Problem 38 - Chemistry for Allied Health

Question

How many moles of hydrogen are in \(2.5\) moles of \(\mathrm{H}_{2} \mathrm{O}\) ? How many moles of oxygen?

Step-by-Step Solution

Answer

5 moles of hydrogen and 2.5 moles of oxygen.

Step 1: Understand the composition of water

Water, denoted by the chemical formula \(\mathrm{H}_{2} \mathrm{O}\), consists of two hydrogen atoms and one oxygen atom per molecule. This means in every mole of water, there are \(2\) moles of hydrogen atoms and \(1\) mole of oxygen atoms.

Step 2: Calculate moles of hydrogen

We have \(2.5\) moles of water. Since each mole of water contains \(2\) moles of hydrogen, we calculate the moles of hydrogen by multiplying \(2.5\) moles of water by \(2\):\[2.5 \text{ moles H}_2\text{O} \times 2 \text{ moles H/mole H}_2\text{O} = 5 \text{ moles H}\]

Step 3: Calculate moles of oxygen

For every mole of water, there is \(1\) mole of oxygen. Therefore, \(2.5\) moles of water contain \(2.5\) moles of oxygen, calculated as:\[2.5 \text{ moles H}_2\text{O} \times 1 \text{ mole O/mole H}_2\text{O} = 2.5 \text{ moles O}\]

Key Concepts

Chemical Composition of Water

Water's chemical structure is expressed by the formula \(\mathrm{H}_{2}\mathrm{O}\). This notation indicates the elements and quantities present within each water molecule.
In every water molecule, there are:

• Two hydrogen atoms
• One oxygen atom

This is crucial for understanding the proportions of each element in water. These proportions mean that for every mole of water, two moles of hydrogen atoms exist, alongside one mole of oxygen atoms.
Knowing this allows for the calculation of the number of moles of each element present when dealing with a given amount of water.
This understanding lays the groundwork for determining the quantities of hydrogen and oxygen in chemical reactions involving water.

Moles of Hydrogen

When dealing with water, it is essential to recognize the quantity of hydrogen present. In each mole of \(\mathrm{H}_{2}\mathrm{O}\), there are 2 moles of hydrogen atoms. Therefore, the moles of hydrogen can be calculated by multiplying the moles of water by two.
For example, if you have \(2.5\) moles of water, the number of hydrogen moles can be quickly calculated:

• Given: \(2.5\) moles of \(\mathrm{H}_{2}\mathrm{O}\)
• Each mole of \(\mathrm{H}_{2}\mathrm{O}\) contains 2 moles of hydrogen

This means: \[2.5 \text{ moles of } \mathrm{H}_2\mathrm{O} \times 2 \text{ moles of H/mole H}_2\mathrm{O} = 5 \text{ moles of H}\]
Understanding this relationship is key in mastering the calculations involved in chemical equations that include water.

Moles of Oxygen

Similar to hydrogen, every mole of \(\mathrm{H}_{2}\mathrm{O}\) contains a fixed amount of oxygen atoms. Each mole of water always contains one mole of oxygen atoms.
This makes calculating the moles of oxygen straightforward. With \(2.5\) moles of water, the calculation for oxygen is as follows:

• Each mole of \(\mathrm{H}_{2}\mathrm{O}\) has 1 mole of oxygen
• Given water: 2.5 moles

The calculation is:\[2.5 \text{ moles of } \mathrm{H}_2\mathrm{O} \times 1 \text{ mole of O/mole } \mathrm{H}_2\mathrm{O} = 2.5 \text{ moles of O}\]
Recognizing the fixed ratio of moles of oxygen to moles of water is instrumental in solving chemical balance equations and in various applications, such as in stoichiometry and reaction predictions.