Question

Write the charge balance for a solution containing ${\mathrm{H}}^{+},{\mathrm{OH}}^{-},{\mathrm{Ca}}^{2+},{\mathrm{HCO}}_3^{-},{\mathrm{CO}}_3^{2-},\mathrm{Ca}{\left({\mathrm{HCO}}_3\right)}^{+},\mathrm{Ca}{\left(\mathrm{OH}\right)}^{+},{\mathrm{K}}^{+}\mathrm{and}{\mathrm{ClO}}_4^{-}$

Short answer

The charge balance of solution is,

$\left[{\mathrm{H}}^{+}\right]+2\left[{\mathrm{Ca}}^{2+}\right]+\left[\mathrm{Ca}{\left({\mathrm{HCO}}_3\right)}^{+}\right]+\left[\mathrm{Ca}{\left(\mathrm{OH}\right)}^{+}\right]+\left[{\mathrm{K}}^{+}\right]=\left[{\mathrm{OH}}^{-}\right]+\left[{\mathrm{HCO}}_3^{-}\right]+2\left[{\mathrm{CO}}_3^{2-}\right]+\left[{\mathrm{ClO}}_4^{-}\right]$

Step-by-step solution

Definition of charge balance

The charge balance is an algebraic statement of electroneutrality: The sum of the positive charges in solution equals the sum of the negative charges in solution.

We are given,

${\mathrm{H}}^{+},{\mathrm{OH}}^{-},{\mathrm{Ca}}^{2+},{\mathrm{HCO}}_3^{-},{\mathrm{CO}}_3^{2-},\mathrm{Ca}{\left({\mathrm{HCO}}_3\right)}^{+},\mathrm{Ca}{\left(\mathrm{OH}\right)}^{+},{\mathrm{K}}^{+}\mathrm{and}{\mathrm{ClO}}_4^{-}$

Balancing the charge for given solution

We have to note that, the Solution must have zero total charge.

${\mathrm{H}}^{+},{\mathrm{OH}}^{-},{\mathrm{Ca}}^{2+},{\mathrm{HCO}}_3^{-},{\mathrm{CO}}_3^{2-},\mathrm{Ca}{\left({\mathrm{HCO}}_3\right)}^{+},\mathrm{Ca}{\left(\mathrm{OH}\right)}^{+},{\mathrm{K}}^{+}\mathrm{and}{\mathrm{ClO}}_4^{-}$

Balancing the chargefor the above solution, we get

$\left[{\mathrm{H}}^{+}\right]+2\left[{\mathrm{Ca}}^{2+}\right]+\left[\mathrm{Ca}{\left({\mathrm{HCO}}_3\right)}^{+}\right]+\left[\mathrm{Ca}{\left(\mathrm{OH}\right)}^{+}\right]+\left[{\mathrm{K}}^{+}\right]=\left[{\mathrm{OH}}^{-}\right]+\left[{\mathrm{HCO}}_3^{-}\right]+2\left[{\mathrm{CO}}_3^{2-}\right]+\left[{\mathrm{ClO}}_4^{-}\right]$

Where, the coefficient of each term in the charge balance equals the magnitude of the charge on each ion.

Therefore, the charge balance of the given solution is,

$\left[{\mathrm{H}}^{+}\right]+2\left[{\mathrm{Ca}}^{2+}\right]+\left[\mathrm{Ca}{\left({\mathrm{HCO}}_3\right)}^{+}\right]+\left[\mathrm{Ca}{\left(\mathrm{OH}\right)}^{+}\right]+\left[{\mathrm{K}}^{+}\right]=\left[{\mathrm{OH}}^{-}\right]+\left[{\mathrm{HCO}}_3^{-}\right]+2\left[{\mathrm{CO}}_3^{2-}\right]+\left[{\mathrm{ClO}}_4^{-}\right]$