Calculate the pH of a solution obtained dissolving 10 g of NH3 and 15 g of NH4Cl in 300 ml of water (Kb NH3 = 1.8 x10-5).
To calculate the pH of a solution, we need to consider the dissociation of NH3 (ammonia) in water and the subsequent formation of NH4+ ions and OH- ions. Here's how you can calculate the pH step by step:
1. Calculate the number of moles of NH3:
The molar mass of NH3 is 17.03 g/mol. To find the number of moles, divide the given mass by the molar mass:
Number of moles of NH3 = 10 g / 17.03 g/mol = 0.587 mol
2. Calculate the number of moles of NH4Cl:
The molar mass of NH4Cl is 53.49 g/mol. To find the number of moles, divide the given mass by the molar mass:
Number of moles of NH4Cl = 15 g / 53.49 g/mol = 0.280 mol
3. Calculate the total volume of the solution:
The total volume of the solution is given as 300 mL, which is equivalent to 0.3 L.
4. Calculate the concentration of NH3:
The concentration of NH3 can be calculated by dividing the number of moles of NH3 by the total volume of the solution:
Concentration of NH3 = (0.587 mol) / (0.3 L) = 1.96 M
5. Calculate the concentration of NH4+:
Since NH4Cl dissociates completely in water, the concentration of NH4+ ions is the same as the concentration of NH4Cl. So, the concentration of NH4+ is 0.280 M.
6. Calculate the concentration of OH- ions:
Using the Kb value for NH3, we can calculate the concentration of OH- ions. The Kb value is given as 1.8 x 10^ -5.
To find the concentration of OH-, divide the Kb by the concentration of NH4+:
Concentration of OH- = (Kb NH3) / (Concentration of NH4+)
Concentration of OH- = (1.8 x 10^ -5) / (0.280 M) = 6.43 x 10^ -5 M
7. Calculate the pOH:
pOH is the negative logarithm (base 10) of the concentration of OH-. So:
pOH = -log10(Concentration of OH-)
pOH = -log10(6.43 x 10^ -5)
pOH = 4.19
8. Calculate the pH:
Since pOH + pH = 14, we can find the pH by subtracting the pOH from 14:
pH = 14 - pOH
pH = 14 - 4.19
pH = 9.81
So, the pH of the solution obtained after dissolving 10 g of NH3 and 15 g of NH4Cl in 300 mL of water is approximately 9.81.