The volume of the gas = 9.14 L
Further explanation
Given
Kb = 6.3 x 10⁻⁵
2.5 L solution
pOH= 2.5
Required
Volume of gas
Solution
pOH = 2.5
![\tt [OH^-]=10^(-2.5)=3.2* 10^(-3)](https://img.qammunity.org/2022/formulas/chemistry/high-school/yecxo9i3o3s3tm3wig5shg7o0kqy2v3qn1.png)
For weak base :
![\tt [OH^-]=√(Kb.M)](https://img.qammunity.org/2022/formulas/chemistry/high-school/s1cq3q1h6f46nn2rm53uaipy4inec600qr.png)
( 3.2 x 10⁻³)² = 6.3 x 10⁻⁵ x M
M = 0.163
mol = M x V
mol = 0.163 x 2.5 L
mol = 0.408
At STP(1 atm, 273 K) 1 mol = 22.4 L
so the volume = 0. 408 x 22.4 L = 9.14 L