constant
T = Temperature of the gas.
Answer to Problem 118AP
Temperature of gas mixture = 225 K
Total moles of gas mixture = 0.447 mol
Total pressure of gas mixture = 1 atm
Volume of balloon = 8.26 L.
Explanation of Solution
Given, 10.0 g of oxygen is added.
Moles of oxygen are to be found.
Moles of oxygen = 0.3125 mol
Moles of monatomic gas = 0.135 mol
Total number of moles = 0.3125 mol + 0.135 mol = 0.447 mol
Air inside the balloon and atmospheric air pressure has very small pressure difference.
Therefore, one can consider it same and assume here that pressure of air inside balloon is equal to atmospheric pressure that is 1 atm.
Since, there is no change in temperature so, the temperature of the mixture is 225 K.
Total volume of gas mixture is found using ideal gas equation.
Thus,
Temperature of gas mixture = 225 K
Total moles of gas mixture = 0.447 mol
Total pressure of gas mixture = 1 atm
Volume of balloon = 8.26 L.
(c)
Interpretation:
To determine the values of different variables when another gas is added to the rigid steel container this already has a monatomic gas in it.
Concept Introduction:
The ideal gas equation is:
Where,
P = Pressure of the gas
V = Volume of the gas
n = moles of the gas
R = Universal gas constant
T = Temperature of the gas.
Answer to Problem 118AP
Temperature of gas mixture = 225 K
Total moles of gas mixture = 0.447 mol
Total pressure of gas mixture = 3.303 atm
Volume of rigid container = 2.5 L.
Explanation of Solution
Given, 10.0 g of oxygen is added.
Moles of oxygen are to be found.
Moles of oxygen = 0.3125 mol
Moles of monatomic gas = 0.135 mol
Total number of moles = 0.3125 mol + 0.135 mol = 0.447 mol
Since, there is no change in temperature so, the temperature of the mixture is 225 K.
Since, the given container is rigid so, the volume of the mixture is 2.50 L.
Total pressure of gas mixture is found using ideal gas equation.
Thus,
Temperature of gas mixture = 225 K
Total moles of gas mixture = 0.447 mol
Total pressure of gas mixture = 3.303 atm
Volume of rigid container = 2.5 L.
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Chapter 13 Solutions
Introductory Chemistry: A Foundation
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