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To solve the question about a compound with the empirical formula [tex]\( CH_3 \)[/tex], let's carefully analyze each option given:
### Option A: It contains three times as many hydrogen atoms as carbon atoms.
- The empirical formula [tex]\( CH_3 \)[/tex] tells us the ratio of atoms.
- For each carbon atom ([tex]\(C\)[/tex]), there are three hydrogen atoms ([tex]\(H\)[/tex]).
- Therefore, it must be true that the compound contains three times as many hydrogen atoms as carbon atoms.
### Option B: It consists of 75% hydrogen by mass.
- Let's calculate the mass percentages.
- The atomic mass of carbon ([tex]\(C\)[/tex]) is approximately 12 g/mol.
- The atomic mass of hydrogen ([tex]\(H\)[/tex]) is approximately 1 g/mol.
- For one mole of [tex]\(CH_3\)[/tex], we have:
- 1 mole of [tex]\(C\)[/tex], which is 12 g
- 3 moles of [tex]\(H\)[/tex], which is [tex]\(3 \times 1 = 3\)[/tex] g
- The total mass of one mole of [tex]\(CH_3\)[/tex] is [tex]\(12 + 3 = 15\)[/tex] g.
- The percentage of hydrogen by mass is [tex]\(\left( \frac{3}{15} \right) \times 100\%\)[/tex], which equals 20%.
- Therefore, it is not true that it consists of 75% hydrogen by mass.
### Option C: Each molecule contains exactly four atoms.
- The formula [tex]\( CH_3 \)[/tex] consists of:
- 1 carbon atom
- 3 hydrogen atoms
- Summing these up, each molecule indeed contains [tex]\(1 + 3 = 4\)[/tex] atoms.
- Therefore, this must be true.
### Option D: Each carbon atom is bonded to three hydrogen atoms.
- In a strict sense, the bonding in [tex]\(CH_3\)[/tex] could vary depending on the molecular structure.
- The empirical formula [tex]\(CH_3\)[/tex] simply gives the ratio of atoms, not the exact bonding arrangement.
- So, this statement is not necessarily true in every context.
Given this analysis, the correct answers provided are the ones that must be true:
- A. It contains three times as many hydrogen atoms as carbon atoms.
- C. Each molecule contains exactly four atoms.
However, we must select the single answer that must be true about the compound. The choice that directly relates to the given empirical formula [tex]\(CH_3\)[/tex] without ambiguity is:
A. It contains three times as many hydrogen atoms as carbon atoms.
### Option A: It contains three times as many hydrogen atoms as carbon atoms.
- The empirical formula [tex]\( CH_3 \)[/tex] tells us the ratio of atoms.
- For each carbon atom ([tex]\(C\)[/tex]), there are three hydrogen atoms ([tex]\(H\)[/tex]).
- Therefore, it must be true that the compound contains three times as many hydrogen atoms as carbon atoms.
### Option B: It consists of 75% hydrogen by mass.
- Let's calculate the mass percentages.
- The atomic mass of carbon ([tex]\(C\)[/tex]) is approximately 12 g/mol.
- The atomic mass of hydrogen ([tex]\(H\)[/tex]) is approximately 1 g/mol.
- For one mole of [tex]\(CH_3\)[/tex], we have:
- 1 mole of [tex]\(C\)[/tex], which is 12 g
- 3 moles of [tex]\(H\)[/tex], which is [tex]\(3 \times 1 = 3\)[/tex] g
- The total mass of one mole of [tex]\(CH_3\)[/tex] is [tex]\(12 + 3 = 15\)[/tex] g.
- The percentage of hydrogen by mass is [tex]\(\left( \frac{3}{15} \right) \times 100\%\)[/tex], which equals 20%.
- Therefore, it is not true that it consists of 75% hydrogen by mass.
### Option C: Each molecule contains exactly four atoms.
- The formula [tex]\( CH_3 \)[/tex] consists of:
- 1 carbon atom
- 3 hydrogen atoms
- Summing these up, each molecule indeed contains [tex]\(1 + 3 = 4\)[/tex] atoms.
- Therefore, this must be true.
### Option D: Each carbon atom is bonded to three hydrogen atoms.
- In a strict sense, the bonding in [tex]\(CH_3\)[/tex] could vary depending on the molecular structure.
- The empirical formula [tex]\(CH_3\)[/tex] simply gives the ratio of atoms, not the exact bonding arrangement.
- So, this statement is not necessarily true in every context.
Given this analysis, the correct answers provided are the ones that must be true:
- A. It contains three times as many hydrogen atoms as carbon atoms.
- C. Each molecule contains exactly four atoms.
However, we must select the single answer that must be true about the compound. The choice that directly relates to the given empirical formula [tex]\(CH_3\)[/tex] without ambiguity is:
A. It contains three times as many hydrogen atoms as carbon atoms.
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