To determine the concentration of [tex]\( H_2(g) \)[/tex] in parts per million (ppm) in a solution that contains [tex]\( 0.0001 \, \text{g} \)[/tex] of [tex]\( H_2(g) \)[/tex] dissolved in [tex]\( 100.0 \, \text{g} \)[/tex] of [tex]\( H_2O(l) \)[/tex], follow these steps:
1. Identify the masses involved:
- Mass of [tex]\( H_2(g) \)[/tex]: [tex]\( 0.0001 \, \text{g} \)[/tex]
- Mass of [tex]\( H_2O(l) \)[/tex]: [tex]\( 100.0 \, \text{g} \)[/tex]
2. Understand the definition of ppm:
Parts per million (ppm) is calculated as the mass of the solute divided by the mass of the solution, multiplied by [tex]\( 1{,}000{,}000 \)[/tex].
3. Set up the concentration formula:
[tex]\[
\text{Concentration (ppm)} = \left( \frac{\text{Mass of } H_2(g)}{\text{Mass of } H_2O(l)} \right) \times 1{,}000{,}000
\][/tex]
4. Plug in the given values:
[tex]\[
\text{Concentration (ppm)} = \left( \frac{0.0001 \, \text{g}}{100.0 \, \text{g}} \right) \times 1{,}000{,}000
\][/tex]
5. Carry out the division:
[tex]\[
\frac{0.0001 \, \text{g}}{100.0 \, \text{g}} = 1 \times 10^{-6}
\][/tex]
6. Multiply by [tex]\( 1{,}000{,}000 \)[/tex] to convert to ppm:
[tex]\[
1 \times 10^{-6} \times 1{,}000{,}000 = 1
\][/tex]
Therefore, the concentration of [tex]\( H_2(g) \)[/tex] in the solution is [tex]\( 1 \)[/tex] ppm.
The correct answer is:
A. [tex]\( 1 \, \text{ppm} \)[/tex]
