A certain village famine, the government decided to give households each member apotato to avoid hunger. Each box contains an equal number of 6 potatoes. They are 12 households in the village who members are 2, 3, 4, 5, 7, 8, 9, 11, 12 and 10. To determine the number of box of potatoes the government will give to the village. Are there any remaining potatoes? If yes, advise what the government can do with them.

Mathematics
A certain village famine, the government decided to give households each member apotato to avoid hunger. Each box contains an equal number of 6 potatoes. They are 12 households in the village who members are 2, 3, 4, 5, 7, 8, 9, 11, 12 and 10. To determine the number of box of potatoes the government will give to the village. Are there any remaining potatoes? If yes, advise what the government can do with them.

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Answer

92.31%~\ce{C},~7.69%~\ce{H}

Step 1: Molecular formula of benzene is C6H6C_6H_6.

M=6×12+6×1=72+6=78 g/molM = 6 \times 12 + 6 \times 1 = 72 + 6 = 78~\mathrm{g/mol}

Step 2: Mass of carbon in benzene.

6×12=72 g6 \times 12 = 72~\mathrm{g}

Step 3: Percentage of carbon.

7278×100%\frac{72}{78} \times 100\%

First, simplify fraction:
72÷678÷6=1213\frac{72 \div 6}{78 \div 6} = \frac{12}{13}

Then,
1213≈0.9231\frac{12}{13} \approx 0.9231

0.9231×100%=92.31%0.9231 \times 100\% = 92.31\%

Step 4: Percentage of hydrogen.

6×1=6 g6 \times 1 = 6~\mathrm{g}
678×100%=7.69%\frac{6}{78} \times 100\% = 7.69\%

Step 5: Reason for sooty flame.
Benzene has high carbon content (92.31%92.31\%). Oxygen is insufficient for complete combustion to \ceCO2\ce{CO2} and \ceH2O\ce{H2O}, so unburnt carbon forms soot (black smoke).

92.31%~\ce{C,~7.69%~\ce{H}}

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Quick Answer

Molecular formula of benzene is C_6H_6. M = 6 × 12 + 6 × 1 = 72 + 6 = 78~g/mol Step 2: Mass of carbon in benzene.

A certain village famine, the government decided to give households each member apotato to avoid hunger. Each box contains an equal number of 6 potatoes. They are 12 households in the village who members are 2, 3, 4, 5, 7, 8, 9, 11, 12 and 10. To determine the number of box of potatoes the government will give to the village. Are there any remaining potatoes? If yes, advise what the government can do with them.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: Molecular formula of benzene is C_6H_6. M = 6 × 12 + 6 × 1 = 72 + 6 = 78~g/mol Step 2: Mass of carbon in benzene. 6 × 12 = 72~g Step 3: Percentage of carbon. (72)/(78) × 100\% First, simplify fraction: (72 ÷ 6)/(78 ÷ 6) = (12)/(13) Then, (12)/(13) ≈ 0.9231 0.9231 × 100\% = 92.31\% Step 4: Percentage of hydrogen. 6 × 1 = 6~g (6)/(78) × 100\% = 7.69\% Step 5: Reason for sooty flame. Benzene has high carbon content (92.31\%). Oxygen is insufficient for complete combustion to CO2 and H2O, so unburnt carbon forms soot (black smoke). 92.31\%~C,~7.69\%~H