To determine the percentage purity of impure sodium trioxocarbonate (commonly known as sodium carbonate, Na2CO3), we can follow these steps:
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Calculate the moles of HCl used in the reaction: We know the volume and molarity (concentration) of the HCl solution.
- Volume of HCl = 20.40 cm³ = 20.40 × 10⁻³ L
- Molarity of HCl = 0.092 M
We can calculate the moles of HCl:
\[ \text{Moles of HCl} = \text{Volume (L)} \times \text{Molarity (M)} = (20.40 \times 10^{-3} , \text{L}) \times (0.092 , \text{mol/L}) \] \[ = 0.00188 , \text{mol} \]
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Determine the moles of sodium carbonate that reacted: The balanced equation for the reaction between sodium carbonate and hydrochloric acid is:
\[ \text{Na}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{NaCl} + \text{H}_2\text{O} + \text{CO}_2 \]
This tells us that 1 mole of Na2CO3 reacts with 2 moles of HCl. Therefore, we can calculate the moles of Na2CO3 in the reaction:
\[ \text{Moles of Na}_2\text{CO}_3 = \frac{\text{Moles of HCl}}{2} = \frac{0.00188 , \text{mol}}{2} = 0.00094 , \text{mol} \]
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Calculate the mass of pure sodium carbonate that corresponds to the moles calculated: The molar mass of sodium carbonate (Na2CO3) is calculated as follows:
- Na: \( 22.99 , \text{g/mol} , \times 2 \) = \( 45.98 , \text{g/mol} \)
- C: \( 12.01 , \text{g/mol} \)
- O: \( 16.00 , \text{g/mol} , \times 3 \) = \( 48.00 , \text{g/mol} \)
Adding these together: \[ \text{Molar mass of Na}_2\text{CO}_3 = 45.98 + 12.01 + 48.00 = 105.99 , \text{g/mol} \]
Now we can calculate the mass of pure Na2CO3: \[ \text{Mass of Na}_2\text{CO}_3 = \text{Moles of Na}_2\text{CO}_3 \times \text{Molar mass} = 0.00094 , \text{mol} \times 105.99 , \text{g/mol} \] \[ = 0.0996 , \text{g} \approx 0.0996 , \text{g} \]
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Calculate the concentration of Na2CO3 in 1000 cm³ of solution: Since 28 cm³ of the solution corresponds to the amount of Na2CO3 that reacted, the concentration of Na2CO3 in the entire 1000 cm³ can be found using the ratio of volumes:
\[ \text{Concentration of Na}_2\text{CO}_3 = \text{Mass of Na}_2\text{CO}_3 \times \frac{1000}{28} \approx 0.0996 \times \frac{1000}{28} \approx 3.55 , \text{g} \]
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Calculate the percentage purity of the Na2CO3: Now that we know the total mass of the impure salt is 4.2 g, we can calculate the percentage purity:
\[ \text{Percentage purity} = \left( \frac{\text{mass of pure Na}_2\text{CO}_3}{\text{mass of impure Na}_2\text{CO}_3} \right) \times 100 = \left( \frac{0.0996}{4.2} \right) \times 100 \] \[ \approx 2.37 % \]
Therefore, the percentage purity of the impure sodium trioxocarbonate solution is approximately 2.37%.