The new volume of the gas is 93750 liters.
Given,
The volume of gas in a container is 125,000 liters.
The pressure is 1.2 atmospheres.
Suppose the temperature remains constant.
The pressure changes to 1.6 atmospheres.
We have to find the new volume of the gas.
What is the ideal gas law equation?
The equation is given by:
PV = nRT
Where P is the pressure of the gas.
V is its volume.
n is the number of moles of the gas.
T is its kelvin temperature.
R is the ideal (universal) gas constant.
Let the initial volume and pressure of the gas be [tex]V_{1}[/tex] and [tex]P_{1}[/tex].
The final volume and pressure of the gas be [tex]V_{2}[/tex] and [tex]P_{2}[/tex].
We have,
[tex]V_{1}[/tex] = 125000 litres.
[tex]P_{1}[/tex] = 1.2 atmospheres.
Since temperature remains constant.
[tex]P_{1} V_{1}[/tex] / nR = T and [tex]P_{2} V_{2}[/tex] / nR = T
We can write as:
[tex]P_{1} V_{1}[/tex] / nR = [tex]P_{2} V_{2}[/tex] / nR
[tex]P_{1} V_{1}[/tex] = [tex]P_{2} V_{2}[/tex]
Putting the values we get,
[tex]P_{1} V_{1}[/tex] = [tex]P_{2} V_{2}[/tex]
1.2 x 125000 = 1.6 x [tex]V_{2}[/tex]
[tex]V_{2}[/tex] = (1.2 x 125000) / 1.6
= 93750 litres.
Thus the new volume of the gas is 93750 liters.
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