Successive approximation methodTo determine [H3O+] in 0.00250 M HNO2(aq) (Ka = 4.5. × 10-4), the first equation we[H;O*] isIf we assume that x is very small compared to 0.00250, the first iteration gives x = (0.00250 × 4.5 × 10-4)/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,would obtain in solving for x =[H3O*][NO2¯][HNO2]Ка0.00250-r= 4.5 × 10-40.00250-0.00106Normally when x < 5% Minitial, we solve this equation using the quadratic formula. Thistutorial will lead you through an alternative method called successive approximations.and then x = 8.04 × 10–4. Now, we can restrict x to the following range:8.04 x 10¬4 < x< 1.06 × 10–3Use 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,4.5 × 10–40.00250-0.000804which yields x = 8.74 × 104. Now, we can further restrict x to the range8.04 x 10¬4 < x< 8.74 × 10-4Continue this procedure until x attains a constant value. The values of x for the next three iterations are shown in the following table.IterationValue of x48.54 × 10–48.60 × 10-48.59 × 10–4When 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 × 10-4 M.Part ANow 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 (H30+] in 0.00250 MHNO2, 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 [H30+]? Recall that Ka = 4.5 x 10-4 .Express a, b, c, and x numerically separated by commas.• View Available Hint(s)Πνα ΑΣφ?a,b,c,x =Submit Part BUsing the method of successive approximations, what is H30+] in 0.500 M HCIO2 (Ka = 1.1 × 10¬2) and how many iterations (n) are needed to validate that a constant value had been obtained to two significantfigures?Express H3O+] using two significant figures, followed by a comma and the number of iterations as an integer.• View Available Hint(s)[H3O+], n =MSubmitPart CUsing the method of successive approximations, what is [H30+] in 0.00500 M CH2CICOOH(aq) (K = 1.4 x 10-3) and how many iterations (n) are needed to validate that a constant value had been obtained to twosignificant figures?Express (H3O+] using two significant figures, followed by a comma and the number of iterations as an integer.• View Available Hint(s)Π ΑΣΦ-[H3O+], n =MSubmit

HNO2 ⇔H+ + NO2- Ka = [H+] [NO2-][HNO2] = x2(0.00250-x) 4.5 * 10-4 (0.00250 - x) = x2 1.125 * 10-6 -…

Part B Using the method of successive approximations, what is [H3O*] in 0.500 M HC1O2 (K, = 1.1 x 10-2) and how many iterations (n) are needed to validate that a constant value had been obtained two significant figures? Express (H30+] using two significant figures, followed by a comma and the number of iterations as an integer. • View Available Hint(s) ? (H3O*], n = M Submit Part C Using the method of successive approximations, what is (H30+] in 0.00500 M CH2CICOOH(aq) (K, = 1.4 x 10-3) and how many iterations (n) are needed to validate that a constant value had been obtained to two significant figures? Express H O+ using two significant figures, followed by a comma and the number of iterations as an integer.

Part B Using the method of successive approximations, what is [H3O] in 0.500 M HC1O2 (K, = 1.1 x 10-2) and how many iterations (n) are needed to validate that a constant value had been obtained two significant figures? Express (H30+] using two significant figures, followed by a comma and the number of iterations as an integer. • View Available Hint(s) ? (H3O], n = M Submit Part C Using the method of successive approximations, what is (H30+] in 0.00500 M CH2CICOOH(aq) (K, = 1.4 x 10-3) and how many iterations (n) are needed to validate that a constant value had been obtained to two significant figures? Express H O+ using two significant figures, followed by a comma and the number of iterations as an integer.

Introductory Chemistry: A Foundation

9th Edition

ISBN:9781337399425

Author:Steven S. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Donald J. DeCoste

Chapter17: Equilibrium

Section: Chapter Questions

Problem 2CR

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