A solution of NaOH(aq) contains 6.2 g of NaOH(s) per 100.0 mL of solution. Calculate the pH and the pOH of the solution at 25 °C.
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To calculate the pH and pOH of the NaOH solution, we need to know the concentration of hydroxide ions (OH-) in the solution. We can find this by converting the given mass of NaOH to moles, then dividing by the volume of the solution in liters.
1. Convert the mass of NaOH to moles:
Given mass of NaOH = 6.2 g
Molar mass of NaOH = 22.99 g/mol (Na) + 16.00 g/mol (O) + 1.01 g/mol (H) = 39.99 g/mol
Number of moles of NaOH = mass / molar mass
Number of moles = 6.2 g / 39.99 g/mol = 0.155 mol
2. Convert the volume of the solution to liters:
Given volume = 100.0 mL
Volume in liters = 100.0 mL / 1000 mL/L = 0.100 L
3. Calculate the concentration of hydroxide ions (OH-):
Concentration (mol/L) = moles of NaOH / volume (L)
Concentration = 0.155 mol / 0.100 L = 1.55 M
4. Calculate the pOH:
pOH = -log[OH-]
pOH = -log(1.55) = 0.81
5. Calculate the pH:
Since pH + pOH = 14 (at 25 °C), we can subtract the pOH from 14 to find the pH:
pH = 14 - pOH
pH = 14 - 0.81 = 13.19
Therefore, the pH of the NaOH solution is 13.19, and the pOH is 0.81.
To calculate the pH and pOH of the solution, we need to determine the concentration of hydroxide ions (OH-) in the solution.
First, let's calculate the molarity of NaOH in the solution:
Molarity (M) = moles of solute / volume of solution (in liters)
Given that the solution contains 6.2 g of NaOH, we need to determine the number of moles of NaOH.
1. Calculate the molar mass of NaOH:
Na = 22.99 g/mol
O = 16.00 g/mol
H = 1.01 g/mol
Molar mass of NaOH = (22.99 g/mol) + (16.00 g/mol) + (1.01 g/mol) = 40.00 g/mol
2. Calculate the number of moles of NaOH:
Moles = mass / molar mass
Moles = 6.2 g / 40.00 g/mol = 0.155 mol
3. Convert the volume of the solution from milliliters to liters:
Volume = 100.0 mL / 1000 mL/L = 0.100 L
Now, we can calculate the molarity of NaOH:
Molarity = 0.155 mol / 0.100 L = 1.55 M
The concentration of hydroxide ions (OH-) is equal to the concentration of NaOH, since each NaOH molecule produces one hydroxide ion in solution.
Therefore, the concentration of hydroxide ions (OH-) in the solution is 1.55 M.
Now, let's calculate the pOH and pH of the solution.
pOH = -log10([OH-])
pOH = -log10(1.55) ≈ -0.19
Since pH + pOH = 14 (at 25 °C), we can calculate the pH:
pH = 14 - pOH
pH = 14 - (-0.19) ≈ 14.19
So, the pH of the solution at 25 °C is approximately 14.19, and the pOH is approximately -0.19.