A sample of liquid mercury (Hg) has a mass of 90.3 g.
a) Find the molar mass of mercury (Hg).
b) Determine the number of moles (mol) of mercury in the sample.
1 mol
c) Determine the number of mercury atoms in the sample.
The correct answer and explanation is :
Let’s go step by step to solve this problem.
Given Data:
- Mass of liquid mercury (( m )) = 90.3 g
- Avogadro’s number = ( 6.022 \times 10^{23} ) atoms/mol
Part A: Molar Mass of Mercury (Hg)
The molar mass of an element is its atomic weight in grams per mole. According to the periodic table:
[
Molar\ mass\ of\ Hg = 200.59\ g/mol
]
Part B: Number of Moles of Mercury in the Sample
We use the formula:
[
n = \frac{m}{M}
]
where:
- ( n ) = number of moles
- ( m ) = mass of the sample
- ( M ) = molar mass of mercury
[
n = \frac{90.3\ g}{200.59\ g/mol}
]
[
n \approx 0.4502\ \text{moles of Hg}
]
Part C: Number of Mercury Atoms in the Sample
To find the number of atoms, we multiply the number of moles by Avogadro’s number:
[
N = n \times N_A
]
[
N = (0.4502\ mol) \times (6.022 \times 10^{23} \text{ atoms/mol})
]
[
N \approx 2.71 \times 10^{23} \text{ atoms}
]
Explanation:
- Molar Mass
The molar mass of mercury is the mass of one mole of Hg atoms, which is 200.59 g/mol. This value is taken from the periodic table and represents the average atomic mass of mercury. - Moles Calculation
To determine how many moles are in 90.3 g of mercury, we divide the given mass by the molar mass. This tells us how many units (moles) of mercury atoms are present. - Atoms Calculation
Since one mole of any substance contains ( 6.022 \times 10^{23} ) representative particles (Avogadro’s number), we multiply the moles of Hg by this value to get the number of individual mercury atoms.
Thus, a 90.3 g sample of mercury contains approximately ( 2.71 \times 10^{23} ) atoms of mercury.
