Number of moles of B in the above question

Question

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Question Explanation: Find the number of moles of B.

Concept: Parallel first-order reaction.

Solution:

1. The rates of formation of B and C are:

$\frac{d [ B ]}{d t} = 2 k_{1} [A]$ and $\frac{d [ C ]}{d t} = 2 k_{2} [A]$

2. Ratio of moles formed is $\frac{n _{B}}{n _{C}} = \frac{2 k _{1}}{2 k _{2}} = \frac{k _{1}}{k _{2}} = \frac{1}{2} so$ $n_{C} = 2 n_{B}$

3. From stoichiometry, moles of A reacted n_{A ,reacted} = $\frac{n _{B}}{2} = \frac{n _{C}}{2}$

4. Substituting $n_{C} = 2 n_{B}$ gives $n_{A, re a c t e d} = \frac{n _{B}}{2} + \frac{2 n _{B}}{2} = \frac{3 n _{B}}{2}$

5. For complete reaction, all 2 moles of A react. $2 = \frac{3 n _{B}}{2} = n_{B} = \frac{4}{3} m o l es$

6. The number of moles of B formed is: $\frac{4}{3} \approx 1.333$

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