0
$\begingroup$

Lake water contains dissolved sodium carbonate and sodium hydrogen carbonate. The following equilibrium exists: \begin{align} \ce{HCO3- &<=> H+ + CO3^{2-}}& \frac{\ce{[CO3^{2-}]}}{\ce{[HCO3-]}} &= 0.958 \end{align} When $\pu{10 cm^3}$ of lake water were titrated with $\pu{0.2 mol/dm^3}$ $\ce{HCl}$, $\pu{22 cm^3}$ of acid were required to neutralise all the carbonate and hydrogen carbonate ions according to the following equations: \begin{align} \ce{H+ + HCO3- &-> H2O + CO2}\\ \ce{2H+ + CO3^{2-} &-> H2O + CO2}\\ \end{align} Calculate the total amount of substance of acid used, and thus, by using the ratio quoted, calculate $\ce{[CO3^{2-}]}$ and $\ce{[HCO3-]}$ in the lake.

I was able to find the amount of substance of acid $\ce{HCl}$, which is $\pu{4.4E-3 mol}.$ How do I go on?

$\endgroup$

closed as off-topic by Klaus-Dieter Warzecha, Wildcat, M.A.R., getafix, Todd Minehardt Oct 31 '16 at 13:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

If this question can be reworded to fit the rules in the help center, please edit the question.

1
$\begingroup$

You have correctly identified the amount of substance $\ce{HCl}$ which were necessary to neutralize all $\ce{HCO3-}$ and $\ce{CO3^2-}$ in the sample. With the given sample volume of $\pu{10 cm^3}$, we can calculate the concentration of both ions in the sample: $$ \frac{\pu{4.4E-3 mol}}{\pu{10 cm^3}} = \pu{4.4E-4 mol//cm^3} = [\ce{HCO3-}]+[\ce{CO3^{2-}}] $$

Using the given ratio of $0.958$, we can express $[\ce{CO3^{2-}}]$ in terms of $[\ce{HCO3^{-}}]$: \begin{gather} [\ce{CO3^2-}] = 0.958\times[\ce{HCO3-}]\\ \pu{4.4E-4 mol//cm^3} = [\ce{HCO3-}] + [\ce{CO3^2-}] = [\ce{HCO3-}] + 0.958\times[\ce{HCO3-}] = 1.958[\ce{HCO3-}]\\ [\ce{HCO3-}] = \pu{2.25E-4 mol//cm3} \end{gather}

We then use the calculated hydrogen carbonate concentration and the ratio to find $[\ce{CO3^2-}]$: $$[\ce{CO3^2-}] = 0.958\times[\ce{HCO3-}] = \pu{2.15E-4 mol//cm3}$$

$\endgroup$
-2
$\begingroup$

I would do it like follows: By using the ratio of 0.958 you can simply state the ratio of amount of substances. Then by using the balanced equations you can find the ratio of amount of substances of HCl required for each. Having both the ratio and total amount, you can get the the HCl for each; and then you can find the the required concentraion of those two ions from the balanced equation and total volume.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.