Which of the following series of compounds have same mass percentage of carbon ?

Options

A. `CO_(2)`,CO
B. `CH_(4),C_(2)H_(6),C_(2)H_(2)`
C. `C_(2)H_(2),C_(6)H_(6),C_(10)H_(6)`
D. `HCHO,CH_(3)COOH,C_(6)H_(12)O_(6)`

Answer

To determine which series of compounds have the same mass percentage of carbon, we will calculate the mass percentage of carbon in each compound for the given options.

### Step-by-Step Solution:

**Step 1: Analyze Option A (CO2 and CO)**

1. **Calculate the molar mass of CO2:**
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Molar mass of CO2 = 12 + (2 × 16) = 12 + 32 = 44 g/mol

2. **Calculate the mass percentage of carbon in CO2:**
\[ \text{Mass percentage of C in CO2} = \left( \frac{12}{44} \right) \times 100 \approx 27.27\% \]

3. **Calculate the molar mass of CO:**
- Molar mass of CO = 12 + 16 = 28 g/mol

4. **Calculate the mass percentage of carbon in CO:**
\[ \text{Mass percentage of C in CO} = \left( \frac{12}{28} \right) \times 100 \approx 42.86\% \]

**Conclusion for Option A:** The mass percentages are different (27.27% for CO2 and 42.86% for CO). Thus, Option A does not have the same mass percentage of carbon.

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**Step 2: Analyze Option B (CH4, C2H6, C2H2)**

1. **Calculate the molar mass of CH4:**
- Molar mass of CH4 = 12 + (4 × 1) = 12 + 4 = 16 g/mol
\[ \text{Mass percentage of C in CH4} = \left( \frac{12}{16} \right) \times 100 = 75\% \]

2. **Calculate the molar mass of C2H6:**
- Molar mass of C2H6 = (2 × 12) + (6 × 1) = 24 + 6 = 30 g/mol
\[ \text{Mass percentage of C in C2H6} = \left( \frac{24}{30} \right) \times 100 = 80\% \]

3. **Calculate the molar mass of C2H2:**
- Molar mass of C2H2 = (2 × 12) + (2 × 1) = 24 + 2 = 26 g/mol
\[ \text{Mass percentage of C in C2H2} = \left( \frac{24}{26} \right) \times 100 \approx 92.31\% \]

**Conclusion for Option B:** The mass percentages are different (75% for CH4, 80% for C2H6, and 92.31% for C2H2). Thus, Option B does not have the same mass percentage of carbon.

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**Step 3: Analyze Option C (C2H2, C6H6, C10H6)**

1. **Calculate the molar mass of C2H2:**
- Molar mass of C2H2 = 24 + 2 = 26 g/mol
\[ \text{Mass percentage of C in C2H2} = \left( \frac{24}{26} \right) \times 100 \approx 92.31\% \]

2. **Calculate the molar mass of C6H6:**
- Molar mass of C6H6 = (6 × 12) + (6 × 1) = 72 + 6 = 78 g/mol
\[ \text{Mass percentage of C in C6H6} = \left( \frac{72}{78} \right) \times 100 \approx 92.31\% \]

3. **Calculate the molar mass of C10H6:**
- Molar mass of C10H6 = (10 × 12) + (6 × 1) = 120 + 6 = 126 g/mol
\[ \text{Mass percentage of C in C10H6} = \left( \frac{120}{126} \right) \times 100 \approx 95.24\% \]

**Conclusion for Option C:** The mass percentages are different (92.31% for C2H2 and C6H6, and 95.24% for C10H6). Thus, Option C does not have the same mass percentage of carbon.

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**Step 4: Analyze Option D (HCHO, CH3COOH, C6H12O6)**

1. **Calculate the molar mass of HCHO:**
- Molar mass of HCHO = 1 + 12 + 16 = 29 g/mol
\[ \text{Mass percentage of C in HCHO} = \left( \frac{12}{30} \right) \times 100 \approx 40\% \]

2. **Calculate the molar mass of CH3COOH:**
- Molar mass of CH3COOH = 2 + 4 + 16 = 60 g/mol
\[ \text{Mass percentage of C in CH3COOH} = \left( \frac{24}{60} \right) \times 100 = 40\% \]

3. **Calculate the molar mass of C6H12O6:**
- Molar mass of C6H12O6 = (6 × 12) + (12 × 1) + (6 × 16) = 180 g/mol
\[ \text{Mass percentage of C in C6H12O6} = \left( \frac{72}{180} \right) \times 100 = 40\% \]

**Conclusion for Option D:** All three compounds have the same mass percentage of carbon (40%). Thus, Option D is correct.

### Final Answer:
The series of compounds that have the same mass percentage of carbon is **Option D**.

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