A sample of an oxide of antimony (Sb) contained 51.5 g of antimony combined with 16.9 g of oxygen. What is the simplest formula for the oxide?
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To determine the empirical formula of the oxide, we must first calculate the mole ratio between antimony (Sb) and oxygen (O) using their respective masses.
Step 1: Calculate the number of moles of antimony (Sb).
Given:
Mass of antimony, m(Sb) = 51.5 g
Molar mass of Sb = 121.75 g/mol (from periodic table)
Number of moles, n(Sb) = m(Sb) / Molar mass(Sb)
= 51.5 g / 121.75 g/mol
≈ 0.423 mol
Step 2: Calculate the number of moles of oxygen (O).
Given:
Mass of oxygen, m(O) = 16.9 g
Molar mass of O = 16.00 g/mol (from periodic table)
Number of moles, n(O) = m(O) / Molar mass(O)
= 16.9 g / 16.00 g/mol
≈ 1.056 mol
Step 3: Determine the simplest whole number ratio between Sb and O.
Divide the number of moles by the smaller value of moles (0.423 mol in this case).
Thus, the mole ratio is approximately:
n(Sb) / n(O) ≈ 0.423 mol / 0.423 mol ≈ 1
n(O) / n(O) ≈ 1.056 mol / 0.423 mol ≈ 2.5 (rounded to the nearest whole number)
Step 4: Determine the empirical formula.
The ratio 1:2.5 can be simplified by multiplying both sides by 2 to obtain a whole number ratio:
1:2.5 x 2 = 2:5
Therefore, the empirical formula for the oxide of antimony is Sb2O5.
To determine the simplest formula of the oxide of antimony, we need to find the ratio of antimony to oxygen in the compound.
Step 1: Convert the mass of antimony and oxygen into moles.
- The molar mass of antimony (Sb) is approximately 121.75 g/mol.
- Molar mass of oxygen (O) is approximately 16.00 g/mol.
Moles of antimony = mass of antimony / molar mass of antimony
Moles of antimony = 51.5 g / 121.75 g/mol
Moles of oxygen = mass of oxygen / molar mass of oxygen
Moles of oxygen = 16.9 g / 16.00 g/mol
Step 2: Determine the mole ratio between antimony and oxygen.
Divide both the mole quantities by the smaller mole quantity to get the simplest whole number ratio.
Mole ratio of antimony to oxygen = Moles of antimony / Moles of oxygen
Step 3: Calculate the simplest whole number ratio.
By dividing the moles of antimony and oxygen, we get:
Mole ratio of antimony to oxygen = (51.5 g / 121.75 g/mol) / (16.9 g / 16.00 g/mol)
Now, simplify the expression by canceling out common units:
Mole ratio of antimony to oxygen = (51.5 / 121.75) / (16.9 / 16.00)
Mole ratio of antimony to oxygen = 0.422 / 1.05625
To get a whole number ratio, we multiply by a factor that brings both numbers close to a whole number. In this case, multiplying by 8 gives us:
Mole ratio of antimony to oxygen = (0.422 * 8) / (1.05625 * 8)
Mole ratio of antimony to oxygen = 3.376 / 8.45
Mole ratio of antimony to oxygen ≈ 0.4 / 1
Since the ratio is approximately 0.4/1, we can multiply both sides by 2.5 to get a whole number ratio:
Mole ratio of antimony to oxygen ≈ (0.4/1) * 2.5
Mole ratio of antimony to oxygen ≈ 1 / 2.5
Therefore, the simplest whole number ratio of the oxide of antimony is 2:5 or 2 Sb: 5 O.
The simplest formula for the oxide of antimony is Sb2O5.