Table salt, NaCl(s), and sugar, C12H22O11(s), are accidentally mixed. A 5.50-g sample is burned, and 1.70 g of CO2(g) is produced. What was the mass percentage of the table salt in the mixture?
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To find the mass percentage of table salt (NaCl) in the mixture, we need to determine the mass of NaCl in the 5.50 g sample.
Step 1: Find the molar mass of CO2
The molar mass of CO2 is calculated by summing up the atomic masses of carbon (C) and two oxygen (O) atoms.
Molar mass of C = 12.01 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of CO2 = (12.01 g/mol) + 2(16.00 g/mol) = 44.01 g/mol
Step 2: Convert the mass of CO2 to moles
Using the molar mass of CO2, we can calculate the number of moles of CO2 produced.
1.70 g of CO2 × (1 mol CO2 / 44.01 g CO2) ≈ 0.0386 mol CO2
Step 3: Determine the molar ratio between NaCl and CO2
The balanced equation for the combustion of sugar (C12H22O11) is:
C12H22O11(s) + 12 O2(g) -> 12 CO2(g) + 11 H2O(g)
According to the equation, 1 mol of C12H22O11 produces 12 mol of CO2. Therefore, the molar ratio between CO2 and NaCl is 12:1.
Step 4: Calculate the number of moles of NaCl
Since the molar ratio between CO2 and NaCl is 12:1, the number of moles of NaCl can be calculated using the mole ratio between CO2 and NaCl.
Number of moles of NaCl = 0.0386 mol CO2 × (1 mol NaCl / 12 mol CO2) ≈ 0.00322 mol NaCl
Step 5: Determine the mass of NaCl
To find the mass of NaCl, we need to multiply the number of moles of NaCl by its molar mass.
Molar mass of NaCl = 22.99 g/mol + 35.45 g/mol = 58.44 g/mol
Mass of NaCl = 0.00322 mol NaCl × 58.44 g/mol ≈ 0.1878 g NaCl
Step 6: Calculate the mass percentage of NaCl in the mixture
The mass percentage is calculated by dividing the mass of NaCl by the total mass of the sample and multiplying by 100.
Mass percentage of NaCl = (0.1878 g NaCl / 5.50 g sample) × 100 ≈ 3.42%
Therefore, the mass percentage of table salt (NaCl) in the mixture is approximately 3.42%.
To find the mass percentage of table salt in the mixture, we need to determine the amount of table salt and sugar present in the 5.50-g sample.
First, we'll find the molar mass of table salt (NaCl) and sugar (C12H22O11):
- Molar mass of NaCl = 22.99 g/mol + 35.45 g/mol = 58.44 g/mol
- Molar mass of C12H22O11 = (12.01 g/mol x 12) + (1.01 g/mol x 22) + (16.00 g/mol x 11) = 342.34 g/mol
Next, we'll calculate the moles of CO2 produced from the combustion of the sample:
- Molar mass of CO2 = 12.01 g/mol + (16.00 g/mol x 2) = 44.01 g/mol
- Moles of CO2 = mass of CO2 produced / molar mass of CO2 = 1.70 g / 44.01 g/mol ≈ 0.0386 mol
Now, we can calculate the moles of table salt (NaCl) and sugar (C12H22O11) present in the sample:
- Moles of CO2 produced from the combustion of table salt (NaCl) = Moles of CO2 produced / 2 (according to the balanced chemical equation)
= 0.0386 mol / 2 = 0.0193 mol
- Moles of sugar (C12H22O11) = Moles of CO2 produced - Moles of CO2 produced from table salt
= 0.0386 mol - 0.0193 mol = 0.0193 mol
To determine the mass of table salt and sugar, we can use their respective molar masses:
- Mass of table salt (NaCl) = Moles of table salt * molar mass of NaCl
= 0.0193 mol * 58.44 g/mol = 1.126 g
- Mass of sugar (C12H22O11) = Moles of sugar * molar mass of C12H22O11
= 0.0193 mol * 342.34 g/mol = 6.619 g
Finally, we can calculate the mass percentage of table salt in the mixture:
- Mass percentage of table salt = (Mass of table salt / Mass of mixture) * 100%
= (1.126 g / 5.50 g) * 100% ≈ 20.47%
Therefore, the mass percentage of table salt in the mixture is approximately 20.47%.