Calculate the amount of calcuium oxide required when it reacts with `852 g` of `P_(4) O_(10)`.

Explanation

To calculate the amount of calcium oxide (CaO) required when it reacts with 852 g of phosphorus pentoxide (P₄O₁₀), we will follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction between calcium oxide and phosphorus pentoxide is:
\[ 6 \text{CaO} + \text{P}_4\text{O}_{10} \rightarrow 2 \text{Ca}_3\text{(PO}_4\text{)}_2 \]

### Step 2: Calculate the molar mass of P₄O₁₀
To find the number of moles of P₄O₁₀, we first need to calculate its molar mass.
- Molar mass of P = 31 g/mol
- Molar mass of O = 16 g/mol

Calculating the molar mass of P₄O₁₀:
\[ \text{Molar mass of P}_4\text{O}_{10} = (4 \times 31) + (10 \times 16) = 124 + 160 = 284 \text{ g/mol} \]

### Step 3: Calculate the number of moles of P₄O₁₀
Using the mass given (852 g), we can calculate the number of moles of P₄O₁₀:
\[ \text{Number of moles of P}_4\text{O}_{10} = \frac{\text{mass}}{\text{molar mass}} = \frac{852 \text{ g}}{284 \text{ g/mol}} = 3 \text{ moles} \]

### Step 4: Determine the moles of CaO required
From the balanced equation, we see that 1 mole of P₄O₁₀ reacts with 6 moles of CaO. Therefore, for 3 moles of P₄O₁₀:
\[ \text{Moles of CaO required} = 6 \times \text{moles of P}_4\text{O}_{10} = 6 \times 3 = 18 \text{ moles} \]

### Step 5: Calculate the mass of CaO required
Now, we need to calculate the mass of CaO required using its molar mass.
- Molar mass of CaO = 40 (Ca) + 16 (O) = 56 g/mol

Calculating the mass of CaO:
\[ \text{Mass of CaO} = \text{moles} \times \text{molar mass} = 18 \text{ moles} \times 56 \text{ g/mol} = 1008 \text{ g} \]

### Conclusion
The amount of calcium oxide required when it reacts with 852 g of P₄O₁₀ is **1008 g**.

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