Answer:
1.5V
Explanation:
We can solve this problem by using the equation of state for an ideal gas, which is:
[tex]pV=nRT[/tex]
where
p is the pressure of the gas
V is its volume
n is the number of moles
R is the gas constant
T is the absolute temperature of the gas
In this problem, the pressure and the temperature of the gas are held constant: so we can rewrite the equation as
[tex]V \propto n[/tex]
And so:
[tex]\frac{V_1}{n_1}=\frac{V_2}{n_2}[/tex]
Where here we have:
[tex]n_1=n[/tex] is the initial number of moles
[tex]n_2 = 1.5 n[/tex] is the final number of moles
[tex]V_1=V[/tex] is the initial volume of the gas
Solving for V2, we find the new volume:
[tex]V_2=\frac{n_2 V_1}{n_1}=\frac{1.5n V}{n}=1.5 V[/tex]
So, the volume of the gas increases by 1.5 times.
