To determine the percentage composition of the mixture of calcium carbonate (CaCO3) and sodium chloride (NaCl), we need to analyze the chemical reactions involved and the data provided. Let's break this down step by step.
Understanding the Reactions
When calcium carbonate reacts with hydrochloric acid (HCl), it produces calcium chloride (CaCl2), water (H2O), and carbon dioxide (CO2). The reaction can be represented as:
- CaCO3 + 2 HCl → CaCl2 + H2O + CO2↑
Sodium chloride, on the other hand, does not react with hydrochloric acid under these conditions, so it remains in the solution.
Neutralization with Sodium Hydroxide
After the reaction, the remaining acid in the solution is neutralized by sodium hydroxide (NaOH). The neutralization reaction is:
From the problem, we know that 20 ml of the solution required 25 ml of N/5 NaOH for complete neutralization. First, we need to calculate the number of equivalents of NaOH used:
Calculating Equivalents of NaOH
The normality of NaOH is given as N/5, which means:
- 1 N = 1 equivalent per liter
- N/5 = 0.2 equivalents per liter
Since we used 25 ml (or 0.025 L) of NaOH:
- Equivalents of NaOH = 0.2 equivalents/L × 0.025 L = 0.005 equivalents
Finding the Amount of HCl Neutralized
Since the reaction between HCl and NaOH is a 1:1 ratio, the equivalents of HCl neutralized is also 0.005 equivalents. Now, we can find the number of moles of HCl:
- Moles of HCl = Equivalents of HCl = 0.005 moles
Calculating the Amount of HCl Initially Present
Next, we need to determine how much HCl was initially present before the reaction with CaCO3. The total volume of the solution after filtering is 200 ml, and we used 20 ml for the titration. Therefore, the amount of HCl in the remaining 180 ml is:
- Initial moles of HCl = 0.005 moles (from the titration)
Relating HCl to CaCO3
From the reaction of CaCO3 with HCl, we know that 1 mole of CaCO3 reacts with 2 moles of HCl. Therefore, the moles of CaCO3 that reacted can be calculated as follows:
- Moles of CaCO3 = Moles of HCl / 2 = 0.005 moles / 2 = 0.0025 moles
Calculating the Mass of CaCO3
The molar mass of CaCO3 is approximately 100 g/mol. Thus, the mass of CaCO3 in the mixture is:
- Mass of CaCO3 = Moles × Molar Mass = 0.0025 moles × 100 g/mol = 0.25 g
Finding the Mass of NaCl
Since the total mass of the mixture is 3.2 g, we can find the mass of NaCl by subtracting the mass of CaCO3 from the total mass:
- Mass of NaCl = Total mass - Mass of CaCO3 = 3.2 g - 0.25 g = 2.95 g
Calculating the Percentage Composition
Now, we can calculate the percentage composition of each component in the mixture:
- Percentage of CaCO3 = (Mass of CaCO3 / Total mass) × 100 = (0.25 g / 3.2 g) × 100 ≈ 7.81%
- Percentage of NaCl = (Mass of NaCl / Total mass) × 100 = (2.95 g / 3.2 g) × 100 ≈ 92.19%
Final Results
In summary, the percentage composition of the mixture is approximately:
- Calcium Carbonate (CaCO3): 7.81%
- Sodium Chloride (NaCl): 92.19%
This analysis shows how to systematically approach the problem using stoichiometry and the principles of acid-base reactions. If you have any further questions or need clarification on any steps, feel free to ask!
