Sure, let’s go through the steps to find the percent composition of carbon (C) in the compound step by step.
1. Identify the Masses of Each Element in the Compound:
- Calcium (Ca): 40.08 g
- Carbon (C): 48.04 g
- Hydrogen (H): 6.06 g
- Oxygen (O): 64.00 g
2. Calculate the Total Mass of the Compound:
To find the total mass of the compound, we sum the masses of all the elements present in the compound.
[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]\[
\text{Total mass} = 40.08\ \text{g} + 48.04\ \text{g} + 6.06\ \text{g} + 64.00\ \text{g} = 158.18\ \text{g}
\][/tex]
3. Calculate the Percent Composition of Carbon (C):
The percent composition of an element in a compound is calculated using the formula:
[tex]\[
\%\ \text{composition of C} = \left( \frac{\text{mass of C}}{\text{total mass of compound}} \right) \times 100\%
\][/tex]
Plug in the known values:
[tex]\[
\%\ \text{composition of C} = \left( \frac{48.04\ \text{g}}{158.18\ \text{g}} \right) \times 100\%
\][/tex]
4. Simplify and Calculate:
[tex]\[
\%\ \text{composition of C} = \left( \frac{48.04}{158.18} \right) \times 100\%
\][/tex]
[tex]\[
\%\ \text{composition of C} \approx 30.37\%
\][/tex]
So, the percent composition of carbon (C) in the compound [tex]\( Ca \left( C_2H_3O_2 \right)_2 \)[/tex] is approximately [tex]\( 30.37\% \)[/tex].
