Problem 1

A damaged label on an acid bottle. The label on a bottle containing a dilute aqueous solution of an acid became damaged so that only its concentration was readable. A pH meter showed that the hydrogen-ion concentration was equal to the value on the label (

[\ce{H+}] = c

). (1.1) Give the formulae of four acids that could have been in the solution if the pH changed by one unit after a tenfold dilution. (1.2) Could it be possible that the dilute solution contained sulfuric acid (

pK_{a2} = 1.99

)? Answer Yes or No; if yes, calculate or estimate the pH. (1.3) Could it be possible that the solution contained acetic acid (

pK_a = 4.76

)? Answer Yes or No; if yes, calculate or estimate the pH. (1.4) Could it be possible that the solution contained EDTA (ethylenediaminetetraacetic acid;

pK_{a1} = 1.70

pK_{a2} = 2.60

pK_{a3} = 6.30

pK_{a4} = 10.60

)? Answer Yes or No; if yes, calculate the concentration.

Step 1 of 4: Strong monoprotic acids

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\ce{HCl},\ \ce{HBr},\ \ce{HI},\ \ce{HNO3}\ (\text{or}\ \ce{HClO4}) \;\Rightarrow\; \mathrm{pH} = -\log c \;\rightarrow\; -\log(c/10) = \mathrm{pH} + 1

Analysis

Any univalent strong acid ( $\ce{HCl, HBr, HI, HNO3, HClO4}$ ) is completely dissociated, so $[\ce{H+}] = c$ and a 10-fold dilution lowers $c$ by a factor of 10, increasing pH by exactly 1 unit. $\ce{HF}$ is weak and does not qualify.