To determine the percent composition of oxygen in the compound [tex]\( \text{Ca(C}_2\text{H}_3\text{O}_2)_2 \)[/tex], we need to follow these steps:
1. Compute the total mass of the compound:
We have the following masses for each element in the compound:
- Mass of Calcium (Ca): [tex]\( 40.08 \, \text{g} \)[/tex]
- Mass of Carbon (C): [tex]\( 48.04 \, \text{g} \)[/tex]
- Mass of Hydrogen (H): [tex]\( 6.06 \, \text{g} \)[/tex]
- Mass of Oxygen (O): [tex]\( 64.00 \, \text{g} \)[/tex]
The first step is to calculate the total mass of the compound by summing up the masses of all elements:
[tex]\[
\text{Total mass} = \text{Mass of Ca} + \text{Mass of C} + \text{Mass of H} + \text{Mass of O}
\][/tex]
Substituting the given values:
[tex]\[
\text{Total mass} = 40.08 \, \text{g} + 48.04 \, \text{g} + 6.06 \, \text{g} + 64.00 \, \text{g}
\][/tex]
[tex]\[
\text{Total mass} = 158.18 \, \text{g}
\][/tex]
2. Calculate the percent composition of oxygen:
The percent composition of an element in a compound is calculated using the formula:
[tex]\[
\text{Percent composition of an element} = \left( \frac{\text{Mass of the element}}{\text{Total mass of the compound}} \right) \times 100
\][/tex]
Applying this formula for oxygen:
[tex]\[
\text{Percent composition of O} = \left( \frac{\text{Mass of O}}{\text{Total mass}} \right) \times 100
\][/tex]
Substituting the given mass of oxygen and the calculated total mass:
[tex]\[
\text{Percent composition of O} = \left( \frac{64.00 \, \text{g}}{158.18 \, \text{g}} \right) \times 100
\][/tex]
[tex]\[
\text{Percent composition of O} \approx 40.460235175116956 \%
\][/tex]
Therefore, the percent composition of oxygen in the compound [tex]\( \text{Ca(C}_2\text{H}_3\text{O}_2)_2 \)[/tex] is approximately [tex]\( 40.46\% \)[/tex].
