How many formula units are contained in 23.5 g of Sb2S3
The Correct Answer and Explanation is :
The correct answer is: 4.17 \times 10^{22}
To determine the number of formula units in 23.5 g of antimony(III) sulfide (Sb₂S₃), follow these steps:
Step 1: Calculate the molar mass of Sb₂S₃
First, we need to calculate the molar mass (molecular weight) of Sb₂S₃. The atomic masses are:
- Antimony (Sb): 121.76 g/mol
- Sulfur (S): 32.06 g/mol
The formula Sb₂S₃ has:
- 2 atoms of Sb → (2 \times 121.76 = 243.52) g/mol
- 3 atoms of S → (3 \times 32.06 = 96.18) g/mol
So, the molar mass of Sb₂S₃ = (243.52 + 96.18 = 339.70) g/mol
Step 2: Calculate the number of moles of Sb₂S₃ in 23.5 g
Using the formula:
[
\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}
]
Substitute the values:
[
\text{moles of Sb₂S₃} = \frac{23.5\ \text{g}}{339.70\ \text{g/mol}} \approx 0.0692\ \text{moles}
]
Step 3: Use Avogadro’s number to find the number of formula units
One mole of any substance contains (6.022 \times 10^{23}) formula units (Avogadro’s number). To find the number of formula units in 0.0692 moles:
[
\text{formula units} = 0.0692\ \text{moles} \times 6.022 \times 10^{23}\ \text{units/mole}
]
[
\text{formula units} \approx 4.17 \times 10^{22}
]
Explanation (around 300 words)
In chemistry, a formula unit represents the smallest whole-number ratio of ions in an ionic compound. In this case, antimony(III) sulfide (Sb₂S₃) consists of two antimony (Sb) atoms and three sulfur (S) atoms. To calculate the number of formula units in a given mass of Sb₂S₃, we must first know its molar mass, which is the mass of one mole of Sb₂S₃ formula units. This is calculated by summing the atomic masses of all the atoms present in one formula unit of Sb₂S₃: two antimony atoms and three sulfur atoms.
Once we have the molar mass, the number of moles present in a given mass (in this case, 23.5 g) can be determined using the formula for moles, which divides the mass by the molar mass. For Sb₂S₃, we calculated that the molar mass is 339.70 g/mol, and dividing 23.5 g by this value gives us about 0.0692 moles.
Finally, to find the actual number of formula units, we multiply the number of moles by Avogadro’s number ((6.022 \times 10^{23})). This gives the total number of Sb₂S₃ formula units in the sample, which turns out to be approximately (4.17 \times 10^{22}) formula units. This calculation is essential for understanding the amount of a substance on a microscopic scale, such as in reactions involving Sb₂S₃.