Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Compute the theoretical yield of the product (in grams) for each of the following initial amounts of reactants:

[tex]\[ \text{Ti}(s) + 2\text{F}_2(g) \rightarrow \text{TiF}_4(s) \][/tex]

Given:
- 2.3 g of Ti
- 1.8 g of F[tex]\(_2\)[/tex]

Express your answer using two significant figures.

[tex]\[ m = 2.9 \text{ g} \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's go step-by-step to solve the problem of finding the theoretical yield of TiF₄ given 2.3 grams of Titanium (Ti) and 1.8 grams of Fluorine gas (F₂).

### Step 1: Write the Balanced Chemical Equation
The balanced reaction equation is:
[tex]\[ \text{Ti (s)} + 2 \text{F}_2 \text{(g)} \rightarrow \text{TiF}_4 \text{(s)} \][/tex]

### Step 2: Determine the Molar Mass of Reactants and Product
- Molar mass of Titanium (Ti): 47.87 g/mol
- Molar mass of Fluorine gas (F₂): 2 18.998 g/mol = 37.996 g/mol
- Molar mass of Titanium Tetrafluoride (TiF₄): 47.87 g/mol + 4 18.998 g/mol = 123.862 g/mol

### Step 3: Calculate the Moles of Each Reactant
- Moles of Ti:
[tex]\[ \text{moles of Ti} = \frac{\text{mass of Ti}}{\text{molar mass of Ti}} = \frac{2.3 \text{ g}}{47.87 \text{ g/mol}} \approx 0.048 \][/tex]

- Moles of F₂:
[tex]\[ \text{moles of F}_2 = \frac{\text{mass of F}_2}{\text{molar mass of F}_2} = \frac{1.8 \text{ g}}{37.996 \text{ g/mol}} \approx 0.047 \][/tex]

### Step 4: Determine the Limiting Reactant
According to the balanced equation, 1 mole of Ti reacts with 2 moles of F₂. Therefore:
- The moles of Ti required to react with the given F₂:
[tex]\[ \text{moles of Ti required} = \frac{\text{moles of F}_2}{2} = \frac{0.047}{2} \approx 0.0235 \][/tex]

Compare the moles of Ti required (0.0235) with the moles of Ti available (0.048):
- Since 0.0235 < 0.048, F₂ is the limiting reactant.

### Step 5: Calculate the Moles of TiF₄ Produced
Since F₂ is the limiting reactant, we use its moles to find the moles of TiF₄ produced:
- From the balanced equation, 2 moles of F₂ produce 1 mole of TiF₄. Hence, 0.047 moles of F₂ produce:
[tex]\[ \text{moles of TiF}_4 = \frac{0.047}{2} \approx 0.0235 \][/tex]

### Step 6: Calculate the Theoretical Yield in Grams
- The theoretical yield of TiF₄:
[tex]\[ \text{mass of TiF}_4 = \text{moles of TiF}_4 \times \text{molar mass of TiF}_4 = 0.0235 \times 123.862 \approx 2.91 \][/tex]

### Step 7: Express the Answer Using Two Significant Figures
Rounded to two significant figures, the theoretical yield of TiF₄ is 2.9 grams.

Thus, the theoretical yield of Titanium Tetrafluoride (TiF₄) from 2.3 grams of Titanium and 1.8 grams of Fluorine gas is:
[tex]\[ \boxed{2.9 \text{ grams}} \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.