Final answer:
The concentration of the sodium carbonate solution is 21.2 g dm⁻³ and 0.20 mol dm⁻³, after converting the volume to cubic decimeters and calculating the number of moles of the solute.
Step-by-step explanation:
To calculate the concentration of the sodium carbonate solution in both grams per cubic decimeter (g dm⁻³) and moles per cubic decimeter (mol dm⁻³), we must first convert the volume from cubic centimeters (cm³) to cubic decimeters (dm³). Since there are 1000 cm³ in one dm³, 250 cm³ is equivalent to 0.250 dm³.
Next, we consider the mass of sodium carbonate dissolved. This is given as 5.3 g. To express this in g dm⁻³, we divide the mass by the volume in dm³:
Concentration (g dm⁻³) = Mass of solute (g) / Volume of solution (dm³)
Concentration (g dm⁻³) = 5.3 g / 0.250 dm³ = 21.2 g dm⁻³
For the molar concentration (mol dm⁻³), we need to divide the mass of sodium carbonate by its molar mass to find the number of moles. Na₂CO₃'s molar mass is 106 g/mol. Therefore, the number of moles of Na₂CO₃ is:
Moles of Na₂CO₃ = Mass of Na₂CO₃ (g) / Molar mass of Na₂CO₃ (g/mol)
Moles of Na₂CO₃ = 5.3 g / 106 g/mol = 0.050 moles
Finally, to find the molar concentration, we divide the moles by the volume in dm³:
Molar Concentration (mol dm⁻³) = Moles of solute / Volume of solution (dm³)
Molar Concentration (mol dm⁻³) = 0.050 moles / 0.250 dm³ = 0.20 mol dm⁻³
Therefore, the concentration of the sodium carbonate solution is 21.2 g dm⁻³ and 0.20 mol dm⁻³.