Chapter 17, Problem 71A

Show that there are 4 grams of hydrogen in 16 grams of methane gas. (The chemical formula for methane is $C{H}_4$.)

To determine

To show: The quantity of hydrogen in 16 gm of methane gas is 4 gm.

Explanation of Solution

Given:

Formula of methane gas = ${\text{CH}}_4$

Number of Hydrogen atoms = 4

Number of Carbon atoms = 1

Atomic mass of 1 Hydrogen atom = 1 g/mol

Atomic mass of 1 Carbon atom = 12 g/mol

Formula used:

  $n=\frac{M}{m_{\text{M}}}$

Here, $n$ is number of methane molecules in $M$ grams of methane gas.

Calculation:

Formula of methane gas = ${\text{CH}}_4$

Number of Hydrogen atoms = 4

Number of Carbon atoms = 1

Atomic mass of 1 Hydrogen atom = 1 g/mol

Atomic mass of 1 Carbon atom = 12 g/mol

  $\begin{array}{l}{m}_{\text{H}}=1\text{unit}\hfill \\ m_{\text{C}}=12\text{unit}\hfill \end{array}$

Here, $m_{\text{H}}$ is mass of one hydrogen and $m_{\text{C}}$ represents mass of one carbon atom.

Find the mass of one methane molecule $\left(m_{\text{M}}\right)$

  $\begin{array}{c}{m}_{\text{M}}=4m_{\text{H}}+m_{\text{C}}\\ =4(1\text{unit})+(12\text{unit})\\ =16\text{unit}\end{array}$

Determine the number of methane molecules in $16\text{g}$ of methane gas by dividing total mass of gas by mass of one methane molecule.

Substitute 16 grams for $M$ and 16 units for $m_{\text{M}}$ in equation (1).

  $n=\frac{16\text{grams}}{16\text{units}}$

  $=1$ gram/unit

Since there are four hydrogen atoms in each methane molecule, hence number of hydrogen atoms in 16 grams of methane gas will be $4n$ .

Calculate the mass of hydrogen atoms $\left(M_{\text{H}}\right)$ in 16 grams of methane by multiplying $4n$ by $m_{\text{H}}$ .

  $M_{\text{H}}=4n\times m_{\text{H}}$

Substitute $\frac{1\text{gram}}{\text{unit}}$ for $n$ and 1 unit for $m_{\text{H}}$ .

  $M_{\text{H}}=4\left(\frac{1\text{gram}}{\text{unit}}\right)\left(1\text{unit}\right)$

  $=4\text{grams}$

Conclusion:

Hence, there is $4\text{grams}$ of hydrogen in 16 grams of methane gas.