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The reaction AB(aq)→A(g)+B(g) is second order in AB and has a rate constant of 0.0164 M −1 ⋅ s −1 at 25.0 ∘ C . A reaction vessel initially contains 250.0 mL of 0.104 M AB which is allowed to react to form the gaseous product. The product is collected over water at 25.0 ∘ C . Part A How much time is required to produce 142.0 mL of the products at a barometric pressure of 707.3 mmHg . (The vapor pressure of water at this temperature is 23.8 mmHg .)

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arthurpdc
The reaction is second order in AB, so: [tex]v=k[AB]^2[/tex]. In the statement, we obtain that [tex][AB]=0.104~M[/tex] and, at 25 ºC, [tex]k=0.0164~M^{-1}\cdot s^{-1}[/tex]. Then:

[tex]v=k[AB]^2\\\\ v=0.0164\cdot0.104^2\\\\ v=0.0164\cdot0.010816\\\\ v\approx0.000177=1.77\times10^{-4}~mol/s[/tex]

Now, we'll calculate the number of mols of the products in the gas. Using the Ideal Gas Law:

[tex]\bullet~\text{Pressure:}~p=707.3-23.8=683.5~mmHg\\\\ \bullet~\text{Volume:}~V=142~mL=0.142~L\\\\ \bullet~\text{Number of moles:}~n=n_A+n_B\\\\ \bullet~\text{Ideal gas constant:}~R=62.3~L\cdot mmHg\cdot K^{-1}\cdot mol^{-1}\\\\ \bullet~\text{Temperature:}~T=25^oC=25+273~K=298~K\\\\[/tex]

[tex]pV=nRT\\\\ 683.5\cdot0.142=n\cdot62.3\cdot298\\\\ n=\dfrac{683.5\cdot0.142}{62.3\cdot298}\\\\ n\approx0,0052~mol [/tex]

Since each AB molecule forms one of A and one of B, [tex]n_A=n_B[/tex]. Hence: [tex]2n_A\approx0,0052\Longrightarrow n_A=n_B\approx0.0026~mol[/tex].

We'll consider that in the beginning there was not A or B. So, [tex]\Delta n_A=\Delta n_B=0.0026-0=0.0026~mol[/tex]. Furthermore, since the ratio of AB to A and to B is 1:1, [tex]|\Delta n_{AB}|=|\Delta n_A|=|\Delta n_B|[/tex].

Calculating the time by the expression of velocity:

[tex]v=\dfrac{|\Delta[AB]|}{\Delta t}=\dfrac{1}{\Delta t}\cdot\dfrac{|\Delta n_{AB}|}{V}=\dfrac{1}{\Delta t}\cdot\dfrac{|\Delta n_A||}{250~mL}\\\\ 1.77\cdot10^{-4}=\dfrac{1}{\Delta t}\cdot\dfrac{0.0026~mol}{0.25~L}\\\\ \Delta t=\dfrac{0.0026}{0.25\cdot1.77\cdot10^{-4}}\\\\ \boxed{\Delta t\approx58.76~s}[/tex]
pstnonsonjoku

The time taken is 148 seconds.

What is rate of reaction?

The term rate of reaction refers to how quickly reactants are converted to products.

We have to first obtain the number of moles of the product from;

PV = nRT

P = 707.3 mmHg - 23.8 mmHg = 683.5 mmHg  or 0.89 atm

V = 142.0 mL or 0.142 L

n = ?

R = 0.082 atmLK-1mol-1

T = 25.0 ∘ C or 298 K

n = PV/RT

n= 0.89 atm ×  0.142 L/ 0.082 atmLK-1mol-1 × 298 K

n = 0.126/24.4

n = 0.0052 moles

Concentration = number of moles/volume = 0.0052 moles/250.0 × 10^-3

= 0.021 M

Concentration of AB left = 0.104 M  - 0.021 M = 0.083 M

Using the formula of second order reaction;

1/[A] = kt + 1/[Ao]

[A] = 0.083 M

[Ao] = 0.104 M

t =?

k = 0.0164 M −1 ⋅ s −1

1/[A] - 1/[Ao]/k = t

t = (0.083 M)^-1 - (0.104 M )^-1/0.0164 M −1 ⋅ s −1

t = 12.05 - 9.62/0.0164 M −1 ⋅ s −1

t = 148 seconds

Learn more about rate of reaction: https://brainly.com/question/25857212

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