Respuesta :
Answer:
The total pressure of the mixture in the tank of volume 6.25 litres at 51°C is 1291.85 kPa.
Explanation:
For N2,
Pressure(P₁)=125 kPa
Volume(V₁)=15·1 L
Temperature (T₁)=25°C=25+273 K=298 K
Similarly, for Oxygen,
Pressure(P₂)= 125 kPa
Volume(V₂)= 44.3 L
Temperature(T₂)=25°C= 298 K
Then, for the mixture,
Volumeof the mixture( V)= 6.25 L
Pressure(P)=?
Temperature (T)= 51°C = 51+273 K=324 K
Then, By Combined gas laws,
[tex]\frac{P_{1} V_{1} }{T_{1} } +\frac{P_{2} V_{2} }{T_{2} } =\frac{PV}{T}[/tex]
or, [tex]\frac{15.1*125}{298} +\frac{44.3*125}{298} =\frac{P*6.25}{324}[/tex]
or, [tex]6.34+18.58=\frac{P*6.25}{324}[/tex]
or, [tex]P=\frac{24.92*324}{6.25}[/tex]
∴P=1291.85 kPa
So the total pressure of the mixture in the tank of volume 6.25 litres at 51°C is 1291.85 kPa.
The total pressure of the gas mixture which were transferred to a tank of 6.25 L at 51 °C is 1291.7 KPa
We'll begin by calculating the number of mole of N₂ and O₂ which was transferred. This can be obtained as follow:
For N₂:
Volume (V) = 15.1 L
Temperature (T) = 25 °C = 25 + 273 = 298 K
Pressure (P) = 125 KPa
Gas constant (R) = 8.314 L.KPa/Kmol
Number of mole (n) =?
PV = nRT
125 × 15.1 = n × 8.314 × 298
1887.5 = n × 2477.572
Divide both side by 2477.572
n = 1887.5 / 2477.572
n = 0.762 mole
For O₂:
Volume (V) = 44.3 L
Temperature (T) = 25 °C = 25 + 273 = 298 K
Pressure (P) = 125 KPa
Gas constant (R) = 8.314 L.KPa/Kmol
Number of mole (n) =?
PV = nRT
125 × 44.3 = n × 8.314 × 298
5537.5 = n × 2477.572
Divide both side by 2477.572
n = 5537.5 / 2477.572
n = 2.235 moles
- Next, we shall determine the total mole of the mixture.
Mole of N₂ = 0.762 mole
Mole of O₂ = 2.235 moles
Total mole = 0.762 + 2.235
Total mole = 2.997 moles
- Finally, we shall determine the total pressure at 51 °C. This can be obtained as follow:
Volume (V) = 6.25 L
Temperature (T) = 51 °C = 51 + 273 = 324 K
Gas constant (R) = 8.314 L.KPa/Kmol
Total of mole (n) = 2.997 moles
Total Pressure (P) =?
PV = nRT
P × 6.25 = 2.997 × 8.314 × 324
P × 6.25 = 8073.126792
Divide both side by 6.25
P = 8073.126792 / 6.25
P = 1291.7 KPa
Therefore, the total pressure of the gas mixture at 51 °C is 1291.7 KPa
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