Percent Ionization calculation EXPLAIN THE PART USING THE QUADRATIC FORMULA CLEA

Question

Percent Ionization calculation

EXPLAIN THE PART USING THE QUADRATIC FORMULA CLEARLY. ANSWER BOTH PROBLEM A AND B.

I personally have gotten to the point where you're supposed to input variables into the quadratic formula, but thats where I get stuck. Someone please explain how to solve for x.

A certain weak acid, HA, has a Ka value of 2.1 Times 10-7. Calculate the percent ionization of HA in a 0.10 M solution. Express your answer to two significant figures and include the appropriate units. Calculate the percent ionization of HA in a 0.010 M solution. Express your answer to two significant figures, and include the appropriate units.

Explanation / Answer

Ka = x^2/(0.1 - x )

2.1 x 10^-7 = x^2/(0.1-x)

Since we know that x will be very less than 0.1 we can assume 0.1 - x = 0.1

Hence

2.1 x 10^-7 = x^2/0.1

x ^2 = 2.1 x 10^-7 *0.1

x^2 = 2.1*10^-8

x = sqrt( 2.1*10^-8)

x = 1.449 x 10^-4

Percent dissociation = ( 1.449 x 10^-4/0.1) * 100

= 0.145 %

2)

Ka = x^2/(0.01 - x )

2.1 x 10^-7 = x^2/(0.01-x)

Since we know that x will be very less than 0.01 we can assume 0.01 - x = 0.01

Hence

2.1 x 10^-7 = x^2/0.01

x ^2 = 2.1 x 10^-7 *0.01

x^2 = 2.1*10^-9

x = sqrt( 2.1*10^-9) = 4.582 x 10^-5

Percent dissociation = ( 4.582 x 10^-5 /0.01) * 100

= 0.485 %

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