Question

In the determination of the percentage of purity of impure solution, Sodium trioxocarbonate4, 4.2g of the salt was dissolved in distilled water. the solution was then made up to 1000cm3 mark. If 28cm3 of the resultant solution is neutralised by 20.40cm3 of 0.092M HCL. Calculate the percentage purity of the salt

Answer 1

To determine the percentage purity of impure sodium trioxocarbonate (commonly known as sodium carbonate, Na2CO3), we can follow these steps:

1. 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:

   \[ \text{Moles of HCl} = \text{Volume (L)} \times \text{Molarity (M)} = (20.40 \times 10^{-3} , \text{L}) \times (0.092 , \text{mol/L}) \] \[ = 0.00188 , \text{mol} \]

2. 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:

   \[ \text{Moles of Na}_2\text{CO}_3 = \frac{\text{Moles of HCl}}{2} = \frac{0.00188 , \text{mol}}{2} = 0.00094 , \text{mol} \]

3. 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: \[ \text{Mass of Na}_2\text{CO}_3 = \text{Moles of Na}_2\text{CO}_3 \times \text{Molar mass} = 0.00094 , \text{mol} \times 105.99 , \text{g/mol} \] \[ = 0.0996 , \text{g} \approx 0.0996 , \text{g} \]

4. 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:

   \[ \text{Concentration of Na}_2\text{CO}_3 = \text{Mass of Na}_2\text{CO}_3 \times \frac{1000}{28} \approx 0.0996 \times \frac{1000}{28} \approx 3.55 , \text{g} \]

5. 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%.