Chapter 17, Problem 70A

Show that there are 16 grams of oxygen in 18 grams of water.

To determine

To show: 16 grams of oxygen in present in 18 grams of water.

Explanation of Solution

Given:

Formula of water = ${\text{H}}_2\text{O}$

Number of hydrogen atoms = 2

Number of Oxygen atoms = 1

Atomic mass of 1 Hydrogen atom = 1 g/mol

Atomic mass of 1 Oxygen atom = 16 g/mol

Formula used:

  $n=\frac{M}{m_{\text{w}}}$(1)

Here, $n$ is the number of water molecules in $M$ grams of water.

Calculation:

Formula of water = ${\text{H}}_2\text{O}$

Number of hydrogen atoms = 2

Number of Oxygen atoms = 1

Atomic mass of 1 Hydrogen atom = 1 g/mol

Atomic mass of 1 Oxygen atom = 16 g/mol

  $\begin{array}{l}{m}_{\text{H}}=1\text{unit}\hfill \\ m_{\text{O}}=16\text{unit}\hfill \end{array}$

  $m_H$ is the mass of one hydrogen atom

  $m_O$ is the mass of one oxygen atom.

Now ,the mass of one water molecule $\left(m_{\text{w}}\right)$

  $\begin{array}{c}{m}_{\text{w}}=2m_{\text{H}}+m_{\text{o}}\\ =2(1\text{unit})+(16\text{unit})\\ =18\text{unit}\end{array}$ .

Now determine the number of water molecules in 18g of water by dividing the mass of water by mass of one water molecule.

Substitute 18 grams for $M$ and 18 unit for $m_{\text{w}}$ in equation (1).

  $n=\frac{(18\text{grams})}{(18\text{unit})}$

  $=1$

Since there is one oxygen atom in each water molecule, hence the number of oxygen atoms in 18 grams of water will also be $n$ . Find out mass of oxygen atoms $\left(M_{\text{o}}\right)$ in 18 grams of water by multiplying $n$ by $m_{\text{o}}$ .

  $M_{\text{o}}=n{m}_{\text{o}}$

Substitute 1 grams/ unit for $n$ and 16 unit for $m_{\text{o}}$ in the equation $M_{\text{o}}=n\times m_{\text{O}}$ .

  $M_{\text{o}}=(1\text{grams/unit})(16\text{unit})$

  $=16\text{grams}$

Conclusion:

Hence, there will be 16 grams of oxygen in 18 grams of water.