Problem: Finding the Percent Composition
The task involves calculating the percent composition of elements in a compound or mixture. The percent composition is defined as the percentage (by mass) of each element in a compound. The formula to calculate percent composition is:
\[
\text{Percent Composition} = \left( \frac{\text{Mass of Element}}{\text{Total Mass of Compound}} \right) \times 100
\]
Let's solve each example step by step.
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Example 1: Percent Composition of Red Candies
-
Total Candies: 200
-
Red Candies: 26
-
Blue Candies: 174
Step 1: Calculate the percent composition of red candies.
\[
\text{Percent Composition of Red Candies} = \left( \frac{\text{Number of Red Candies}}{\text{Total Number of Candies}} \right) \times 100
\]
\[
= \left( \frac{26}{200} \right) \times 100 = 13.0\%
\]
Step 2: Calculate the percent composition of blue candies.
\[
\text{Percent Composition of Blue Candies} = \left( \frac{\text{Number of Blue Candies}}{\text{Total Number of Candies}} \right) \times 100
\]
\[
= \left( \frac{174}{200} \right) \times 100 = 87.0\%
\]
Final Answer for Example 1:
\[
\boxed{13.0\% \text{ red}, 87.0\% \text{ blue}}
\]
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####
Example 2: Percent Composition of MgCl₂
-
Total mass of MgCl₂: 95.21 g
-
Mass of Mg: 24.31 g
-
Mass of Cl₂: 70.91 g
Step 1: Calculate the percent composition of Mg.
\[
\text{Percent Composition of Mg} = \left( \frac{\text{Mass of Mg}}{\text{Total Mass of MgCl₂}} \right) \times 100
\]
\[
= \left( \frac{24.31}{95.21} \right) \times 100 = 25.53\%
\]
Step 2: Calculate the percent composition of Cl₂.
\[
\text{Percent Composition of Cl₂} = \left( \frac{\text{Mass of Cl₂}}{\text{Total Mass of MgCl₂}} \right) \times 100
\]
\[
= \left( \frac{70.91}{95.21} \right) \times 100 = 74.47\%
\]
Final Answer for Example 2:
\[
\boxed{25.53\% \text{ Mg}, 74.47\% \text{ Cl₂}}
\]
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####
Example 3: Percent Composition of H₂SO₄
-
Total mass of H₂SO₄: 98.08 g
-
Mass of H₂: 2.02 g
-
Mass of S: 32.07 g
-
Mass of O₄: 64.00 g
Step 1: Calculate the percent composition of H₂.
\[
\text{Percent Composition of H₂} = \left( \frac{\text{Mass of H₂}}{\text{Total Mass of H₂SO₄}} \right) \times 100
\]
\[
= \left( \frac{2.02}{98.08} \right) \times 100 = 2.06\%
\]
Step 2: Calculate the percent composition of S.
\[
\text{Percent Composition of S} = \left( \frac{\text{Mass of S}}{\text{Total Mass of H₂SO₄}} \right) \times 100
\]
\[
= \left( \frac{32.07}{98.08} \right) \times 100 = 32.70\%
\]
Step 3: Calculate the percent composition of O₄.
\[
\text{Percent Composition of O₄} = \left( \frac{\text{Mass of O₄}}{\text{Total Mass of H₂SO₄}} \right) \times 100
\]
\[
= \left( \frac{64.00}{98.08} \right) \times 100 = 65.25\%
\]
Final Answer for Example 3:
\[
\boxed{2.06\% \text{ H₂}, 32.70\% \text{ S}, 65.25\% \text{ O₄}}
\]
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Summary of Final Answers:
1.
Example 1: \(\boxed{13.0\% \text{ red}, 87.0\% \text{ blue}}\)
2.
Example 2: \(\boxed{25.53\% \text{ Mg}, 74.47\% \text{ Cl₂}}\)
3.
Example 3: \(\boxed{2.06\% \text{ H₂}, 32.70\% \text{ S}, 65.25\% \text{ O₄}}\)
Parent Tip: Review the logic above to help your child master the concept of percentage composition worksheet.