Question

A solution contains \(40 . \mathrm{mEq} / \mathrm{L}\) of \(\mathrm{Cl}^{-}\) and \(15 \mathrm{mEq} / \mathrm{L}\) of \(\mathrm{HPO}_{4}{ }^{2-}\). If \(\mathrm{Na}^{+}\) is the only cation in the solution, what is the Na concentration, in milliequivalents per liter?

Short answer

The Na concentration is 55 mEq/L.

Step-by-step solution

- Identify the Total Equivalent Anions

Begin by determining the total concentration of anions in the solution. Sum the concentrations of \(Cl^{-}\) and \(HPO_{4}^{2-}\) which are given as \(40 \ \text{mEq/L}\) and \(15 \ \text{mEq/L}\) respectively.

- Calculate the Total Anion Concentration

Add the two concentrations together: \[40 \ \text{mEq/L} + 15 \ \text{mEq/L} = 55 \ \text{mEq/L}\]

- Equalize With the Cation Concentration

Since \(Na^+\) is the only cation and the solution must be electrically neutral, the total concentration of \(Na^+\) must be equal to the total concentration of anions. Therefore, \( [Na^{+}] = 55 \ \text{mEq/L} \).

Key concepts

Equivalent Anions

In chemistry, anions are negatively charged ions. Equivalent anions refer to the total amount of these anions in a solution, counted in milliequivalents per liter (mEq/L). To find this in a given solution, sum the concentrations of all anions present. For example, if you have 40 mEq/L of chloride ions (oindent Cl^{-}) and 15 mEq/L of hydrogen phosphate ions (oindent HPO_{4}^{2-}), you add them together to find the total equivalent anions: oindent 40 oindent mEq/L + 15 oindent mEq/L = 55 oindent mEq/L. This tells you that the solution has 55 milliequivalents per liter of negatively charged ions.

Cation Concentration

Cations are positively charged ions. In many solutions, knowing the total equivalent anions helps determine the cation concentration needed to maintain electrical neutrality. For instance, if the solution must balance a total of 55 mEq/L of anions, and sodium (oindent Na^{+}) is the only cation present, then the concentration of sodium must also be 55 mEq/L. This equal balance ensures the solution remains electrically neutral.

Milliequivalents per Liter

Milliequivalents per liter (mEq/L) is a unit used to express the concentration of ions in a solution. One milliequivalent is one-thousandth (1/1000) of an equivalent, and it reflects the number of charge units (whether positive or negative) provided by the ions in one liter of solution. For instance, 40 mEq/L of oindent Cl^{-} means 40 milliequivalents of chloride ions are present in each liter of solution. This unit is particularly useful because it directly correlates to the ion's ability to balance charges in a solution.

Electrical Neutrality

Electrical neutrality means the total positive charge in the solution equals the total negative charge. This balance is essential in solutions to prevent electrochemical imbalances. For example, in a solution with 55 mEq/L of anions (negative ions), the cations (positive ions) must also total 55 mEq/L. Since sodium (oindent Na^{+}) is the only cation in our exercise, its concentration must match the total anions to uphold the neutrality. Thus, the oindent Na^{+} concentration would be 55 mEq/L, ensuring that the solution remains balanced.