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Answer :
The answer is B (1.3L)
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The volume of the gas is 1.27 L at a temperature is 47°C and the pressure is 5.0 atm. Therefore, option (B) is correct.
What is the ideal gas equation?
The ideal gas equation is described as the equation of the state of a perfect gas. The ideal gas equation is the product of the pressure and volume of one-mole gas is equal to the multiplication of the absolute temperature and gas constant.
The mathematical equation for a perfect gas is as follows:
PV = nRT
where n is the moles of an ideal gas, P is the pressure of the gas, V is the volume, and R is the universal gas constant.
Given, the initial volume of the gas, V₁ = 2.0 L
The initial temperature of the gas, T₁ = 27° C = 300.15 K
The initial pressure of the gas, P₁ = 3.0 atm
The final temperature of the gas, T₂ = 47° C = 320.15 K
The initial pressure of the gas, P₂ = 5.0 atm
We know that for an ideal gas:
[tex]\frac{P_1V_1}{T_1} =\frac{P_2V_2}{T_2}[/tex]
[tex]V_2=\frac{P_1V_1T_2}{T_1P_2}[/tex]
[tex]V_2= \frac{3.0\times2.0\times320.15}{5.0\times 300.15}[/tex]
[tex]V_2= 1.27 L[/tex]
Therefore, the volume of the gas in its final state is equal to 1.27 L when the gas is heated to 47ºC and compressed to 5.0 atm.
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