Answer:
8.9L is the volume of the gas that must be dissolved.
Explanation:
For a weak base, we can find [(CH₃)₃N] using the equation:
Kb = [OH⁻] [[(CH₃)₃NH⁺] / [(CH₃)₃N]
As [OH⁻] = [[(CH₃)₃NH⁺] and [OH⁻] = 10^-pOH = 3.16x10⁻³M:
6.3x10⁻⁵ = [3.16x10⁻³M][3.16x10⁻³M] / [(CH₃)₃N]
[(CH₃)₃N] = 0.1587M
As the volume is 2.5L, moles are:
2.5L * (0.1587mol / L) = 0.3968moles
Using:
PV = nRT
We can solve for volume of the gas as follows:
P = 1atm at STP; n = 0.3968moles; R = 0.082atmL/molK; T = 273.15K at STP
V = 0.3968mol*0.082atmL/molK*273.15K/1atm
V = 8.9L is the volume of the gas that must be dissolved.
