What mass of hydrochloric acid is needed to decompose 50 g of limestone?

Options

A. 36.5 g
B. 73 g
C. 50 g
D. 100 g

Explanation

To find the mass of hydrochloric acid (HCl) needed to decompose 50 g of limestone (CaCO₃), we will follow these steps:

### Step 1: Write the chemical formula of limestone
The chemical formula for limestone is:
\[ \text{CaCO}_3 \]

### Step 2: Write the balanced chemical equation
The reaction of hydrochloric acid with calcium carbonate can be represented as:
\[ \text{CaCO}_3 + 2 \text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \]

### Step 3: Determine the molar mass of calcium carbonate (CaCO₃)
To find the molar mass of CaCO₃, we add the atomic masses of its constituent elements:
- Calcium (Ca): 40 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol (and there are 3 oxygen atoms)

Calculating the molar mass:
\[ \text{Molar mass of CaCO}_3 = 40 + 12 + (3 \times 16) = 40 + 12 + 48 = 100 \text{ g/mol} \]

### Step 4: Calculate the number of moles of CaCO₃ in 50 g
Using the formula for moles:
\[ \text{Moles of CaCO}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{50 \text{ g}}{100 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 5: Determine the moles of HCl required
From the balanced equation, we see that 1 mole of CaCO₃ reacts with 2 moles of HCl. Therefore, for 0.5 moles of CaCO₃:
\[ \text{Moles of HCl required} = 0.5 \text{ moles CaCO}_3 \times 2 = 1 \text{ mole HCl} \]

### Step 6: Calculate the mass of 1 mole of HCl
The molar mass of hydrochloric acid (HCl) is calculated as follows:
- Hydrogen (H): 1 g/mol
- Chlorine (Cl): 35.5 g/mol

Calculating the molar mass:
\[ \text{Molar mass of HCl} = 1 + 35.5 = 36.5 \text{ g/mol} \]

### Step 7: Calculate the mass of HCl needed
Since we need 1 mole of HCl, the mass required is:
\[ \text{Mass of HCl} = 1 \text{ mole} \times 36.5 \text{ g/mol} = 36.5 \text{ g} \]

### Final Answer
The mass of hydrochloric acid needed to decompose 50 g of limestone is:
\[ \boxed{36.5 \text{ g}} \]

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