Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

[tex]\[2 C_4H_{10}(g) + 13 O_2(g) \stackrel{\Delta}{\rightarrow} 8 CO_2(g) + 10 H_2O(g)\][/tex]

How many moles of [tex]\[O_2\][/tex] are needed to react completely with 3.4 moles of [tex]\[C_4H_{10}\][/tex]?

Round your answer to 2 significant figures.


Sagot :

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.