Determine the concentrations of Na2CO3, Na , and CO32– in a solution prepared by dissolving 2.22 × 10–4 g Na2CO3 in 2.25 L of water. Express all three concentrations in molarity. Additionally, express the concentrations of the ionic species in parts per million (ppm). Note: Determine the formal concentration of CO32–. Ignore any reactions with water.
To determine the concentrations of Na2CO3, Na, and CO32– in the solution, we need to use the molar mass and the volume of the solution.
Step 1: Calculate the molar mass of Na2CO3.
The molar mass of Na2CO3 is calculated by summing the atomic masses of its constituent elements:
Na: 22.99 g/mol
C: 12.01 g/mol
O: 16.00 g/mol
Molar mass of Na2CO3 = (2 × 22.99 g/mol) + 12.01 g/mol + (3 × 16.00 g/mol)
Molar mass of Na2CO3 = 105.99 g/mol
Step 2: Convert the mass of Na2CO3 to moles.
Mass of Na2CO3 = 2.22 × 10^–4 g
To convert from mass to moles, divide by the molar mass:
moles of Na2CO3 = (2.22 × 10^–4 g) / (105.99 g/mol)
moles of Na2CO3 = 2.093 × 10^–6 mol
Step 3: Calculate the concentration of Na2CO3 in molarity (M).
Molarity is calculated by dividing the number of moles of solute by the volume of solution in liters:
concentration (M) = moles of Na2CO3 / volume of solution (in liters)
The volume of the solution is given as 2.25 L:
concentration of Na2CO3 (M) = 2.093 × 10^–6 mol / 2.25 L
concentration of Na2CO3 (M) = 9.30 × 10^–7 M
Step 4: Calculate the concentration of Na and CO32– in molarity.
Since Na2CO3 dissociates into 2 Na+ ions and 1 CO32– ion, the concentrations of Na and CO32– will have the same numerical value as the concentration of Na2CO3.
concentration of Na (M) = concentration of CO32– (M) = 9.30 × 10^–7 M
Step 5: Calculate the concentrations of the ionic species in parts per million (ppm).
To convert from molarity to ppm, multiply the concentration in molarity by the molar mass of the ion and then by 10^6:
ppm of Na = concentration of Na (M) × molar mass of Na × 10^6
ppm of CO32– = concentration of CO32– (M) × molar mass of CO32– × 10^6
The molar mass of Na is 22.99 g/mol and the molar mass of CO32– is 60.01 g/mol.
ppm of Na = 9.30 × 10^–7 M × 22.99 g/mol × 10^6
ppm of CO32– = 9.30 × 10^–7 M × 60.01 g/mol × 10^6
Calculating the values:
ppm of Na ≈ 21.32 ppm
ppm of CO32– ≈ 56.05 ppm
Therefore, the concentrations of Na2CO3, Na, and CO32– in the solution are approximately 9.30 × 10^–7 M. The concentrations of Na and CO32– in parts per million (ppm) are approximately 21.32 ppm and 56.05 ppm, respectively.
To determine the concentrations of Na2CO3, Na, and CO32– in the solution, we need to use the given mass of Na2CO3 and the volume of the water to calculate the molarity of each species. The molarity (M) is defined as the number of moles of solute per liter of solution.
Step 1: Calculate the number of moles of Na2CO3
To find the moles of Na2CO3, we need to convert the given mass of Na2CO3 to moles using its molar mass. The molar mass of Na2CO3 is calculated by adding up the atomic masses of each element.
Na: atomic mass = 22.99 g/mol (sodium)
C: atomic mass = 12.01 g/mol (carbon)
O: atomic mass = 16.00 g/mol (oxygen)
Na2CO3: (2 * Na) + C + (3 * O) = (2 * 22.99) + 12.01 + (3 * 16.00) = 105.99 g/mol
Now we can calculate the number of moles of Na2CO3:
moles = mass / molar mass
moles = 2.22 × 10–4 g / 105.99 g/mol
Step 2: Calculate the molarity of Na2CO3
The molarity (M) is defined as moles of solute per liter of solution.
Molarity (Na2CO3) = moles / volume
Molarity (Na2CO3) = moles / 2.25 L
Step 3: Calculate the molar concentration of Na+ and CO32–
The Na2CO3 dissociates in solution to provide two Na+ ions and one CO32– ion. So, to find the molar concentrations of Na+ and CO32–, we multiply the molarity of Na2CO3 by the appropriate stoichiometric coefficients:
Molarity (Na) = 2 * Molarity (Na2CO3)
Molarity (CO32–) = 1 * Molarity (Na2CO3)
Step 4: Convert concentrations to ppm
To convert the molar concentrations into parts per million (ppm), we need to multiply by the conversion factor:
ppm = molarity * (molar mass solute / molar mass solution) * 10^6
For Na2CO3, Na, and CO32–, use the respective molar masses:
Na2CO3: 105.99 g/mol
Na: 22.99 g/mol
CO32–: 60.01 g/mol
Now, follow the steps above to find the concentrations of Na2CO3, Na, and CO32– in molarity and parts per million (ppm).
mols Na2CO3 = grams/formal mass = ?
L = 2.25
M Na2CO3 = mols/L.
(Na^+) = ? ppm
1 ppm = 1 mg/L
g Na^+ = 2.22E-4 x 2 = 4.44E-4 g/2.25 L = ?g/L. Convert to mg/L to obtain ppm.
(CO3^2-) in ppm is 1/2 that.