7. A solution is prepared by dissolving 8.5 g NaHCO3 and 12.7 g Na2CO3 in 500.0 mL of water. Calculate the pH.
To calculate the pH of the solution, we need to determine the concentration of hydroxide ions (OH-) or hydronium ions (H3O+), as well as the concentration of sodium ions (Na+).
First, let's find the concentration of sodium ions (Na+):
1. Calculate the moles of NaHCO3:
- NaHCO3 molar mass = 22.99 g/mol (Na) + 1.01 g/mol (H) +
12.01 g/mol (C) + 3 * 16.00 g/mol (O) = 84.01 g/mol
- Moles of NaHCO3 = mass / molar mass = 8.5 g / 84.01 g/mol = 0.101 mol
2. Calculate the moles of Na2CO3:
- Na2CO3 molar mass = 2 * 22.99 g/mol (Na) + 12.01 g/mol (C) +
3 * 16.00 g/mol (O) = 105.99 g/mol
- Moles of Na2CO3 = mass / molar mass = 12.7 g / 105.99 g/mol = 0.120 mol
3. Calculate the total moles of sodium ions:
- Total moles of Na+ = moles of NaHCO3 + 2 * moles of Na2CO3
= 0.101 mol + 2 * 0.120 mol = 0.341 mol
Next, let's determine the concentration of hydroxide ions (OH-) or hydronium ions (H3O+):
4. Calculate the volume of the solution in liters:
- Volume of the solution = 500.0 mL = 500.0 mL / 1000 mL/L = 0.500 L
5. Calculate the concentration of sodium ions (Na+):
- Na+ concentration = moles of Na+ / volume of the solution
= 0.341 mol / 0.500 L = 0.682 M
6. Since Na+ is the conjugate acid of OH-, the concentration of OH- is also 0.682 M.
7. Calculate the concentration of hydronium ions (H3O+):
- Since we have an ionic compound dissolved in water, we can assume complete ionization.
- Therefore, the concentration of H3O+ is equal to the concentration of OH-,
which is 0.682 M.
8. Finally, calculate the pH:
- pH = -log[H3O+]
- pH = -log(0.682)
- pH ≈ 0.166
Therefore, the pH of the solution is approximately 0.166.
To calculate the pH of a solution, you need to know the concentration or molarity of the hydrogen ion concentration ([H+]). In this case, the information provided is the mass of the solute (sodium bicarbonate and sodium carbonate) and the volume of the solution.
To find the [H+], you can calculate the molarities of the two solutes separately, then use the dissociation equations to find the concentration of H+ ions. Finally, you can convert the concentration of H+ ions into pH using the formula for pH.
Here are the steps to calculate the pH:
Step 1: Convert the mass of each solute to moles.
The molar mass of NaHCO3 (sodium bicarbonate) is:
Na = 22.99 g/mol
H = 1.01 g/mol
C = 12.01 g/mol
O = 16.00 g/mol
Using these values, you can calculate the moles of NaHCO3:
moles of NaHCO3 = mass of NaHCO3 / molar mass of NaHCO3
Similarly, calculate the moles of Na2CO3 (sodium carbonate):
moles of Na2CO3 = mass of Na2CO3 / molar mass of Na2CO3
Step 2: Calculate the molarities of NaHCO3 and Na2CO3.
Molarity (M) = moles of solute / volume of solution (in liters)
Convert the volume of water to liters:
volume of solution = 500.0 mL = 500.0 mL / 1000 mL/L = 0.500 L
Calculate the molarity of NaHCO3:
Molarity of NaHCO3 = moles of NaHCO3 / volume of solution
Similarly, calculate the molarity of Na2CO3.
Step 3: Calculate the concentration of H+ ions.
The dissociation equation for NaHCO3 is:
NaHCO3 -> Na+ + HCO3-
From this equation, you can see that 1 mole of NaHCO3 produces 1 mole of HCO3- ions. Therefore, the concentration of H+ ions is equal to the concentration of HCO3- ions.
Use the molarity of NaHCO3 to calculate the concentration of H+ ions.
Similarly, calculate the concentration of H+ ions for Na2CO3. The dissociation equation for Na2CO3 is:
Na2CO3 -> 2Na+ + CO3^2-
Step 4: Calculate the pH.
The pH can be calculated using the concentration of H+ ions using the formula:
pH = -log10[H+]
Calculate the pH using the concentration of H+ ions obtained from both NaHCO3 and Na2CO3.
By following these steps and performing the necessary calculations, you should be able to determine the pH of the solution.