Answer :
Answer:
For 1: The concentration after the given time is 0.077 M
For 2: The time taken to reach the given value is 6.39 days
Explanation:
The integrated rate law equation for second order reaction follows:
[tex]k=\frac{1}{t}\left (\frac{1}{[A]}-\frac{1}{[A]_o}\right)[/tex] ......(1)
where,
k = rate constant = [tex]9.7\times 10^{-6}M^{-1}s^{-1}[/tex]
t = time taken
[tex][A][/tex] = concentration of substance after time 't'
[tex][A]_o[/tex] = Initial concentration = 0.140 M
- For 1:
We are given:
t = 7.00 days = (7 × 24 × 60 × 60) = 604800 seconds (1 day = 24 hours, 1 hour = 60 mins, 1 min = 60 sec)
[A] = ?
Putting values in equation 1, we get:
[tex]9.7\times 10^{-6}=\frac{1}{604800}\left (\frac{1}{[A]}-\frac{1}{0.140}\right)[/tex]
[tex][A]=0.077M[/tex]
Hence, the concentration after the given time is 0.077 M
- For 2:
We are given:
[A] = [tex]8.0\times 10^{-2}M[/tex]
Putting values in equation 1, we get:
[tex]9.7\times 10^{-6}=\frac{1}{t}\left (\frac{1}{(8.0\times 10^{-2})}-\frac{1}{0.140}\right)[/tex]
[tex]t=552283s=6.39days[/tex]
Hence, the time taken to reach the given value is 6.39 days
The time when the HI concentration reaches a value of 8.0 × 10⁻² M will be "6.39 days".
Hydrogen Iodide
According to the question,
Rate constant, k = 9.7 × 10⁻⁶ H⁻¹ s⁻¹ or,
= 9.7 × 10⁻⁶ L/mol.s
Concentration of HI = 0.140 M
We know that,
→ [tex]\frac{1}{[HI]}[/tex] = kt + [tex]\frac{1}{[HI]_0}[/tex]
Now,
[HI] = [tex][kt + \frac{1}{[HI]_0} ]^{-1}[/tex]
By substituting the values, we get
= (9.7 × 10⁻⁶ × [tex]\frac{60}{1}[/tex] × [tex]\frac{60}{1}[/tex] × [tex]\frac{24}{1}[/tex] × 7.00 + [tex]\frac{1}{0.140}[/tex])⁻¹
= (5866560 × 10⁻⁶ + [tex]\frac{1}{0.140}[/tex])⁻¹
= ([tex]\frac{(0.140\times 5.866560)(1\times 1)}{0.140}[/tex])⁻¹
= (13.00941714)⁻¹ or,
= 0.0786 mol/L (Molarity of [HI])
Now,
[HI] = [tex][kt + \frac{1}{[HI]_0} ]^{-1}[/tex]
t = [tex]\frac{1}{k}[/tex] ([tex]\frac{1}{[HI]} -\frac{1}{[HI]_0}[/tex])
By substituting the values,
= [tex]\frac{1}{9.7\times 10^{-6}}\times \frac{1}{60}\times \frac{1}{60}\times \frac{1}{24}[/tex] ([tex]\frac{1}{0.080} -\frac{1}{0.140}[/tex])
= [tex]\frac{1}{838080\times 10^{-6}}[/tex] × ([tex]\frac{0.06}{0.0112}[/tex])
= 6.39 days
Thus the above answer is correct.
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