How to find the pH of a saturated solution of sodium carbonate (Na2CO3)?

What is the pH of a saturated solution of sodium carbonate (Na2CO3)?

(solubility in water is 21.6 g/100mL at room temperature and for carbonic acid, H2CO3, Ka1 = 4.5 x 10-7, Ka2 = 4.7 x 10-11)

Give the answer in three sig. figs.

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  • 1 month ago
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    First, find the molarity:

    21.6 g/0.100 L = 216 g/L / 106 g/mol = 2.04 M CO32-

    The carbonate ion acts as a base by the equilibrium:

    CO32- + H2O <--> HCO3- + OH-

    Kb = [HCO3-][OH-]/[CO32-] 

    The value of Kb can be calculated from the value of Ka2 as:

    Kb =1X10^-14 / 4.7X10^-11 = 2.1X10^-4

    In that saturated solution, let x = [HCO3-] - [OH-] and [CO32-] = 2.04-x. As a first approximation, assume that x will be small compared to 2.04 and can be ignored. Then,

    Kb = 2.1X10^-4 = x^2 / 2.04

    x = 0.021 M = [OH-]

    pOH = 1.68

    pH = 14-pOH = 12.3

    x is only about 1% of 2.04, and so ignoring it in the denominator was a reasonable assumption to make.

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