To determine the number of moles of [tex]\( H_2 \)[/tex] produced when 5.82 moles of [tex]\( C_7H_5(NO_2)_3 \)[/tex] are decomposed, we can use the balanced chemical equation provided:
[tex]\[ 2 C_7 H_5(NO_2)_3 \rightarrow 2 C + 12 CO + 5 H_2 + 3 N_2 \][/tex]
Here’s a step-by-step approach to solve the problem:
1. Identify the stoichiometric relationship: From the balanced equation, we see that 2 moles of [tex]\( C_7H_5(NO_2)_3 \)[/tex] produce 5 moles of [tex]\( H_2 \)[/tex].
2. Determine the stoichiometric ratio: We need to find out how many moles of [tex]\( H_2 \)[/tex] are produced per mole of [tex]\( C_7H_5(NO_2)_3 \)[/tex]. We do this by dividing the moles of [tex]\( H_2 \)[/tex] by the moles of [tex]\( C_7H_5(NO_2)_3 \)[/tex] in the balanced equation.
[tex]\[ \text{Stoichiometric ratio of } ( H_2 ) \text{ to } ( C_7 H_5(NO_2)_3 ) = \frac{5 \text{ moles } H_2}{2 \text{ moles } C_7H_5(NO_2)_3} = 2.5 \][/tex]
3. Calculate the moles of [tex]\( H_2 \)[/tex] produced: Multiply the initial moles of [tex]\( C_7H_5(NO_2)_3 \)[/tex] by the stoichiometric ratio to get the number of moles of [tex]\( H_2 \)[/tex] produced.
[tex]\[ \text{Moles of } H_2 = 5.82 \text{ moles } C_7H_5(NO_2)_3 \times 2.5 \][/tex]
[tex]\[ \text{Moles of } H_2 = 14.55 \text{ moles} \][/tex]
Therefore, when 5.82 moles of [tex]\( C_7H_5(NO_2)_3 \)[/tex] are decomposed, 14.55 moles of [tex]\( H_2 \)[/tex] are produced.
