Question

A solution to replace potassium loss contains \(40 . \mathrm{mEq} / \mathrm{L}\) each of \(\mathrm{K}^{+}\) and \(\mathrm{Cl}^{-}\). How many moles each of \(\mathrm{K}^{+}\) and \(\mathrm{Cl}^{-}\) are in \(1.5 \mathrm{~L}\) of the solution?

Short answer

There are 0.06 moles each of \(\text{K}^+\) and \(\text{Cl}^-\) in 1.5 L of the solution.

Step-by-step solution

Understand the Given Information

The solution contains 40 mEq/L of \(\text{K}^+\) and 40 mEq/L of \(\text{Cl}^-\). The volume of the solution is 1.5 L.

Convert mEq to Equivalents

Since 1 mEq = 0.001 Eq, we can convert the concentration from mEq/L to Eq/L. Therefore, 40 mEq/L is equivalent to 0.04 Eq/L.

Calculate Equivalents in Given Volume

To find the total number of equivalents for \(\text{K}^+\) and \(\text{Cl}^-\) in 1.5 L of the solution, multiply the concentration in Eq/L by the volume in liters. \[0.04 \text{ Eq/L} \times 1.5 \text{ L} = 0.06 \text{ Eq}\]

Convert Equivalents to Moles

Since 1 Eq = 1 mole of charge for \(\text{K}^+\) and \(\text{Cl}^-\), the total equivalents calculated in Step 3 also represent the moles. Therefore, there are 0.06 moles each of \(\text{K}^+\) and \(\text{Cl}^-\).

Key concepts

milliequivalents

Milliequivalents (mEq) are a unit of measurement often used in chemistry, especially in the context of solutions. Milliequivalents represent one-thousandth of an equivalent (Eq), which measures the amount of a substance in relation to its chemical reactivity. When dealing with ions, such as \(\text{K}^+\) and \(\text{Cl}^-\), each milliequivalent reflects the charge carried by these ions.
For instance, if a solution has a concentration of 40 mEq/L, it indicates that there are 40 milliequivalents of the ion per liter of solution. This is particularly useful in medical and laboratory settings for precise dosing and reactions.
Understanding how to convert between milliequivalents and equivalents is crucial. Since 1 mEq is equal to 0.001 Eq, you can easily switch between these units.

moles

Moles are a fundamental unit in chemistry representing a fixed number of molecules or atoms, based on Avogadro's number, which is approximately \[6.022 \times 10^{23} \] entities per mole. This allows for easy quantification and comparison in chemical reactions.
In the given exercise, after converting milliequivalents to equivalents, we determine the number of moles from the equivalents. Since the relationship between equivalents and moles is direct — 1 Eq is equivalent to 1 mole of charge for ions like \(\text{K}^+\) and \(\text{Cl}^-\) — the conversion becomes straightforward.
For example, if you have 0.06 Eq of \(\text{K}^+\), it translates directly to 0.06 moles of \(\text{K}^+\). The same applies to \(\text{Cl}^-\).

solution concentration

Solution concentration refers to the amount of solute present in a given volume of solvent. It is usually expressed in various units like mol/L (molarity), mEq/L (milliequivalents per liter), or wt% (weight percent). Here, the concentration given is 40 mEq/L of both \(\text{K}^+\) and \(\text{Cl}^-\).
When tackling problems involving solution concentration, you typically need to:

• Understand the concentration in the units provided.
• Convert units if necessary.
• Use the volume of the solution to find the total amount of solute.

For example, knowing the concentration in mEq/L and the volume in liters allows us to find the total contents of the solution. In this case, multiplying the concentration (40 mEq/L) by the volume (1.5 L) gives the total milliequivalents, which we then convert to equivalents and eventually to moles.

equivalent conversion

Equivalent conversion is a fundamental concept when working with electrolyte solutions. It involves three main steps:

• Converting concentration units from milliequivalents (mEq) to equivalents (Eq).
• Calculating the total equivalents in the solution based on its volume.
• Relating equivalents to moles, where 1 Eq corresponds to 1 mole of charge for the given ion.

In our example, we start with a concentration of 40 mEq/L and convert it to 0.04 Eq/L (since 1 mEq = 0.001 Eq). We multiply this by the solution volume (1.5 L) to get 0.06 Eq, which directly translates to 0.06 moles for both \(\text{K}^+\) and \(\text{Cl}^-\).
Mastering these conversions is essential for accurately determining quantities in chemical and biological processes.