A mixture containing 28 gof CaO and 20 g of NaOH is treated with aqueous HCl till the reactions are complete. The resulting solution is evaporated to dryness. What is the mass of the solid obtained?

Options

A. 169.50 g
B. 84.75 g
C. 42.37 g
D. 100.0 g

Explanation

To solve the problem step-by-step, we will follow these steps:

### Step 1: Write the Chemical Reactions
The reactions that occur when CaO and NaOH react with HCl are:

1. **For Calcium Oxide (CaO)**:
\[ \text{CaO} + 2\text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} \]

2. **For Sodium Hydroxide (NaOH)**:
\[ \text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]

### Step 2: Calculate Moles of Reactants
Next, we need to calculate the number of moles of CaO and NaOH.

- **For CaO**:
- Mass of CaO = 28 g
- Molar mass of CaO = 40 (Ca) + 16 (O) = 56 g/mol
\[ \text{Moles of CaO} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{28 \, \text{g}}{56 \, \text{g/mol}} = 0.5 \, \text{mol} \]

- **For NaOH**:
- Mass of NaOH = 20 g
- Molar mass of NaOH = 23 (Na) + 16 (O) + 1 (H) = 40 g/mol
\[ \text{Moles of NaOH} = \frac{20 \, \text{g}}{40 \, \text{g/mol}} = 0.5 \, \text{mol} \]

### Step 3: Determine Moles of Products Formed
From the stoichiometry of the reactions:
- 0.5 moles of CaO will produce 0.5 moles of CaCl₂.
- 0.5 moles of NaOH will produce 0.5 moles of NaCl.

### Step 4: Calculate Mass of Products
Now, we will calculate the mass of the products formed.

- **For CaCl₂**:
- Molar mass of CaCl₂ = 40 (Ca) + 35.5 × 2 (Cl) = 110 g/mol
\[ \text{Mass of CaCl}_2 = \text{Moles} \times \text{Molar Mass} = 0.5 \, \text{mol} \times 110 \, \text{g/mol} = 55 \, \text{g} \]

- **For NaCl**:
- Molar mass of NaCl = 23 (Na) + 35.5 (Cl) = 58.5 g/mol
\[ \text{Mass of NaCl} = \text{Moles} \times \text{Molar Mass} = 0.5 \, \text{mol} \times 58.5 \, \text{g/mol} = 29.25 \, \text{g} \]

### Step 5: Calculate Total Mass of Solid
Finally, we sum the masses of the solid products:
\[ \text{Total Mass} = \text{Mass of CaCl}_2 + \text{Mass of NaCl} = 55 \, \text{g} + 29.25 \, \text{g} = 84.25 \, \text{g} \]

### Final Answer
The mass of the solid obtained after evaporation is **84.25 g**.

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