Chemistry, 21.04.2020 16:40 briizy

In their notebook you see that it takes 9 hours for a sixth of a 0.5M solution of BC2 to react. Unfortunately, you have somewhere you need to be in 3.5 hours and will not be able to monitor the reaction properly. What concentration of BC2 should you originally use in order to have 0.42 M remaining in 3.5 hours

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Answer from: jordanmazer17

Complete Question

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The concentration of BC_2 that should used originally is C_Z_o = 0.4492M

Explanation:

From the question we are told that

The necessary elementary step is

2BC_2 -----4C + B_2

The time taken for sixth of 0.5 M of reactant to react t = 9 hr

The time available is t_a = 3.5 hr

The desired concentration to remain C = 0.42M

Let Z be the reactant , Y be the first product and X the second product

Generally the elementary rate law is mathematically as

$-r_Z = kC_Z^2 = - \frac{d C_Z}{dt}$

Where k is the rate constant , C_Z is the concentration of Z

From the elementary rate law we see that the reaction is second order (This because the concentration of the reactant is raised to power 2 )

For second order reaction

$\frac{1}{C_Z} - \frac{1}{C_Z_o} = kt$

Where C_Z_o is the initial concentration of Z which a value of C_Z_o = 0.5M

From the question we are told that it take 9 hours for the concentration of the reactant to become

$C_Z = C_Z_o - \frac{1}{6} C_Z_o$

$C_Z = 0.5 - \frac{0.5}{6}$

= 0.4167 M

$\frac{1}{0.4167} - \frac{1}{0.50} = 9 k$

0.400 = 9 k

=> $k = 0.044\ L/ mol \cdot hr^{-1}$

For C_Z = 0.42M

$\frac{1}{0.42} - \frac{1}{C_Z_o} = 3.5 * 0.044$

$2.38 - 0.154 = \frac{1}{C_Z_o}$

$2.226 = \frac{1}{C_Z_o}$

$C_Z_o = \frac{1}{2.226}$

C_Z_o = 0.4492M

In their notebook you see that it takes 9 hours for a sixth of a 0.5M solution of BC2 to react. Unfo

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In their notebook you see that it takes 9 hours for a sixth of a 0.5M solution of BC2 to react. Unfo...