To calculate the quantity of moles of [tex]\( NO_2 \)[/tex] gas that forms when [tex]\( 5.20 \times 10^{-3} \)[/tex] moles of [tex]\( N_2O_5 \)[/tex] gas completely reacts, follow these steps:
1. Identify the balanced chemical equation:
Given the reaction:
[tex]\[
2 N_2O_5(g) \rightarrow 4 NO_2(g) + O_2(g)
\][/tex]
2. Determine the mole ratio:
According to the balanced equation, 2 moles of [tex]\( N_2O_5 \)[/tex] produce 4 moles of [tex]\( NO_2 \)[/tex]. This can be simplified to a mole ratio of 1:2 (for every 1 mole of [tex]\( N_2O_5 \)[/tex], 2 moles of [tex]\( NO_2 \)[/tex] are formed).
3. Calculate the moles of [tex]\( NO_2 \)[/tex] formed:
Given that we start with [tex]\( 5.20 \times 10^{-3} \)[/tex] moles of [tex]\( N_2O_5 \)[/tex], use the mole ratio to find the moles of [tex]\( NO_2 \)[/tex]:
[tex]\[
\text{Moles of } NO_2 = 5.20 \times 10^{-3} \times \frac{4}{2}
\][/tex]
4. Simplify the calculation:
[tex]\[
\text{Moles of } NO_2 = 5.20 \times 10^{-3} \times 2
\][/tex]
5. Final computation:
[tex]\[
\text{Moles of } NO_2 = 10.40 \times 10^{-3}
\][/tex]
[tex]\[
\text{Moles of } NO_2 = 0.0104
\][/tex]
Therefore, the quantity of moles of [tex]\( NO_2 \)[/tex] gas that forms is [tex]\( 0.0104 \)[/tex] moles.
