Item 9 9 of 32 Constants| Periodic Table Part A The reaction AB(aq)+A(g) +B(g) i

Question

Item 9 9 of 32 Constants| Periodic Table Part A The reaction AB(aq)+A(g) +B(g) is second order in AB and has a rate constant of 0.0170 M-1. at 25.0°C. A reaction vessel initally contains 250.0 mL of 0.192 M AB which is allowed to react to form the gaseous product The product is collected over water at 25.0 C How much time is required to produce 283.0 mL of the products at a barometric pressure of 799.6 mmHg.(The vapor pressure of water at this temperature is 23.8 mmHg.) Express your answer to two significant figures and include the appropriate units. IA t. Value Units Submit Request Answer Provide Feedback Next >

Explanation / Answer

Since,

P(A+B) = Ptotal - PH2O

= 799.6 mmHg - 23.8mmHg

= 775.8 mmHg

So,
PA = 1/2 P(A+B) = 387.9 mmHg

nA = PA x V/(RT)

= 387.9 mmHg x (1atm/760mmHg) x 0.283 L / (0.082 Latm/moleK x 298.15K)
= 0.0059 moles A

then..
from the balanced equation, 1 mole AB ---> 1 mole A
so. moles AB reacted = 0.0059 moles

and...
initial moles AB = 0.250 L x (0.192 moles / L) = 0.048 mol
remaining moles AB = 0.048 - 0.0059 = 0.0421
final molarity = 0.0421 moles / 0.250 L = 0.168 M

For second order reaction, we have:

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

so..
t = (1/[At] - 1/[Ao]) / k
t = (1/0.168 M - 1/0.192 M) / (0.0170 / Msec)

t = 43.8 sec

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