Question

If we assume that x is very small compared to 0.00250, the first iteration gives x=(0.00250×4.5×10−4)1/2=0.00106. Even though the assumption is not valid, it seems likely that [HNO2] is closer to (0.00250−0.00106)M than to 0.00250 M. Substitute the new value into the original equation to obtain the second iteration,

x20.00250−0.00106=4.5×10−4

and then x=8.04×10−4. Now, we can restrict x to the following range:

8.04×10−4<x<1.06×10−3

Use the new value of x to write that [HNO2]=(0.00250−0.000804)M and solve the equation once again for x to obtain the third iteration,

x20.00250−0.000804=4.5×10−4

which yields x=8.74×10−4. Now, we can further restrict x to the range

8.04×10−4<x<8.74×10−4

Continue this procedure until x attains a constant value. The values of x for the next three iterations are shown in the following table.

Iteration	Value of x
4	8.54×10−4
5	8.60×10−4
6	8.59×10−4

When the value of x (rounded to two significant figures) becomes constant, such as in iterations 5 and 6, the process ends. In this case, we can say that, to two significant figures, [H3O+]=8.6×10−4M.

Part A

Now you will solve the same problem as above, but using the quadratic formula instead of iterations, to show that the same value of x is obtained either way.

Using the quadratic equation to calculate [H3O+] in 0.00250 M HNO2, what are the values of a, b, c and x , where a, b, and c are the coefficients in the quadratic equation ax2+bx+c=0, and x is [H3O+]? Recall that Ka=4.5×10−4 .

Express a, b, c, and x numerically separated by commas.

Part B

Using the method of successive approximations, what is [H3O+] in 0.500 M  HClO2 (Ka=1.1×10−2) and how many iterations (n) are needed to validate that a constant value had been obtained to two significant figures?

Express [H3O+] using two significant figures, followed by a comma and the number of iterations as an integer.

Part C

Using the method of successive approximations, what is [H3O+] in 0.00500 M  CH2ClCOOH(aq) (Ka=1.4×10−3) and how many iterations (n) are needed to validate that a constant value had been obtained to two significant figures?

Express [H3O+] using two significant figures, followed by a comma and the number of iterations as an integer.

Answer 1

Equation representing the ionization of HCIO2 is as follows: Acidionization constant K ofHCIO-1.1x102 Concentration ofHClO-0.500 M Initial concentration (M): 0.500 Change(M) Equilibriumconcentration(M):0.500-x 0 0 Acid ionization constant, Ka = Idol 1.1x10- (x) 0.500 -x x" + 0.011x-0.0055 = 0 Solve the value of x by using the quadriatic expression 2a (0.011)t(0.011)-4(1)(-0.0055) 0.011 +0.15 0.0695(or) -0.0805 Since the 2nd root leads to the negative answers, the value of x is 0.0695 From the equilibrium table, | H,0+-X

Part C: Concentration of CH CICOOH ICE table 0.00500 M I(M): C(M): E(M): 0.00500 0 0 + X 0.00500-х Acidionization constant, K, - ÍCH2CICOH1 1.4 ×10% = (0.00500-x) x2 +1.4x103x-7.1x106 0 Solve the value of x by using the quadriatic expression 2a (14x1014x10)-4)(-7.1x10) 4(111-7.1x10 1.4×10づ± 0.00551 = 2.1×10-3 (or) -3.4×10-3 Since the 2nd root leads to the negative answers, the value ofx is 2.1x10- From the equilibrium table, | H,0+-X = 2.1 x 10-3 M