1. The molar mass of oleic acid is 282.5 g/mol and its density is 0.895 g/cm? Use this information to calculate the molar volume of oleic acid. (Use the appropriate units, those associated with the two numbers given here.)
2. Figure out a way to estimate the number of molecules in one mole of oleic acid. (This is Avogadro's number.) Report the result to the appropriate number of significant figures.
The Correct Answer and Explanation is :
1. Molar Volume of Oleic Acid
The molar volume is the volume occupied by one mole of a substance, and it can be calculated using the formula:
[
\text{Molar Volume} = \frac{\text{Molar Mass}}{\text{Density}}
]
Given:
- Molar mass of oleic acid = 282.5 g/mol
- Density of oleic acid = 0.895 g/cm³
Now, let’s plug in the values:
[
\text{Molar Volume} = \frac{282.5 \, \text{g/mol}}{0.895 \, \text{g/cm}^3}
]
[
\text{Molar Volume} = 316.3 \, \text{cm}^3/\text{mol}
]
Thus, the molar volume of oleic acid is 316.3 cm³/mol.
2. Estimating the Number of Molecules in One Mole of Oleic Acid (Avogadro’s Number)
Avogadro’s number is a fundamental constant in chemistry, which is the number of atoms, ions, or molecules in one mole of a substance. To estimate the number of molecules in one mole of oleic acid, we can use the following approach:
We know that 1 mole of any substance contains 6.022 × 10²³ entities (atoms or molecules), which is Avogadro’s number. This value is universal for any substance, whether it is oleic acid or any other compound.
So, the number of molecules in one mole of oleic acid is:
[
6.022 \times 10^{23} \, \text{molecules/mol}
]
This is the most accurate estimate of the number of molecules in one mole of oleic acid, based on Avogadro’s number. Therefore, the result is:
6.022 × 10²³ molecules/mol
Explanation of the Calculations
Molar Volume Calculation:
To calculate the molar volume, we divide the molar mass by the density. The units of g/mol (molar mass) and g/cm³ (density) cancel the grams, leaving cm³/mol as the unit for molar volume. This calculation gives us the volume occupied by one mole of oleic acid at its given density.
Avogadro’s Number:
Avogadro’s number is a universal constant that defines how many entities (atoms or molecules) are present in one mole of a substance. This number is fixed, and for every mole of any substance, the number of molecules will always be 6.022 × 10²³. In the case of oleic acid, the number of molecules in one mole of oleic acid is exactly the same.