Question

How many moles of magnesium phosphate, \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) will contain \(0.25\) mole of oxygen atoms? (a) \(0.02\) (b) \(3.125 \times 10^{-2}\) (c) \(1.25 \times 10^{-2}\) (d) \(2.5 \times 10^{-2}\)

Short answer

The answer is (b) \(3.125 \times 10^{-2}\) moles.

Step-by-step solution

Understand the Compound

Magnesium phosphate, represented by \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\), consists of magnesium, phosphorus, and oxygen atoms. Each formula unit contains 2 phosphate ions (\(\mathrm{PO}_4\)).

Count Total Oxygen Atoms per Molecule

Each phosphate ion \((\mathrm{PO}_4)\) contains 4 oxygen atoms. Since there are 2 \((\mathrm{PO}_4)\) ions in \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\), there are \(2 \times 4 = 8\) oxygen atoms in one formula unit of \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\).

Relate Moles of Oxygen to Moles of Compound

If 1 mole of \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\) provides 8 moles of oxygen, then the number of moles of \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\) needed for 0.25 moles of oxygen atoms is calculated using a proportion: \[\text{Number of moles of } \mathrm{Mg}_3(\mathrm{PO}_4)_2 = \frac{0.25}{8} = 0.03125\text{ moles}\]

Convert to Scientific Notation

Write the result in scientific notation: \[0.03125 = 3.125 \times 10^{-2}\] moles of \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\).

Verify Against Options

Compare the calculated result with the given options. The answer \(3.125 \times 10^{-2}\) matches option (b).

Key concepts

Magnesium Phosphate

Magnesium phosphate, with its chemical formula \( \mathrm{Mg}_3(\mathrm{PO}_4)_2 \), is a compound made up of magnesium, phosphorus, and oxygen atoms. It's an integral part of the chemistry world due to its ability to combine with various elements.

In magnesium phosphate, you come across three magnesium atoms for every pair of phosphate ions. Phosphate ions are themselves made of phosphorus and oxygen, with each ion carrying four oxygen atoms. As a result, magnesium phosphate holds a total of eight oxygen atoms in its formula unit. This specific arrangement plays a crucial role during chemical reactions and conversions, especially when you calculate how many moles of a compound equals a specific number of atoms, such as in the exercise you've encountered.

Chemical Formula

A chemical formula is a simple way of representing a chemical compound using element symbols and numerical subscripts. In the case of magnesium phosphate, the formula is \( \mathrm{Mg}_3(\mathrm{PO}_4)_2 \).

This formula tells us several things:

• There are three magnesium atoms, represented by \( \mathrm{Mg}_3 \), required for the compound.
• The \( (\mathrm{PO}_4)_2 \) indicates two phosphate ions, each consisting of one phosphorus atom and four oxygen atoms.
• The formula unit thus includes eight oxygen atoms and two phosphorus atoms in its entirety.

The arrangement and subscripts found in chemical formulas guide chemists to understand the exact composition of a compound. They also assist in performing calculations like determining mole ratios in reactions or decomposing compounds into their elemental forms.

Scientific Notation

Scientific notation is a method to express very large or very small numbers concisely using powers of ten. It becomes especially useful in chemistry where you may frequently encounter such numbers.

For instance, in the solved exercise, the number of moles of \( \mathrm{Mg}_3(\mathrm{PO}_4)_2 \) required to provide 0.25 moles of oxygen atoms was calculated as 0.03125 moles. To express this efficiently, it's written as \[ 3.125 \times 10^{-2} \]. This notation helps make calculations more manageable and presentation of data succinct.

Here's how to do it:

• Move the decimal point to create a new number from 1 up to 10. For 0.03125, the decimal moves two places to the right, giving 3.125.
• Count how many places you moved the decimal. This becomes the power of ten. In our case, two places make an exponent of \( -2 \).

This way of writing numbers is vital for simplifying calculations in chemistry, physics, and various other scientific fields.