What is the theoretical yield (in g) of PCl3 when 62.54 g of Cl2 are reacted with 12.39 g of P?



To calculate the theoretical yield of phosphorus trichloride (PCl₃) when chlorine gas (Cl₂) is reacted with phosphorus (P), we need to follow these steps:

### Step 1: Write the balanced chemical equation.

The balanced reaction between phosphorus and chlorine gas to form phosphorus trichloride is:

\[
P + 3Cl_2 \rightarrow PCl_3
\]

### Step 2: Calculate the molar masses of the reactants and product.

- Molar mass of \( P \) (Phosphorus) = 30.97 g/mol
- Molar mass of \( Cl_2 \) (Chlorine gas) = 70.90 g/mol (since 1 Cl atom = 35.45 g/mol)
- Molar mass of \( PCl_3 \) (Phosphorus trichloride) = 137.33 g/mol

### Step 3: Determine the limiting reagent.

#### a) Moles of \( Cl_2 \):

\[
\text{Moles of } Cl_2 = \frac{62.54 \text{ g}}{70.90 \text{ g/mol}} = 0.882 \text{ mol}
\]

#### b) Moles of \( P \):

\[
\text{Moles of } P = \frac{12.39 \text{ g}}{30.97 \text{ g/mol}} = 0.400 \text{ mol}
\]

#### c) Determine the limiting reagent.

From the balanced equation, 1 mole of phosphorus reacts with 3 moles of chlorine gas. So, to react with 0.400 moles of phosphorus, we would need:

\[
\text{Required } Cl_2 = 0.400 \text{ mol} \times 3 = 1.200 \text{ mol}
\]

However, we only have 0.882 moles of chlorine gas, which is less than the required amount. Thus, chlorine gas (\( Cl_2 \)) is the limiting reagent.

### Step 4: Calculate the theoretical yield of \( PCl_3 \).

Since \( Cl_2 \) is the limiting reagent, we use its moles to calculate the theoretical yield of \( PCl_3 \). From the balanced equation, 3 moles of \( Cl_2 \) produce 1 mole of \( PCl_3 \). Therefore, the moles of \( PCl_3 \) produced will be:

\[
\text{Moles of } PCl_3 = \frac{0.882 \text{ mol of } Cl_2}{3} = 0.294 \text{ mol of } PCl_3
\]

Now, calculate the mass of \( PCl_3 \) produced:

\[
\text{Mass of } PCl_3 = 0.294 \text{ mol} \times 137.33 \text{ g/mol} = 40.38 \text{ g}
\]

### Final Answer:
The theoretical yield of \( PCl_3 \) is **40.38 g**.

---

Would you like more details on any step or have questions?  
Here are five related questions you might explore:
1. How do you identify the limiting reagent in a reaction?
2. What factors can cause the actual yield to differ from the theoretical yield?
3. Can you calculate the percent yield if the actual yield is given?
4. What are some common applications of phosphorus trichloride in industry?
5. How does the concept of stoichiometry apply to other reactions?

**Tip:** Always make sure your chemical equation is balanced before performing stoichiometric calculations!

What is the theoretical yield (in g) of PCl3 when 62.54 g of Cl2 are reacted with 12.39 g of P?

Calculate the theoretical yield of phosphorus trichloride (PCl3) when 62.54 g of chlorine gas (Cl2) is reacted with 12.39 g of phosphorus (P). Learn about stoichiometry, limiting reagents, and molar mass calculations in this detailed step-by-step solution, suitable for students in Grades 10-12.

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