Answer to Question #170698 in General Chemistry for Hyeri

Question

What is the HS- ion concentration of a 0.1 F H2S solution which is also 0.1 F in present to HC2H3O2?

Answer 1

ionization constant of acetic acid $= 1.8×10^{-5}$

the first ionization constant of H2S (about $1.26×10^{-7},$ a datum not present in the problem).

For a 0.1 F aqueous solution of acetic acid only, the concentration of H3O⁺ ions is readily found to be about $1.34×10^{-3} mol/L.$

Then you write the 1st ionization constant of H2S as $1.26×10^{-7 }= (1.34×10^{-3}+ x)× \frac{x}{(0.1 - x)} ,$

where x is the molar concentration of HS^- ions.

This is a 2nd degree equation in x. It can be reasonably assumed that x is very small with respect to $1.34×10^{-3}$ , and, a fortiori, with respect to 0.1 , so that, as a first approximation, you can write $1.26×10^{-7 }= (1.34×10^{-3} )×\frac{x}{(0.1)}$ ,

which yields $x = 9.4×10^{-6} mol/L$ .

By employing this first-approximation value of x, you rewrite $1.26×10^{-7} = (1.34×10^{-3} +( 9.4×10^-6)×\frac{x}{(0.1) }$

and find $x = 9.3×10^{-6} mol/L,$ a value that needs no further to be improved, on the basis of the significant figures present in the data of the problem. As a conclusion, the equilibrium concentration of HS^- ions should be about $9.3×10^{-6} mol/L.$