Questions: For the following reactions, determine the value of x (in mol). a. 4 C+S8 → 4 CS2 2.2 mol S8 yields x mol CS2 b. CS2+3 O2 → CO2+2 SO2 3.2 mol O2 yields x mol SO2 c. N2H4+3 O2 → 2 NO2+2 H2O d. SiH4+2 O2 → SiO2+2 H2O 2.3 mol O2 yields x mol NO2

For the following reactions, determine the value of x (in mol).
a. 4 C+S8 → 4 CS2
2.2 mol S8 yields x mol CS2
b. CS2+3 O2 → CO2+2 SO2
3.2 mol O2 yields x mol SO2
c. N2H4+3 O2 → 2 NO2+2 H2O
d. SiH4+2 O2 → SiO2+2 H2O
2.3 mol O2 yields x mol NO2

Transcript text: For the following reactions, determine the value of $x$ (in mol ). a. $4 \mathrm{C}+\mathrm{S}_{8} \rightarrow 4 \mathrm{CS}_{2}$ $2.2 \mathrm{~mol} \mathrm{~S}_{8}$ yields $x \mathrm{~mol} \mathrm{CS}_{2}$ b. $\mathrm{CS}_{2}+3 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{SO}_{2}$ $3.2 \mathrm{~mol} \mathrm{O}_{2}$ yields $x \mathrm{~mol} \mathrm{SO}{ }_{2}$ c. $\mathrm{N}_{2} \mathrm{H}_{4}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$ d. $\mathrm{SiH}_{4}+2 \mathrm{O}_{2}$ $\rightarrow \mathrm{SiO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$ $2.3 \mathrm{~mol} \mathrm{O}{ }_{2}$ yields $x \mathrm{~mol} \mathrm{NO}{ }_{2}$

Solution

Solution Steps

Step 1: Determine the Stoichiometry for Reaction (a)

The balanced chemical equation for reaction (a) is: \[ 4 \mathrm{C} + \mathrm{S}_{8} \rightarrow 4 \mathrm{CS}_{2} \]

From the equation, 1 mole of $\mathrm{S}_{8}$ produces 4 moles of $\mathrm{CS}_{2}$.

Step 2: Calculate the Moles of $\mathrm{CS}_{2}$ Produced in Reaction (a)

Given that 2.2 moles of $\mathrm{S}_{8}$ are used, we can calculate the moles of $\mathrm{CS}_{2}$ produced using the stoichiometry: \[ x = 2.2 \, \text{mol} \, \mathrm{S}_{8} \times \frac{4 \, \text{mol} \, \mathrm{CS}_{2}}{1 \, \text{mol} \, \mathrm{S}_{8}} = 8.8 \, \text{mol} \, \mathrm{CS}_{2} \]

Step 3: Determine the Stoichiometry for Reaction (b)

The balanced chemical equation for reaction (b) is: \[ \mathrm{CS}_{2} + 3 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + 2 \mathrm{SO}_{2} \]

From the equation, 3 moles of $\mathrm{O}_{2}$ produce 2 moles of $\mathrm{SO}_{2}$.

Step 4: Calculate the Moles of $\mathrm{SO}_{2}$ Produced in Reaction (b)

Given that 3.2 moles of $\mathrm{O}_{2}$ are used, we can calculate the moles of $\mathrm{SO}_{2}$ produced using the stoichiometry: \[ x = 3.2 \, \text{mol} \, \mathrm{O}_{2} \times \frac{2 \, \text{mol} \, \mathrm{SO}_{2}}{3 \, \text{mol} \, \mathrm{O}_{2}} = 2.1333 \, \text{mol} \, \mathrm{SO}_{2} \]

Step 5: Determine the Stoichiometry for Reaction (c)

The balanced chemical equation for reaction (c) is: \[ \mathrm{N}_{2} \mathrm{H}_{4} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \]

This equation shows that 3 moles of $\mathrm{O}_{2}$ produce 2 moles of $\mathrm{NO}_{2}$.

Final Answer

For reaction (a), the moles of $\mathrm{CS}_{2}$ produced are $\boxed{8.8 \, \text{mol}}$.
For reaction (b), the moles of $\mathrm{SO}_{2}$ produced are $\boxed{2.1333 \, \text{mol}}$.
For reaction (c), the stoichiometry is established, but no specific calculation is required as no moles are given.

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