Answer
$ 1.34\times 10^{26}$ molecules were released.
Work Step by Step
We can find the original number of molecules in the tank:
$P~V = N_1~k~T$
$N_1 = \frac{P~V}{k~T}$
$N_1 = \frac{(20.0\times 1.01\times 10^5~Pa)(1.0~m^3)}{(1.38\times 10^{-23}~J/K)(273~K)}$
$N_1 = 5.36\times 10^{26}$
We can find the new number of molecules in the tank after the valve is opened:
$P~V = N_2~k~T$
$N_2 = \frac{P~V}{k~T}$
$N_2 = \frac{(15.0\times 1.01\times 10^5~Pa)(1.0~m^3)}{(1.38\times 10^{-23}~J/K)(273~K)}$
$N_2 = 4.02\times 10^{26}$
We can find the number of molecules that were released:
$N_1-N_2 = (5.36\times 10^{26}) - (4.02\times 10^{26}) = 1.34\times 10^{26}$
$ 1.34\times 10^{26}$ molecules were released.
