a) Mass of potassium sulfate = 177 mg =0.177 g

1 g= 1000 mg

Molecular mass of potassium sulfate = 174.24 g/mol

Moles of potassium sulfate,n =frac{0.177 g}{174.24 g/mol}=0.001016 mol

b) 1 mol = 1000 milli moles

0.001016  mol =0.001016 × 1000 milli moles = 1.016 milli moles

c) Molarity=frac{n}{V}

n = moles of substance

V = Volume of the solution in L

Molarity of of potassium sulfate:

Volume of the solution = 775 mL = 0.775 L (Mass of solute is very less)

[K_2SO_4]=frac{0.001016 mol}{0.775 L}=0.001311 mol/L

K_2SO_4rightarrow 2K++SO_4^{2-}

1 mol potassium sulfate gives 2 mol of potassium ions and 1 mole of sulfate ions.

Molarity of potassium ions:

[K^+]=2times [K_2SO_4]=2times 0.001311 mol/L=0.002622 mol/L

Molarity of sulfate ions:

[SO_4^{2-}]=1times [K_2SO_4]=1times 0.001311 mol/L=0.001311  mol/L

d) ppm=frac{text{Amount of solute in mg}}{text{Volume of the solution in L}}

Volume of solution = 0.775 L

Amount of potassium sulfate = 177 mg

ppm=frac{177 mg}{0.775 L}=228.39 mg/L

e) Volume of the solution = 775 mL

Mass of potassium sulfate = 177 mg =0.177 g

(w/w)%=frac{text{Mass of the solute}}{text{Volume of the solution in mL}}times 100

(w/w)%=frac{0.177 g}{775 mL}times 100=0.023%

f) pK^=-log[K^+]

pK^+=-log[0.002622 M]=2.58


pK^+=-log[0.001311 M]=2.88