When a sample of hydrate is heated, water of hydration is lost.

If you start with 60.0-gram sample of Na₂CO₃⦁10H₂O, what will be the mass of the sample (in grams) after all of the water is removed by heating?
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1 answer

To calculate the mass of the sample after all the water is removed, we first need to determine the mass of the anhydrous sodium carbonate (Na₂CO₃) remaining after the water of hydration is lost.

  1. Calculate the molar mass of Na₂CO₃·10H₂O:

    • Molar mass of Na₂CO₃:

      • Sodium (Na): \( 2 \times 22.99 , \text{g/mol} = 45.98 , \text{g/mol} \)
      • Carbon (C): \( 1 \times 12.01 , \text{g/mol} = 12.01 , \text{g/mol} \)
      • Oxygen (O): \( 3 \times 16.00 , \text{g/mol} = 48.00 , \text{g/mol} \)
    • Total for Na₂CO₃: \[ 45.98 + 12.01 + 48.00 = 105.99 , \text{g/mol} \]

    • Molar mass of 10H₂O:

      • Hydrogen (H): \( 2 \times 10 \times 1.01 , \text{g/mol} = 20.20 , \text{g/mol} \)
      • Oxygen (O): \( 10 \times 16.00 , \text{g/mol} = 160.00 , \text{g/mol} \)
    • Total for 10H₂O: \[ 20.20 + 160.00 = 180.20 , \text{g/mol} \]

    • Total molar mass of Na₂CO₃·10H₂O: \[ 105.99 + 180.20 = 286.19 , \text{g/mol} \]

  2. Determine the mass contribution of the anhydrous Na₂CO₃:

    • The mass of Na₂CO₃ in the hydrate can be calculated using the ratio of the molar masses: \[ \text{mass of Na₂CO₃} = \left( \frac{105.99 , \text{g/mol}}{286.19 , \text{g/mol}} \right) \times 60.0 , \text{g} \]

    • Calculate this value: \[ \text{mass of Na₂CO₃} = \left( \frac{105.99}{286.19} \right) \times 60.0 \approx 22.18 , \text{g} \]

Therefore, after heating and removing all water from the original 60.0-gram sample of Na₂CO₃·10H₂O, the mass of the remaining sample (anhydrous Na₂CO₃) is approximately 22.18 grams.