Answer:
pH of the solution is 11.24
Explanation:
Total mass of caffeine in 225 mL solution upon dissolution of two tablets = [tex](2\times 2.00\times 10^{2})mg=(2\times 2.00\times 10^{2}\times 10^{-3})g=0.4g[/tex]
So molarity of caffeine in solution = [tex]\frac{0.4\times 1000}{225\times 194}M=0.00916M[/tex]
We have to construct an ice table to calculate change in concentration at equilibrium
[tex]C_{8}H_{10}N_{4}O_{2}+H_{2}O\rightleftharpoons HC_{8}H_{10}N_{4}O_{2}^{+}+OH^{-}[/tex]
I:0.00916 0 0
C:-x +x +x
E:0.00916-x x x
So, [tex]\frac{[HC_{8}H_{10}N_{4}O_{2}^{+}][OH^{-}]}{[C_{8}H_{10}N_{4}O_{2}]}=K_{b}[/tex]
Species inside third bracket represent equilibrium concentrations
So,[tex]\frac{x^{2}}{0.00916-x}=0.00041[/tex]
or, [tex]x^{2}+0.00041x-(3.76\times 10^{-6})=0[/tex]
Hence [tex]x=\frac{-0.00041+\sqrt{(0.00041)^{2}+(4\times 3.76\times 10^{-6})}}{2}[/tex]
So, [tex]x=0.001745[/tex]M
So, [tex]pH=14-pOH=14+log[OH^{-}]=14+logx=14+log(0.001745)=11.24[/tex]
