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To determine which compounds have the empirical formula [tex]\(CH_2O\)[/tex], we need to analyze the given compounds and simplify their formulas to see if they match the empirical formula [tex]\(CH_2O\)[/tex].
The empirical formula represents the simplest whole number ratio of the atoms in the molecule. To find this ratio for each compound, follow these steps:
1. Identify the number of carbon (C), hydrogen (H), and oxygen (O) atoms in each compound.
2. Simplify the ratio of these atoms to their smallest whole numbers.
3. Compare the simplified ratio to the empirical formula [tex]\(CH_2O\)[/tex], which corresponds to a ratio of 1:2:1 for C:H:O.
Let's go through each compound one by one:
1. [tex]\(C_2H_4O_2\)[/tex]:
- Number of atoms: C = 2, H = 4, O = 2
- Simplified ratio: 2:4:2.
- Divide each by the greatest common divisor (GCD) of 2: [tex]\(2/2 : 4/2 : 2/2\)[/tex] which gives [tex]\(1:2:1\)[/tex].
- This matches [tex]\(CH_2O\)[/tex].
2. [tex]\(C_3H_6O_3\)[/tex]:
- Number of atoms: C = 3, H = 6, O = 3
- Simplified ratio: 3:6:3.
- Divide each by the GCD of 3: [tex]\(3/3 : 6/3 : 3/3\)[/tex] which gives [tex]\(1:2:1\)[/tex].
- This matches [tex]\(CH_2O\)[/tex].
3. [tex]\(CH_2O_2\)[/tex]:
- Number of atoms: C = 1, H = 2, O = 2
- Simplified ratio: 1:2:2.
- This ratio cannot be simplified further.
- This does not match [tex]\(CH_2O\)[/tex].
4. [tex]\(C_5H_{10}O_5\)[/tex]:
- Number of atoms: C = 5, H = 10, O = 5
- Simplified ratio: 5:10:5.
- Divide each by the GCD of 5: [tex]\(5/5 : 10/5 : 5/5\)[/tex] which gives [tex]\(1:2:1\)[/tex].
- This matches [tex]\(CH_2O\)[/tex].
5. [tex]\(C_6H_{12}O_6\)[/tex]:
- Number of atoms: C = 6, H = 12, O = 6
- Simplified ratio: 6:12:6.
- Divide each by the GCD of 6: [tex]\(6/6 : 12/6 : 6/6\)[/tex] which gives [tex]\(1:2:1\)[/tex].
- This matches [tex]\(CH_2O\)[/tex].
After simplifying and comparing, the compounds that have the empirical formula [tex]\(CH_2O\)[/tex] are:
- [tex]\(C_2H_4O_2\)[/tex]
- [tex]\(C_3H_6O_3\)[/tex]
- [tex]\(C_5H_{10}O_5\)[/tex]
- [tex]\(C_6H_{12}O_6\)[/tex]
So the correct answers are:
- [tex]\(C_2H_4O_2\)[/tex]
- [tex]\(C_3H_6O_3\)[/tex]
- [tex]\(C_5H_{10}O_5\)[/tex]
- [tex]\(C_6H_{12}O_6\)[/tex]
These correspond to the indices [0, 1, 3, 4].
The empirical formula represents the simplest whole number ratio of the atoms in the molecule. To find this ratio for each compound, follow these steps:
1. Identify the number of carbon (C), hydrogen (H), and oxygen (O) atoms in each compound.
2. Simplify the ratio of these atoms to their smallest whole numbers.
3. Compare the simplified ratio to the empirical formula [tex]\(CH_2O\)[/tex], which corresponds to a ratio of 1:2:1 for C:H:O.
Let's go through each compound one by one:
1. [tex]\(C_2H_4O_2\)[/tex]:
- Number of atoms: C = 2, H = 4, O = 2
- Simplified ratio: 2:4:2.
- Divide each by the greatest common divisor (GCD) of 2: [tex]\(2/2 : 4/2 : 2/2\)[/tex] which gives [tex]\(1:2:1\)[/tex].
- This matches [tex]\(CH_2O\)[/tex].
2. [tex]\(C_3H_6O_3\)[/tex]:
- Number of atoms: C = 3, H = 6, O = 3
- Simplified ratio: 3:6:3.
- Divide each by the GCD of 3: [tex]\(3/3 : 6/3 : 3/3\)[/tex] which gives [tex]\(1:2:1\)[/tex].
- This matches [tex]\(CH_2O\)[/tex].
3. [tex]\(CH_2O_2\)[/tex]:
- Number of atoms: C = 1, H = 2, O = 2
- Simplified ratio: 1:2:2.
- This ratio cannot be simplified further.
- This does not match [tex]\(CH_2O\)[/tex].
4. [tex]\(C_5H_{10}O_5\)[/tex]:
- Number of atoms: C = 5, H = 10, O = 5
- Simplified ratio: 5:10:5.
- Divide each by the GCD of 5: [tex]\(5/5 : 10/5 : 5/5\)[/tex] which gives [tex]\(1:2:1\)[/tex].
- This matches [tex]\(CH_2O\)[/tex].
5. [tex]\(C_6H_{12}O_6\)[/tex]:
- Number of atoms: C = 6, H = 12, O = 6
- Simplified ratio: 6:12:6.
- Divide each by the GCD of 6: [tex]\(6/6 : 12/6 : 6/6\)[/tex] which gives [tex]\(1:2:1\)[/tex].
- This matches [tex]\(CH_2O\)[/tex].
After simplifying and comparing, the compounds that have the empirical formula [tex]\(CH_2O\)[/tex] are:
- [tex]\(C_2H_4O_2\)[/tex]
- [tex]\(C_3H_6O_3\)[/tex]
- [tex]\(C_5H_{10}O_5\)[/tex]
- [tex]\(C_6H_{12}O_6\)[/tex]
So the correct answers are:
- [tex]\(C_2H_4O_2\)[/tex]
- [tex]\(C_3H_6O_3\)[/tex]
- [tex]\(C_5H_{10}O_5\)[/tex]
- [tex]\(C_6H_{12}O_6\)[/tex]
These correspond to the indices [0, 1, 3, 4].
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