To solve the problem step by step, we will follow these calculations:
### Step 1: Determine the amount of CaCO₃ that reacted
We start with 2.5 g of CaCO₃ and are left with 1.05 g after the reaction.
\[
\text{Amount of CaCO}_3 \text{ that reacted} = \text{Initial amount} - \text{Remaining amount}
\]
\[
= 2.5 \, \text{g} - 1.05 \, \text{g} = 1.45 \, \text{g}
\]
### Step 2: Calculate the number of moles of CaCO₃ that reacted
The molar mass of CaCO₃ (calcium carbonate) is calculated as follows:
- Calcium (Ca) = 40 g/mol
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol × 3 = 48 g/mol
\[
\text{Molar mass of CaCO}_3 = 40 + 12 + 48 = 100 \, \text{g/mol}
\]
Now, we can calculate the number of moles of CaCO₃ that reacted:
\[
\text{Number of moles of CaCO}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{1.45 \, \text{g}}{100 \, \text{g/mol}} = 0.0145 \, \text{mol}
\]
### Step 3: Determine the number of moles of HCl that reacted
From the balanced chemical equation for the reaction of CaCO₃ with HCl:
\[
\text{CaCO}_3 + 2 \text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{CO}_3
\]
This shows that 1 mole of CaCO₃ reacts with 2 moles of HCl. Therefore, the number of moles of HCl that reacted is:
\[
\text{Number of moles of HCl} = 2 \times \text{Number of moles of CaCO}_3 = 2 \times 0.0145 \, \text{mol} = 0.029 \, \text{mol}
\]
### Step 4: Calculate the mass of HCl that reacted
The molar mass of HCl is approximately 36.5 g/mol. Therefore, the mass of HCl that reacted is:
\[
\text{Mass of HCl} = \text{Number of moles} \times \text{Molar mass} = 0.029 \, \text{mol} \times 36.5 \, \text{g/mol} = 1.0585 \, \text{g}
\]
### Step 5: Calculate the concentration of HCl in grams per liter
We know that the volume of the HCl solution used is 50 mL, which is equivalent to 0.050 L. To find the weight of HCl per liter, we can use the mass of HCl and the volume of the solution:
\[
\text{Weight of HCl per liter} = \frac{\text{Mass of HCl}}{\text{Volume in liters}} = \frac{1.0585 \, \text{g}}{0.050 \, \text{L}} = 21.17 \, \text{g/L}
\]
### Final Answer
The weight of HCl per liter is approximately **21.17 g/L**.
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