To determine how many moles of titanium (Ti) can form when 50 moles of titanium dioxide (TiO₂) react with 80 moles of carbon (C), we also need to identify the limiting reagent. Let's go through the problem step-by-step.
Step 1: Understand the reaction
The balanced chemical equation is:
[tex]\[ TiO_2(s) + 2C(s) \longrightarrow Ti(s) + 2CO(g) \][/tex]
This tells us that:
- 1 mole of [tex]\( TiO_2 \)[/tex] reacts with 2 moles of [tex]\( C \)[/tex] to produce 1 mole of [tex]\( Ti \)[/tex] and 2 moles of [tex]\( CO \)[/tex].
Step 2: Calculate the moles of Ti formed from TiO₂
Given:
- 50 moles of [tex]\( TiO_2 \)[/tex]
From the equation:
[tex]\[ 1 \text{ mole of } TiO_2 \text{ produces} 1 \text{ mole of } Ti \][/tex]
Thus,
[tex]\[ 50 \text{ moles of } TiO_2 \text{ will produce } 50 \text{ moles of } Ti \][/tex]
Step 3: Calculate the moles of Ti formed from C
Given:
- 80 moles of [tex]\( C \)[/tex]
From the equation:
[tex]\[ 2 \text{ moles of } C \text{ are needed to produce} 1 \text{ mole of } Ti \][/tex]
Thus,
[tex]\[ 80 \text{ moles of } C \div 2 \text{ moles of } C = 40 \text{ moles of } Ti \][/tex]
Step 4: Determine the limiting reagent
The limiting reagent is the one that produces the lesser amount of product.
Comparing the amounts of [tex]\( Ti \)[/tex] we can get from each:
- From [tex]\( TiO_2 \)[/tex]: 50 moles of [tex]\( Ti \)[/tex]
- From [tex]\( C \)[/tex]: 40 moles of [tex]\( Ti \)[/tex]
Since 40 moles is less than 50 moles, carbon ([tex]\( C \)[/tex]) is the limiting reagent.
Step 5: Determine the number of moles of Ti formed
Since carbon ([tex]\( C \)[/tex]) is the limiting reagent, the actual number of moles of [tex]\( Ti \)[/tex] that can form is 40 moles.
Final Answer:
The number of moles of titanium (Ti) that can form is 40 moles. The limiting reagent is carbon ([tex]\( C \)[/tex]).
