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.

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Successive approximation method
To determine [H3O+] in 0.00250 M HNO2(aq) (Ka = 4.5. × 10-4), the first equation we
[H;O*] is
If 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]
Ка
0.00250-r
= 4.5 × 10-4
0.00250-0.00106
Normally when x < 5% Minitial, we solve this equation using the quadratic formula. This
tutorial 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 × 10–3
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,
4.5 × 10–4
0.00250-0.000804
which yields x = 8.74 × 104. Now, we can further restrict x to the range
8.04 x 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
8.60 × 10-4
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 × 10-4 M.
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 (H30+] 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 [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
Transcribed Image Text:Successive approximation method To determine [H3O+] in 0.00250 M HNO2(aq) (Ka = 4.5. × 10-4), the first equation we [H;O*] is If 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] Ка 0.00250-r = 4.5 × 10-4 0.00250-0.00106 Normally when x < 5% Minitial, we solve this equation using the quadratic formula. This tutorial 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 × 10–3 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, 4.5 × 10–4 0.00250-0.000804 which yields x = 8.74 × 104. Now, we can further restrict x to the range 8.04 x 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 8.60 × 10-4 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 × 10-4 M. 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 (H30+] 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 [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 B
Using 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 significant
figures?
Express H3O+] 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 (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 =
M
Submit
Transcribed Image Text:Part B Using 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 significant figures? Express H3O+] 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 (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 = M Submit
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