Let's calculate the number of moles of benzoic acid (C₆H₅COOH) from the given mass of [tex]\( 1.890 \)[/tex] grams.
First, we need to determine the molar mass of benzoic acid. The chemical formula for benzoic acid is [tex]\( \text{C}_6\text{H}_5\text{COOH} \)[/tex], which consists of:
- 7 carbon (C) atoms
- 6 hydrogen (H) atoms
- 2 oxygen (O) atoms
The atomic masses for each element are:
- Carbon (C) = [tex]\( 12.01 \)[/tex] g/mol
- Hydrogen (H) = [tex]\( 1.008 \)[/tex] g/mol
- Oxygen (O) = [tex]\( 16.00 \)[/tex] g/mol
We calculate the molar mass of benzoic acid by adding the contributions from each element:
[tex]\[ \text{Molar mass of C}_6\text{H}_5\text{COOH} = (7 \times 12.01) + (6 \times 1.008) + (2 \times 16.00) \][/tex]
From calculations, the molar mass is determined to be [tex]\( 122.118 \)[/tex] g/mol.
Now, we use the given mass of benzoic acid ([tex]\( 1.890 \)[/tex] grams) to find the number of moles. The number of moles is obtained using the formula:
[tex]\[ \text{Number of moles} = \frac{\text{mass of substance (g)}}{\text{molar mass (g/mol)}} \][/tex]
Substituting the given values:
[tex]\[ \text{Number of moles} = \frac{1.890 \, \text{g}}{122.118 \, \text{g/mol}} \][/tex]
This calculation results in:
[tex]\[ \text{Number of moles} \approx 0.015476833881983 \][/tex]
Therefore, [tex]\( 1.890 \)[/tex] grams of benzoic acid corresponds to approximately [tex]\( 0.0155 \)[/tex] moles of benzoic acid.
To summarize, the number of moles of benzoic acid (C₆H₅COOH) that undergoes combustion is approximately [tex]\( 0.0155 \)[/tex] moles.
