## Quick Answer

To calculate the number of moles of ions in milligrams (mg) of a compound, you need to know the molar mass of the compound. For ionic compounds like nitric oxide (NO3 2), the molar mass can be calculated by summing the atomic masses of each element multiplied by the number of atoms of that element in the formula.

For NO3 2, there are:

– 1 nitrogen atom (atomic mass 14.01 g/mol)

– 3 oxygen atoms (atomic mass 16.00 g/mol)

So the molar mass of NO3 2 is:

(1 x 14.01 g/mol) + (3 x 16.00 g/mol) = 62.01 g/mol

Knowing the molar mass allows us to use the formula:

moles = mass (g) / molar mass (g/mol)

So if we are given a mass in mg, we first convert it to grams before plugging into the formula. For example, if we had 100 mg of NO3 2:

100 mg = 0.1 g

moles of NO3 2 = 0.1 g / 62.01 g/mol = 0.0016 mol

Since NO3 2 dissociates into 2 moles of ions per formula unit, the number of moles of ions is:

0.0016 mol NO3 2 x (2 mol ions/1 mol NO3 2) = 0.0032 mol ions

So 100 mg of NO3 2 contains 0.0032 moles of ions. The general process can be applied to any ionic compound to determine the mole amount from a given mass.

In chemistry, the mole is a fundamental unit used to quantify the amount of a substance. The mole allows us to easily convert between the mass of a substance and the number of individual elements or molecules comprising that substance. This conversion is extremely useful across many chemical calculations and stoichiometric relationships.

One key use of the mole concept is determining the number of ions present in an ionic compound from a known mass. Ionic compounds like salts dissolve into their constituent cations and anions, which then exist as independent charged particles or ions in solution. Knowing the mole amount allows us to determine the number of dissociated ions in the solution.

In this article, we will provide a detailed walkthrough of how to calculate the moles of ions present in a given mass of an ionic compound. We will look specifically at the example of nitric acid (NO3 2), but the process can be applied generally to any ionic compound.

## Molar Mass

The first step in relating mass to moles of ions is determining the molar mass of the ionic compound. Molar mass is defined as the mass in grams of one mole of a substance. For ionic compounds, the molar mass can be easily calculated by summing the atomic masses of the constituent atoms, taking into account the numbers of each atom in the molecular formula.

The atomic masses used are relative atomic masses, which are weighted averages of the isotopic masses for each element. Relative atomic mass values can be found on the periodic table.

For nitric oxide (NO3 2), the molar mass is calculated as follows:

Element | Atomic Mass (g/mol) | # of atoms | Mass contribution |

Nitrogen (N) | 14.01 | 1 | 14.01 g/mol |

Oxygen (O) | 16.00 | 3 | 16.00 x 3 = 48.00 g/mol |

Total | 14.01 + 48.00 = 62.01 g/mol |

So the molar mass of NO3 2 is 62.01 g/mol. This molar mass is then used to interconvert between mass in grams and moles of the compound.

## Converting Mass to Moles

Once the molar mass of the ionic compound is known, we can use it to calculate the number of moles present in any given mass following a simple mathematical relationship:

Moles = Mass (g) / Molar Mass (g/mol)

This formula is applied by plugging in the known mass of the compound and the molar mass calculated earlier. Note that the mass must be in units of grams, even if it is provided in another unit like milligrams or kilograms. Appropriate unit conversions must be carried out before using the mass in the formula.

As an example, say we are given a mass of 100 mg NO3 2. We would carry out the following calculation:

Known:

Mass NO3 2 = 100 mg

Molar Mass NO3 2 = 62.01 g/mol (calculated earlier)

Conversion: 100 mg = 0.1 g (converting mg to g)

Moles NO3 2 = 0.1 g / 62.01 g/mol = 0.0016 mol

So if we started with 100 mg of NO3 2, it corresponds to 0.0016 moles based on the molar mass.

This calculation can be extended to any ionic compound, allowing us to determine the mole amount from the mass. The only requirement is knowing the molar mass, either from calculation or reference sources. The same formula applies in each case.

## Relating Moles of Compound to Ions

Ionic compounds like NO3 2 dissociate completely when dissolved, forming cations and anions corresponding to the component elements. So the final step is to relate the moles of the compound to the moles of ions produced upon dissociation.

This requires us to understand the stoichiometric ratio between the compound and the ions. For a generic ionic compound MAx consisting of cation M and anion A:

– 1 mole of MAx produces x moles of M+ cations

– 1 mole of MAx produces x moles of A- anions

Where x is the ratio coefficient in the formula. For NO3 2:

– 1 mole of NO3 2 produces 1 mole of N+ cations

– 1 mole of NO3 2 produces 2 moles of O2- anions

So using the mole amount of NO3 2 calculated earlier:

0.0016 mol NO3 2 x (1 mol N+ / 1 mol NO3 2) = 0.0016 mol N+ cations

0.0016 mol NO3 2 x (2 mol O2- / 1 mol NO3 2) = 0.0032 mol O2- anions

The total moles of ions is therefore the sum of the individual cation and anion amounts:

0.0016 mol N+ + 0.0032 mol O2- = 0.0032 mol total ions

This demonstrates that 100 mg of NO3 2 dissociates to produce 0.0032 moles of ions in solution.

The same process can be applied to any ionic compound by accounting for the stoichiometric ratios. Combined with the molar mass calculation, this provides a complete method to determine moles of ions from a mass of compound.

## Example Calculations

Let’s go through a few more example calculations to demonstrate determining ion amounts from different masses of ionic compounds:

### Example 1

Calculate the moles of ions in 75 mg of calcium chloride (CaCl2)

**Solution**

– Molar mass CaCl2 = 40.08 g/mol

– 75 mg CaCl2 = 0.075 g

– Moles CaCl2 = 0.075 g / 40.08 g/mol = 0.00187 mol

– 1 mol CaCl2 produces 1 mol Ca2+ cations

– 1 mol CaCl2 produces 2 mol Cl- anions

– So:

– 0.00187 mol Ca2+

– 0.00374 mol Cl-

– Total ions = 0.00187 + 0.00374 = 0.00561 mol

Therefore, 75 mg of CaCl2 contains 0.00561 moles of ions.

### Example 2

Calculate the moles of ions in 250 mg of magnesium sulfate (MgSO4)

**Solution**

– Molar mass MgSO4 = 120.37 g/mol

– 250 mg MgSO4 = 0.250 g

– Moles MgSO4 = 0.250 g / 120.37 g/mol = 0.00208 mol

– 1 mol MgSO4 produces 1 mol Mg2+ cations

– 1 mol MgSO4 produces 1 mol SO42- anions

– So:

– 0.00208 mol Mg2+

– 0.00208 mol SO42-

– Total ions = 0.00208 + 0.00208 = 0.00416 mol

Therefore, 250 mg of MgSO4 contains 0.00416 moles of ions.

### Example 3

Calculate the moles of ions in 125 mg of sodium carbonate (Na2CO3)

**Solution**

– Molar mass Na2CO3 = 105.99 g/mol

– 125 mg Na2CO3 = 0.125 g

– Moles Na2CO3 = 0.125 g / 105.99 g/mol = 0.00118 mol

– 1 mol Na2CO3 produces 2 mol Na+ cations

– 1 mol Na2CO3 produces 1 mol CO32- anions

– So:

– 0.00118 mol x (2 mol Na+/1 mol Na2CO3) = 0.00236 mol Na+

– 0.00118 mol x (1 mol CO32-/1 mol Na2CO3) = 0.00118 mol CO32-

– Total ions = 0.00236 + 0.00118 = 0.00354 mol

Therefore, 125 mg of Na2CO3 contains 0.00354 moles of ions.

## Conclusion

Determining the number of moles of ions from a mass of an ionic compound involves:

1. Calculating the molar mass of the compound from the atomic masses

2. Converting the given mass to moles using the molar mass

3. Accounting for the stoichiometric ratios to get moles of ions

This step-by-step process can be applied to any ionic compound, allowing the mole amount of dissociated ions to be determined from any provided mass. Mastering these calculations is key for quantitatively analyzing ionic reactions and solutions.