To calculate the molar mass of t-butanol (tert-butanol), we first identify the number of each type of atom in the formula \((CH_3)_3COH\).
Breaking down the formula:
- There are 4 carbon (C) atoms: 3 from the three methyl groups (CH3) and 1 from the hydroxyl group (C).
- There are 10 hydrogen (H) atoms: 9 from the three methyl groups (3 \(\times\) 3) and 1 from the hydroxyl group (OH).
- There is 1 oxygen (O) atom from the hydroxyl group (OH).
Now, we calculate the molar mass by using the atomic masses of each element:
- Carbon (C): approximately 12.01 g/mol
- Hydrogen (H): approximately 1.008 g/mol
- Oxygen (O): approximately 16.00 g/mol
Calculating the total molar mass: \[ \text{Molar mass of t-butanol} = (4 \times 12.01) + (10 \times 1.008) + (1 \times 16.00) \] \[ = 48.04 + 10.08 + 16.00 \] \[ = 74.12 \text{ g/mol} \]
Therefore, the molar mass of t-butanol, rounded to two decimal places, is 74.12 g/mol.