Table salt, NaCl(s), and sugar, C12H22O11(s), are accidentally mixed. A 4.00-g sample is burned, and 2.70 g of CO2(g) is produced. What was the mass percentage of the table salt in the mixture?
C12H22O11 + 12CO2 + 11H2O
mols CO2 = grams/molar mass = ?
mols sugar = mols CO2 x (1/12) = ?
grams sugar = mols x molar mass
4.00-g sugar = g salt
% salt = (g salt/4.00)*100 = ?
To determine the mass percentage of table salt in the mixture, we need to calculate the mass of table salt and the total mass of the mixture.
Here's how to do it:
1. Start by finding the molar masses 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 * 12) + (1.01 * 22) + (16.00 * 11) = 342.30 g/mol
2. Calculate the moles of CO2 produced by dividing the given mass of CO2 by its molar mass.
- Moles of CO2 = 2.70 g / 44.01 g/mol (molar mass of CO2) ≈ 0.0614 mol
3. Determine the moles of carbon in the CO2 produced. Since each mole of CO2 contains 1 mole of carbon, the moles of carbon is also approximately 0.0614 mol.
4. Calculate the moles of table salt in the mixture by multiplying the moles of carbon by the ratio of moles of table salt to moles of carbon in the chemical equation for the combustion of sugar.
- From the balanced equation:
C12H22O11 + 12 O2 -> 12 CO2 + 11 H2O
There are 12 moles of carbon for every mole of sugar combusted.
- Moles of table salt = 0.0614 mol * (1 mol table salt / 12 mol carbon) ≈ 0.00512 mol
5. Calculate the mass of table salt using its molar mass and moles.
- Mass of table salt = 0.00512 mol * 58.44 g/mol ≈ 0.30 g
6. Determine the total mass of the mixture by dividing the mass of CO2 produced by the mass percentage of CO2 in the mixture.
- Suppose the mass of the mixture is M grams.
- Mass of CO2 in the mixture = (2.70 g / 0.0614 mol) * M mol ≈ 44.01M g
- Since the mass of CO2 in the mixture is 2.70 g, we can set up the following equation:
44.01M g = 2.70 g
- Solving for M gives us: M ≈ 0.06135 g
7. Calculate the mass percentage of table salt in the mixture.
- Mass percentage of table salt = (Mass of table salt / Total mass of the mixture) * 100%
- Mass percentage of table salt = (0.30 g / 0.06135 g) * 100% ≈ 489.2%
Therefore, the mass percentage of table salt in the mixture is approximately 489.2%.