To determine the molar mass of [tex]\( \text{H}_2\text{CO}_3 \)[/tex], we need to use the molar masses of its constituent elements: hydrogen (H), carbon (C), and oxygen (O).
Firstly, let's list the molar masses given:
- The molar mass of hydrogen (H) is [tex]\(1.0079 \ \text{g/mol}\)[/tex].
- The molar mass of carbon (C) is [tex]\(12.010 \ \text{g/mol}\)[/tex].
- The molar mass of oxygen (O) is [tex]\(15.999 \ \text{g/mol}\)[/tex].
Next, we note the number of each type of atom in [tex]\( \text{H}_2\text{CO}_3 \)[/tex]:
- There are 2 hydrogen (H) atoms.
- There is 1 carbon (C) atom.
- There are 3 oxygen (O) atoms.
Now, we calculate the total mass contributed by each type of atom:
1. For hydrogen:
[tex]\[ \text{Mass contribution of H} = 2 \times 1.0079 \ \text{g/mol} = 2.0158 \ \text{g/mol} \][/tex]
2. For carbon:
[tex]\[ \text{Mass contribution of C} = 1 \times 12.010 \ \text{g/mol} = 12.010 \ \text{g/mol} \][/tex]
3. For oxygen:
[tex]\[ \text{Mass contribution of O} = 3 \times 15.999 \ \text{g/mol} = 47.997 \ \text{g/mol} \][/tex]
Finally, we sum these contributions to find the total molar mass of [tex]\( \text{H}_2\text{CO}_3 \)[/tex]:
[tex]\[ \text{Total molar mass} = 2.0158 \ \text{g/mol} + 12.010 \ \text{g/mol} + 47.997 \ \text{g/mol} = 62.0228 \ \text{g/mol} \][/tex]
Given the available options:
- [tex]\(29.02 \ \text{g/mol}\)[/tex]
- [tex]\(46.04 \ \text{g/mol}\)[/tex]
- [tex]\(62.02 \ \text{g/mol}\)[/tex]
- [tex]\(72.08 \ \text{g/mol}\)[/tex]
The total molar mass most closely matches [tex]\(62.02 \ \text{g/mol}\)[/tex].
Hence, the molar mass of [tex]\( \text{H}_2\text{CO}_3 \)[/tex] is [tex]\(62.02 \ \text{g/mol}\)[/tex].
