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Using the quadratic equation to calculate [H_3O+] in 0.00250 M HNO_2, what are t

ID: 1019323 • Letter: U

Question

Using the quadratic equation to calculate [H_3O+] in 0.00250 M HNO_2, what are the values of a, b, c and x, where a, b, and c are the coefficients in the quadratic equation ax^2 + bx + c = 0, and x is [H_3O+]? Recall that K_a = 4.5 times 10^-4. Express a, b, c, and x numerically separated by commas. Using the method of successive approximations, what is [H_3O+] in 0.500 M HC1O_2 (K_a = 1.1 times 10^2) and how many iterations (n) are needed to validate that a constant value had been obtained to two significant figures? Express [H_3 O+] using two significant figures, followed by a comma and the number of iterations as an integer. Using the method of successive approximations, what is [H_3O+] in 0.00500 M CH_2ClCOOH(aq) (K_a = 1.4 times 10^3) and how many iterations (n) are needed to validate that a constant value had been obtained to two significant figures? Express [H_3O+] using two significant figures, followed by a comma and the number of iterations as an integer.

Explanation / Answer

      HNO2 +H2O-------> H3O+ + No2-

I    0.0025           0         0

C   -x            +x          +x

E   0.0025-x    +x          +x

Ka   = [H3O+][No2-]/[HNO2]

4.5*10-4   = x*x/0.0025-x

4.5*10-4 (0.0025-x) = x2

    x    = 00086

[H3O+]   = x =0.00086M

       HClO2 + H2O --------> H3O+ + ClO2-

I      0.5                           0              0

C   -x                            +x             +x

E 0.5-x                          +x              +x

     Ka   = [H3O+][ClO2-]/[HClO2]

    1.1*10-2    = x*x/0.5-x

    1.1*10-2 *(0.5-x)   = x2

           x = 0.068

[H3O+] = x = 0.068M

c.

        CH2ClCOOH + H2O ---------> H3O+ + CH2ClCOO-

I        0.005                                0              0

C      -x                                      +x            +x

E     0.005-x                              +x             +x

            Ka = [H3O+][CH2ClCOO-]/[CH2ClCOOH]

            1.4*10-3   = x*x/0.005-x

          1.4*10-3*(0.005-x) = x2

               x = 0.002

[H3O+]   = x = 0.002M