Mass of aluminum sample = 0.97g
Mass of watch glass = 32.1851g
Mass of watch glass & sample = 45.2550g
a) What is the mass of alum produced?
b) What is the theoretical yield of alum?
c) What is the percent yield?
d) What is the molecular mass of alum?
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To solve these questions, we need to use the given information and apply some chemical concepts. Let's go step by step:
Step 1: Find the mass of alum produced (a).
Given:
Mass of aluminum sample = 0.97g
Mass of watch glass = 32.1851g
Mass of watch glass & sample = 45.2550g
First, let's calculate the mass of the watch glass and sample, excluding the watch glass itself:
Mass of sample = Mass of watch glass & sample - Mass of watch glass
Mass of sample = 45.2550g - 32.1851g
Mass of sample = 13.0699g
Since aluminum reacts with a compound to form alum, we know that the mass of alum produced is equal to the mass of aluminum sample used.
Therefore, the mass of alum produced (a) is 0.97g.
Step 2: Find the theoretical yield of alum (b).
The theoretical yield refers to the maximum amount of product that can be obtained from the given reactants. To find the theoretical yield, we need to calculate the number of moles of aluminum sample and then convert it to moles of alum.
The molar mass of aluminum (Al) is 26.98 g/mol, and the molar mass of alum (KAl(SO4)2·12H2O) is 474.39 g/mol.
Number of moles of aluminum (Al):
Moles = Mass / Molar mass
Moles = 0.97g / 26.98 g/mol
Moles ≈ 0.036 mol
The stoichiometric coefficient of aluminum in the balanced equation for the formation of alum is 2. This means that for every 2 moles of aluminum, 1 mole of alum is produced.
Number of moles of alum:
Moles of alum = 0.036 mol / 2
Moles of alum = 0.018 mol
The theoretical yield of alum (b) is equal to the number of moles of alum multiplied by the molar mass of alum:
Theoretical yield = Moles of alum * Molar mass of alum
Theoretical yield = 0.018 mol * 474.39 g/mol
Theoretical yield ≈ 8.53 g
Therefore, the theoretical yield of alum (b) is approximately 8.53 g.
Step 3: Find the percent yield (c).
The percent yield is a measure of the efficiency of the reaction, calculated as the actual yield (mass of alum produced) divided by the theoretical yield, multiplied by 100%.
Percent yield = (Actual yield / Theoretical yield) * 100%
Percent yield = (0.97 g / 8.53 g) * 100%
Percent yield ≈ 11.38%
Therefore, the percent yield (c) is approximately 11.38%.
Step 4: Find the molecular mass of alum (d).
The molecular mass of alum (KAl(SO4)2·12H2O) can be calculated by summing the atomic masses of each element present in the compound.
Molecular mass of alum = (Atomic mass of K * 2) + Atomic mass of Al + (Atomic mass of S * 2) + (Atomic mass of O * 18) + (Atomic mass of H * 24)
Molecular mass of alum = (39.10 g/mol * 2) + 26.98 g/mol + (32.06 g/mol * 2) + (16.00 g/mol * 18) + (1.01 g/mol * 24)
Molecular mass of alum ≈ 474.39 g/mol
Therefore, the molecular mass of alum (d) is approximately 474.39 g/mol.
To answer these questions, we need to understand the concept of mass and moles. The mass of a substance is usually measured in grams, while the amount of a substance is measured in moles. We can calculate the moles using the formula:
moles = mass / molar mass.
a) To find the mass of alum produced, we first need to calculate the moles of aluminum used. We can do this by subtracting the mass of the watch glass from the mass of the watch glass and sample:
moles of aluminum = (mass of watch glass & sample - mass of watch glass) / molar mass of aluminum.
The molar mass of aluminum is 26.98 g/mol. Let's plug in the values:
moles of aluminum = (45.2550 g - 32.1851 g) / 26.98 g/mol.
Calculating this, we find that the moles of aluminum used is approximately 0.4836 mol.
Since the balanced chemical equation for the reaction of aluminum and potassium hydroxide to form alum is:
2Al + 2KOH + 4H₂O -> 2KAl(OH)₄ + 3H₂,
we can see that the mole ratio between aluminum and alum is 2:2. This means that for every 2 moles of aluminum used, we produce 2 moles of alum.
Therefore, the moles of alum produced will be the same as the moles of aluminum used, which is 0.4836 mol.
To find the mass of alum produced, we can use the moles of alum and the molar mass of alum, which is 474.40 g/mol:
mass of alum produced = moles of alum * molar mass of alum.
mass of alum produced = 0.4836 mol * 474.40 g/mol.
Calculating this, we find that the mass of alum produced is approximately 229.70 g.
b) The theoretical yield of alum refers to the maximum amount of alum that can be produced based on the stoichiometry of the reaction. In this case, the theoretical yield is 229.70 g, which we calculated in part (a).
c) The percent yield is the ratio of the actual yield (mass of alum produced) to the theoretical yield, multiplied by 100 to express it as a percentage:
percent yield = (mass of alum produced / theoretical yield) * 100.
Let's calculate the percent yield:
percent yield = (229.70 g / 229.70 g) * 100.
Calculating this, we find that the percent yield is 100%.
d) The molecular mass of alum can be determined by summing the molar masses of the individual elements in the compound. The formula for alum is KAl(SO₄)₂·12H₂O.
The molar mass of potassium (K) is 39.10 g/mol, the molar mass of aluminum (Al) is 26.98 g/mol, the molar mass of sulfur (S) is 32.07 g/mol, the molar mass of oxygen (O) is 16.00 g/mol, and the molar mass of hydrogen (H) is 1.01 g/mol.
We have two sulfur atoms and four oxygen atoms in the formula, so let's calculate the molecular mass:
molecular mass of alum = 2 * (molar mass of potassium) + (molar mass of aluminum) + 2 * (molar mass of sulfur) + 8 * (molar mass of oxygen) + 12 * (molar mass of hydrogen).
Calculating this, we find that the molecular mass of alum is approximately 474.40 g/mol.