A chemist prepared a solution by dissolving 52.0 g of hydrated sodium carbonate in water to a total volume of 5.00 dm3. The concentration was determined to be 0.0366 M. Determine the formula of the hydrated sodium carbonate.
Na2CO3*10H2O
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To determine the formula of the hydrated sodium carbonate, we need to calculate the number of moles of hydrated sodium carbonate in the solution.
First, we need to convert the mass of hydrated sodium carbonate to moles. The molar mass of hydrated sodium carbonate (Na2CO3·xH2O) can be calculated using the atomic masses of the individual elements:
Na (sodium) = 22.99 g/mol
C (carbon) = 12.01 g/mol
O (oxygen) = 16.00 g/mol
H (hydrogen) = 1.01 g/mol
Oxygen from water = 16.00 g/mol
The molar mass of hydrated sodium carbonate is the sum of the molar masses of its constituent elements multiplied by their respective subscripts:
Na2CO3·xH2O = [(22.99 g/mol)(2) + (12.01 g/mol) + (16.00 g/mol)(3) + (1.01 g/mol)(2)] + (16.00 g/mol)(x)
Given the molar concentration (0.0366 M) and the volume of the solution (5.00 dm3), we can calculate the number of moles of hydrated sodium carbonate using the formula:
moles = concentration × volume
moles = 0.0366 M × 5.00 dm3
Now, we can rearrange the formula to solve for the moles of hydrated sodium carbonate:
moles = 0.0366 M × 5.00 dm3 = 0.183 mol
Next, we divide the mass of hydrated sodium carbonate (52.0 g) by the number of moles (0.183 mol) to calculate the molar mass:
molar mass = mass / moles = 52.0 g / 0.183 mol = 284.15 g/mol
To determine the value of x (the number of water molecules attached to each formula unit of sodium carbonate), we subtract the molar mass of the anhydrous sodium carbonate (Na2CO3) from the molar mass of hydrated sodium carbonate (Na2CO3·xH2O):
284.15 g/mol - [(22.99 g/mol)(2) + (12.01 g/mol) + (16.00 g/mol)(3)] = 18.18 g/mol
This value corresponds to the molar mass of x water molecules:
18.18 g/mol = (16.00 g/mol)(x)
Solving for x:
x = 18.18 g/mol / 16.00 g/mol = 1.136
However, in this case, x cannot be a fraction, so we round it to the nearest whole number. Therefore, x equals 1.
Therefore, the formula for the hydrated sodium carbonate is Na2CO3·1H2O.