Respuesta :
Answer
given,
For helium
Volume,V = 46 L
Pressure,P = 1 atm
Temperature,T = 25°C = 273 +25 = 298 K
R=0.0821 L . atm /mole.K
n₁ = ?
number of moles
we know
P V = n R T
[tex]n_1 =\dfrac{46 \times 1}{0.0821\times 298}[/tex]
n₁ = 1.89 moles
For oxygen
Volume,V = 12 L
Pressure,P = 1 atm
Temperature,T = 25°C = 273 +25 = 298 K
R=0.0821 L . atm /mole.K
n₂ = ?
number of moles
we know
P V = n R T
[tex]n_2 =\dfrac{12 \times 1}{0.0821\times 298}[/tex]
n₂ = 0.49 moles
Total volume of tank = 5 L
temperature of tank = 298 K
Partial pressure of helium
[tex]P_1=\dfrac{n_1 R T}{V}[/tex]
[tex]P_1=\dfrac{1.89\times 0.0821\times 298}{5}[/tex]
P₁ = 9.25 atm
Partial pressure of oxygen
[tex]P_2=\dfrac{n_2 R T}{V}[/tex]
[tex]P_2=\dfrac{0.49\times 0.0821\times 298}{5}[/tex]
P₂ = 2.39 atm
total pressure
P = P₁ + P₂
P = 9.25 + 2.39
P = 11.64 atm
The total partial pressure of the mixture is 11.58 atm.
How do you calculate the pressure?
Given that A mixture of helium and oxygen is used in scuba diving tanks to help prevent "the bends".
For helium, volume V is 46 L, pressure P is 1 atm, temperature T is 25 degrees C, the ideal gas constant R is 0.0821 L . atm /mole.K.
For oxygen, volume V is 12 L, pressure P is 1 atm, temperature T is 25 degrees C, the ideal gas constant R is 0.0821 L . atm /mole.K.
Temperature can be written as below.
T = 25°C = 273 +25 = 298 K
The number of moles in helium can be calculated by the ideal gas law.
[tex]P V = n_h R T[/tex]
[tex]1\times 46 = n_h \times 0.0821 \times 298[/tex]
[tex]n_h = 1.88[/tex]
The number of moles in oxygen can be calculated by the ideal gas law.
[tex]PV = n_oRT[/tex]
[tex]1\times 12 = n_o\times 0.0821\times 298[/tex]
[tex]n_o = 0.49[/tex]
The total volume of the tank is 5 L and the temperature is 298 k.
So, the partial pressure of helium is given below.
[tex]P_hV = nRT[/tex]
[tex]P_h =\dfrac { 1.88\times 0.0821\times 298 }{5}[/tex]
[tex]P_h = 9.19 \;\rm atm[/tex]
The partial pressure of oxygen is given below.
[tex]P_oV = nRT[/tex]
[tex]P_o =\dfrac { 0.49\times 0.0821\times 298 }{5}[/tex]
[tex]P_o = 2.39 \;\rm atm[/tex]
The total partial pressure is given below.
[tex]P = P_h+P_o[/tex]
[tex]P = 9.19 +2.39[/tex]
[tex]P = 11.58\;\rm atm[/tex]
Hence the total partial pressure of the mixture is 11.58 atm.
To know more about partial pressure, follow the link given below.
https://brainly.com/question/14623719.
