would all of the lead (ii) bromide (ksp = 6.3 x 10^-6) dissolve if 2.25 g is added to 500 mL of water

To determine whether all of the lead (II) bromide will dissolve in water, we need to compare the initial amount of lead (II) bromide with its solubility product constant (Ksp).

First, let's convert the given mass of lead (II) bromide to moles:

1. Determine the molar mass of lead (II) bromide (PbBr2):
- Atomic mass of Pb = 207.2 g/mol
- Atomic mass of Br = 79.9 g/mol
- Molar mass of PbBr2 = (2 * 79.9 g/mol) + (1 * 207.2 g/mol) = 366 g/mol

2. Convert the given mass of lead (II) bromide to moles:
- Moles of PbBr2 = mass / molar mass
- Moles of PbBr2 = 2.25 g / 366 g/mol

Next, let's calculate the concentration of lead (II) bromide in the solution:

1. Convert the given volume of water to liters:
- Volume of water = 500 mL = 500/1000 = 0.5 L

2. Calculate the concentration (molarity) of lead (II) bromide:
- Concentration (Molarity) = moles of solute / volume of solution in liters
- Concentration = moles of PbBr2 / 0.5 L

Now, we can calculate the ion product (IP) of lead (II) bromide in the solution:

1. The ion product (IP) is calculated by multiplying the concentrations of ions present in the solution:

IP = [Pb2+][Br-]^2

2. Since the stoichiometry of the lead (II) bromide is 1:2 (one Pb2+ ion with two Br- ions), the concentration of Pb2+ is equal to the concentration of PbBr2, and the concentration of Br- is twice the concentration of PbBr2:

IP = [PbBr2][Br-]^2

3. Substituting the known values:
IP = (moles of PbBr2 / 0.5 L) * (2 * moles of PbBr2 / 0.5 L)^2

Finally, we can compare the ion product (IP) with the solubility product constant (Ksp) to determine the solubility of lead (II) bromide:

- If IP > Ksp, the solution is supersaturated, meaning all of the lead (II) bromide would dissolve.
- If IP = Ksp, the solution is saturated, meaning the solution is in equilibrium, and no more lead (II) bromide will dissolve.
- If IP < Ksp, the solution is unsaturated, meaning not all of the lead (II) bromide will dissolve.

By following these steps, you can calculate the ion product (IP) and compare it with the solubility product constant (Ksp) to determine whether all of the lead (II) bromide will dissolve.