In the titration of a solution of weak acid, HX with NaOH ,the pH is 5.8 after 10 mL of NaOH solution has been added and 6.40 after 20.0mL of the NaOH has been added. What is the ionisation constant of the acid HX ?

Options

A. `7. 94 xx 10 ^(-7) `
B. ` 7. 94 xx 10 ^(-6) `
C. ` 7. 94 xx 10 ^(-8) `
D. ` 7. 94 xx 10 ^(-9) `

Answer

A

Explanation

`P^(H) =pK_a +log ""(S)/(A) `
` 5.8 = pKa + log ""(10 xx B)/( A- 10B) ...(1) `
` 6.4 = pKa +log "" ( 20 xx B)/( A - 20 B ) ...(2) `
` 0.6 = log ""( 20 B)/( A- 20B) xx (A-10B)/(10B) `
` 0.6 = log ""(2(A-10 B))/( (A-20B)) =log 4`
` rArr (A- 10B )/( A- 20 B) =2 rArr A =30 B `
substituting in ..........(1)
` 5.8 = PKa+ log ""( 10 B)/( 3 0 B - 10 B) `
` 5.8 = PKa+log ""(10B) /( 30 B -10 B) `
`5.8 = pKa +log ""( 1)/(2) `
` pKa =5.8 -log "" (1)/(2) = 5.8+0.3 =6.1`
` -log Ka =6.1 , log Ka = -7 +0.7 = 7 . 9 4 xx 10 ^(-7) `