Answer:
4.27 g
Explanation:
We can write that for a gas kept at constant pressure and temperature, the number of moles of the gas is directly proportional to its volume:
[tex]n\propto V[/tex]
Which can be rewritten as
[tex]\frac{n_1}{V_1}=\frac{n_2}{V_2}[/tex]
where here we have:
[tex]n_1=0.950 mol[/tex] is the initial number of moles
[tex]V_1=25.5 L[/tex] is the initial volume of the gas
[tex]V_2=17.3 L[/tex] is the final volume of the gas
So the final number of moles is
[tex]n_2=\frac{n_1 V_2}{V_1}=\frac{(0.950)(17.3)}{25.5}=0.645 mol[/tex]
So the number of moles that should be released from the balloon is:
[tex]\Delta n = n_1-n_2=0.950-0.645=0.305 mol[/tex]
The molar mass of gas N2 is
[tex]M=14 g/mol[/tex]
Therefore, the mass of gas that should be released is:
[tex]\Delta m = M\Delta n =(14.0)(0.305)=4.27 g[/tex]
