For this problem, we can use the gas relationship between pressure and temperature at constant volume. This gas law is also called as the Gay-Lussac’s Law which states that:
P is directly proportional to T; as the pressure of the container increased, the total temperature will increase.
`P = k...
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For this problem, we can use the gas relationship between pressure and temperature at constant volume. This gas law is also called as the Gay-Lussac’s Law which states that:
P is directly proportional to T; as the pressure of the container increased, the total temperature will increase.
`P = k T`
`k = (P)/(T)`
Now, for comparing the same substance at two different conditions, this can be expressed as:
`(P_1)/(T_1) = (P_2)/(T_2)`
OR
`(P_1)(T_2) = (P_2)(T_1)`
From this we can solve the problem.
Given:
P1 = 760 mmHg -> initial pressure
T1 = 20 + 273.15 = 293.15K -> initial temperature
T2 = 55 + 273.15 = 328.15 K -> final temperature
P2 = x (unknown) -> final pressure
Substitute the given values and solve for the unknown:
`(P_1)(T_2) = (P_2)(T_1)`
(760)(328.15) = (x)(293.15)
x = (760*328.15)/(293.15)
x = 851 mmHg
Now, to get the number of moles, we will use the Ideal gas equation:
PV = nRT
n = number of moles = `(PV)/(RT)`
We can use any of the P and T sets, for this we shall use the T1 and P1.
Given:
P = 760 mmHg = 1 atm
V = 2600 Liters
R = 0.08201 atm-L / mol K
T = 293.15 K
`n = (1 * 2600)/(0.08201*293.15)`
n = 108.08 moles = 108 moles
For this problem, we can use the gas relationship between pressure and temperature at constant volume. This gas law is also called as the Gay-Lussac’s Law which states that:
P is directly proportional to T; as the pressure of the container increased, the total temperature will increase.
`P = k T`
`k = (P)/(T)`
Now, for comparing the same substance at two different conditions, this can be expressed as:
`(P_1)/(T_1) = (P_2)/(T_2)`
OR
`(P_1)(T_2) = (P_2)(T_1)`
From this we can solve the problem.
Given:
P1 = 760 mmHg -> initial pressure
T1 = 20 + 273.15 = 293.15K -> initial temperature
T2 = 55 + 273.15 = 328.15 K -> final temperature
P2 = x (unknown) -> final pressure
Substitute the given values and solve for the unknown:
`(P_1)(T_2) = (P_2)(T_1)`
(760)(328.15) = (x)(293.15)
x = (760*328.15)/(293.15)
x = 851 mmHg
Now, to get the number of moles, we will use the Ideal gas equation:
PV = nRT
n = number of moles = `(PV)/(RT)`
We can use any of the P and T sets, for this we shall use the T1 and P1.
Given:
P = 760 mmHg = 1 atm
V = 2600 Liters
R = 0.08201 atm-L / mol K
T = 293.15 K
`n = (1 * 2600)/(0.08201*293.15)`
n = 108.08 moles = 108 moles