Two weak acid solutions `HA_1` and `HA_2` each with the same concentration and having `PK_a` values 3 and 5 are placed in contact with hydrogen electrode (1 atm, 25 °C) and are interconnected through a salt bridge. The emf of the cell is

Options

A. 0.21 V
B. 0.059 V
C. 0.018 V
D. 0.021 V

Answer

B

Explanation

`Pt|H_2(1 atm)|HA_2||H_2(1 atm)|Pt`
At anode : `E_(H//H^+)=E_(H//H^+)^@+0.059 (pH)_2` `(because pH=-log[H^+] ) `
At cathode : `E_(H//H^+)=E_(H^+//H)^@-0.059 (pH)_1`
We Know, `[H^+]=Calpha=sqrt(K_aC)`
`(pH)_1=1/2pK_(a_1)-1/1logC, (pH)_2=1/1pK_(a_2)-1/1logC`
`E_(cell)^@=E_(H//H^+)^@=E_(H^+//H)^@`
`=0.059[1/2pK_(a_2)-1/2Pk_(a_1)]=0.059/2(5-3)=0.059` V