To calculate the volume of oxygen gas liberated from the decomposition of hydrogen peroxide, follow these detailed steps:
1. Volume Conversion:
The volume of the hydrogen peroxide solution is given as 25.0 cm³. To work with the units in molarity (mol/dm³), we need to convert this volume to dm³.
- We know that [tex]\(1 dm ^3 = 1000 cm^3 \)[/tex].
- Therefore, [tex]\(25.0 cm^3\)[/tex] is converted to dm³ by dividing by 1000:
[tex]\[
25.0 cm^3 = \frac{25.0}{1000} \, dm^3 = 0.025 \, dm^3
\][/tex]
2. Calculate Moles of H₂O₂:
The concentration of the hydrogen peroxide solution is [tex]\(0.50 mol/dm³\)[/tex].
- To find the moles of hydrogen peroxide [tex]\(H₂O₂\)[/tex] in our volume [tex]\(0.025 dm³\)[/tex], we use:
[tex]\[
\text{Moles of H}_2\text{O}_2 = \text{concentration} \times \text{volume} = 0.50 mol/dm^3 \times 0.025 dm^3 = 0.0125 \, \text{moles}
\][/tex]
3. Calculate Moles of O₂:
The chemical equation for the decomposition shows that [tex]\(2\)[/tex] moles of hydrogen peroxide produce [tex]\(1\)[/tex] mole of oxygen gas:
[tex]\[
2 H₂O₂ \rightarrow 2 H₂O + O₂
\][/tex]
- Therefore, for every [tex]\(2\)[/tex] moles of [tex]\(H₂O₂\)[/tex], [tex]\(1\)[/tex] mole of [tex]\(O₂\)[/tex] is produced. Hence, for [tex]\(0.0125\)[/tex] moles of [tex]\(H₂O₂\)[/tex]:
[tex]\[
\text{Moles of } O₂ = \frac{0.0125 \, \text{moles of } H₂O₂}{2} = 0.00625 \, \text{moles of } O₂
\][/tex]
4. Calculate Volume of O₂:
At standard temperature and pressure (s.t.p.), [tex]\(1\)[/tex] mole of any gas occupies [tex]\(22.4 dm³\)[/tex].
- To find the volume of [tex]\(0.00625\)[/tex] moles of oxygen gas:
[tex]\[
\text{Volume of } O₂ = 0.00625 \, \text{moles} \times 22.4 \, dm^3/mol = 0.14 \, dm^3
\][/tex]
So, the volume of oxygen gas liberated at s.t.p. from [tex]\(25.0 cm^3\)[/tex] of a [tex]\(0.50 mol/dm³\)[/tex] hydrogen peroxide solution is:
[tex]\[
0.14 \, dm^3
\][/tex]
