Question

What is the silver ion concentration in a solution prepared by mixing 335 mL of 0.386 M silver nitrate with 419 mL of 0.410 M sodium carbonate? The Ksp of silver carbonate is 8.1 × 10-12

Answer 1

Moles of AgNO3 = MxV = 0.386Mx335mLx(1L / 1000mL) = 0.129 mol

Moles of Na2CO3 = MxV = 0.410Mx419mLx(1L / 1000mL) = 0.172mol

The following occurs when AgNO3 reacts with Na2CO3.

2AgNO3(aq) + Na2CO3(aq) -------- > Ag2CO3(s) + 2NaNO3(aq)

   2 mol 1 mol 1 mol

1 mole of Na2CO3 reacts with 2 moles of AgNO3.

Hence 0.172 moles of Na2CO3 that will react with the moles of AgNO3

= (0.172 mol Na2CO3)x(2 mol AgNO3 / 1 mol Na2CO3) = 0.344 mol AgNO3, which is much more than the available mol of AgNO3(0.129 mol).

Hence AgNO3 acts as limiting reagent and is exhausted completely.

Hence moles of Na2CO3 reacted = (0.129 mol AgNO3)x(1 mol Na2CO3 / 2 mol AgNO3)

= 0.0645 mol Na2CO3

Now moles of Na2CO3 remain unreacted = (0.172 – 0.0645) mol = 0.1075 mol

Since the solubility of Ag2CO3 is very low, the [CO₃^2-(aq)] due to dissociation of Ag2CO3 can be neglected in comparison to the [CO₃^2-(aq)] due to unreacted Na2CO3

Hence the [CO₃^2-(aq)] = moles of unreacted Na2CO3 / total volume = 0.1075 mol / 0.754L = 0.143 M

Now dissociation of Ag2CO3 can be written as