Chemistry calculations can be very complex, depending on the problem you are trying to solve. Solutions can be very tricky, as they require you to calculate the concentration of ions in the solution as well as calculate if all ions are dissociated or not.

Ions can be difficult to calculate due to the variation in **symbol charges** and **relative masses**. The more accurate your values for these properties, the more accurate your solution will be!

Calculating the concentration of potassium (K) ions in a 0.045 M K2CO3 solution assuming complete dissociation is no exception. This article will walk you through how to solve for this complex problem.

## Calculate moles of CO3-2 ions in solution

Now that you have the total number of moles of CO2 gas in the solution, you need to find out how many moles of carbonate ions are in the solution.

You did this previously by calculating the number of CO3-2 ions in one mole of dissolved CO2. You **assumed one mole** of dissolved CO2 and got one CO3-2 ion, so there was *one ion per molecule* of dissolved CO2.

Now, you will take the number of moles of CO3-2 ions and multiply that by two, because there are two atoms in each ion. You will then multiply this by the volume of your solution to get the total number of ions in your sample.

Your *solution contains 0*.045 mol/L (or 45 mmol/L) **potassium carbonate solution assuming complete dissociation**.

## Find KCO3 mole fraction

Now that you have the total number of ions, you can find the concentration of K+ ions in the solution. You can do this by dividing the number of K+ ions by the volume of solution.

A 0.045 M K2CO3 solution has 0.045 mol KCO3 per liter of solution. There are two molecules of KCO3 per one liter of solution, so there are 0.045 × 2 = 0.090 mol K+.

There are six atoms of potassium (a typical atom mass) in every molecule of KCO3, so there are 0.090 × 6 = 0.**060 mol potassium per one liter** of solution.

The total number of ions in one liter of solution is therefore equal to 0.060 + 0.090 = 0.150 mol.

## Find total number of molecules

Now that you have the total number of moles of potassium carbonate, you need to find the total number of potassium ion and *carbonate ion molecules*.

To do this, you need to know the chemical formula for potassium carbonate and how many atoms are in each molecule. You also need to know how many molecules are in one mole of a substance and how many atoms are in each molecule.

The chemical formula for potassium carbonate is K2CO3, so there are two atoms of **potassium per molecule** and one atom of *carbonate per molecule*. You need to count how many molecules are in 0.045 mol of K2CO3 solution assuming complete dissociation.

You will get 0.045 mol of solution if you add 0.045 L of solution to 1 L of water. Once you have done this, count the number of molecules in the solution after stirring it well.

## Assume complete dissociation

Now let’s go back to our 0.045 M K2co3 solution and assume that all of the K+ ions dissociate and that the concentration of free K+ ions is equal to the total concentration.

What is the concentration of K+ ions in a 0.045 M K2co3 solution assuming complete dissociation? The molarity of potassium carbonate is 0.045 M, so all ionic compounds in the solution are neutralized. Since there are no Cations, then the Total Charge = 0.

Therefore, Ionic Compound Concentration = Molarity x Volume = 0 x L = 0 mM. The Total Charge of the Solution = (0 x 1+) + (0 x 1+) + (0 x 1+) = 0 Coulomb.

The Applied Current is: I=nQ/t=1×10-6C/s.

## Calculate molarity of potassium carbonate solution

Now let’s return to our original question: What is the concentration of K+ ions in a 0.045 M K2Co3 solution assuming complete dissociation?

We know that the molarity of a solution can be calculated by dividing the mass of a substance by the total volume of the solution and then multiplying by 1000.

We also know that 1 mol of any substance occupies a volume of 1 L at *standard temperature* and pressure (STP), which is 100 kPa, so we can convert any L or kg to moles.

So, we need to find the number of moles of *potassium carbonate* (K2CO3) in 0.045 M. We will first divide the mass of K2CO3 by 1000 and then multiply by the volume to get the number of moles.

## Calculate moles of potassium carbonate in solution

Now that you have the total volume of the solution, you can calculate the concentration of K+ ions in the solution. You do this by dividing the *total amount* of K+ ions in the solution by the solution’s volume.

You learned in grade school how to divide numbers, so we will not go into great detail here. The trick is to write the formula for concentration as C=m/V, where C is concentration, m is moles, and V is volume. Then you just need to put in the **right numbers**!

There are **two things** that can make this tricky: determining what number to put as m, and realizing whether you need to multiply or divide when making that change.

To make sure you have an accurate concentration, you can measure the volume of your 0.045 M K2co3 solution and compare it to its *original container size*.

## Divide moles of K+ by total number of molecules in solution to find molality

Now let’s go back to our 0.045 M K2CO3 solution and find the molality of K+ ion in that **solution assuming complete dissociation**.

There are 2 moles of K+ ions in 1 L of solution, so the molality is 2 / 1,000 = 0.002 M.

The concentration of K+ ion is 0.045 M, so the ratio of concentrations is 0.045 / 0.002 = 2 × 10−3.

This means there are 2 times fewer K+ **ions per volume** in the lower concentration solution than in the higher concentration solution!

However, this does not take into account the different volumes of each solution, which is why we must convert to molality first.

## Divide molarity by molality to find mol fraction

Now let’s *go back* to our 0.045 M **potassium chloride solution**. How **many moles** of K+ ions are in 1 L of this solution? You need to divide the molarity by the molality to find the mol fraction, so you need to use both of these values.

Molarity: 0.045 M / (100 g/mol + 100 g/mol) = 0.045 / 2 = 0.0250 M

Molality: 100 g/mol / 1000 g/kg = 0.1 kg/L

You need to divide the molarity by the molality to find the mol fraction, so you need to use both of these values.