Certainly! Let's go through the problem step-by-step to find out how many moles of [tex]\( O_2 \)[/tex] are needed to react completely with 3.4 moles of [tex]\( C_4H_{10} \)[/tex].
### Step 1: Understand the balanced chemical equation
The balanced chemical equation is:
[tex]\[
2 C_4H_{10}(g) + 13 O_2(g) \rightarrow 8 CO_2(g) + 10 H_2O(g)
\][/tex]
From this equation, we can see that 2 moles of [tex]\( C_4H_{10} \)[/tex] requires 13 moles of [tex]\( O_2 \)[/tex].
### Step 2: Set up the molar ratio
The molar ratio of [tex]\( O_2 \)[/tex] to [tex]\( C_4H_{10} \)[/tex] from the balanced equation is:
[tex]\[
\frac{13 \text{ moles of } O_2}{2 \text{ moles of } C_4H_{10}}
\][/tex]
### Step 3: Use the given amount of [tex]\( C_4H_{10} \)[/tex]
We need to find how many moles of [tex]\( O_2 \)[/tex] are required for 3.4 moles of [tex]\( C_4H_{10} \)[/tex]. Using the molar ratio from Step 2:
[tex]\[
\text{Moles of } O_2 \text{ needed} = \left(\frac{13}{2}\right) \times 3.4
\][/tex]
### Step 4: Perform the calculation
Calculating the moles of [tex]\( O_2 \)[/tex] needed:
[tex]\[
\text{Moles of } O_2 \text{ needed} = \frac{13}{2} \times 3.4 = 6.5 \times 3.4 = 22.1
\][/tex]
Thus, the moles of [tex]\( O_2 \)[/tex] needed to react completely with 3.4 moles of [tex]\( C_4H_{10} \)[/tex] is 22.1 when rounded to 2 significant figures.
### Conclusion
To react completely with 3.4 moles of [tex]\( C_4H_{10} \)[/tex], 22.1 moles of [tex]\( O_2 \)[/tex] are needed, rounded to 2 significant figures.
