A sample being given as a laboratory unknown is a mixture of calcium carbonate and magnesium carbonate. Both substances decompose to form calcium oxide and magnesium oxide, respectively, when heated at a high temperature for a prolonged period. An unknown sample weighing 5.424 grams was decomposed by heating for several hours at 950 °C. The oxide residue which remained weighed 2.791 grams. From this laboratory data calculate the percent, by weight, of calcium car-bonate in the unknown.

I do these with two unknowns but they can be worked with just one (but it doesn't help the math).

Let x = mass CaCO3
and y = mass MgCO3
--------------------
x + y = 5.424
[x(molar mass CaO/molar mass CaCO3)] + [y(molar mass MgO/molar mass MgCO3)] = 2.791

Two equations and two unknowns. Solve for x and y (although the question doesn't want to know anything about y).
Then %CaCO3 = (mass CaCO3/mass sample)*100 = ?
Post your work if you get stuck.

thx a lot for all the help ..i got the answer 44.4 % :D

To calculate the percent, by weight, of calcium carbonate in the unknown, we need to determine the amount of calcium carbonate and magnesium carbonate in the mixture and compare it to the total weight of the sample.

1. Calculate the weight of the oxide residue: 2.791 grams
2. Subtract the weight of the oxide residue from the initial weight of the unknown sample to find the weight of the carbonates that decomposed: 5.424 grams - 2.791 grams = 2.633 grams
3. Since calcium carbonate (CaCO3) has a molar mass of 100.09 g/mol and magnesium carbonate (MgCO3) has a molar mass of 84.31 g/mol, we can calculate the number of moles of each carbonate:
- Moles of calcium carbonate: (2.633 grams / 100.09 g/mol) = 0.02631 mol
- Moles of magnesium carbonate: (2.633 grams / 84.31 g/mol) = 0.03118 mol
4. Calculate the mass of calcium carbonate using its stoichiometric ratio in the reaction:
- Moles of calcium carbonate * molar mass of calcium carbonate = 0.02631 mol * 100.09 g/mol = 2.633 grams
5. Calculate the percent, by weight, of calcium carbonate in the unknown:
- (Mass of calcium carbonate / Mass of unknown sample) * 100 = (2.633 grams / 5.424 grams) * 100 = 48.5%

Therefore, the percent, by weight, of calcium carbonate in the unknown sample is approximately 48.5%.

To calculate the percent, by weight, of calcium carbonate in the unknown sample, we need to determine the amount of calcium carbonate and magnesium carbonate that decomposed during heating.

First, we need to find the amount of calcium oxide and magnesium oxide formed from the given oxide residue weight. We know that calcium carbonate decomposes to form calcium oxide with a molecular weight ratio of 1:1, and magnesium carbonate decomposes to form magnesium oxide with a molecular weight ratio of 1:1.

1. Calculate the moles of oxide residue:
- Convert the weight of the oxide residue to moles by dividing it by the molar mass of the combined oxides. The molar mass of calcium oxide (CaO) is 56.08 g/mol, and the molar mass of magnesium oxide (MgO) is 40.31 g/mol.
Moles of oxide residue = (2.791 g / 56.08 g/mol) + (2.791 g / 40.31 g/mol)

2. Calculate the moles of calcium oxide and magnesium oxide:
- Since the molecular weight ratios of calcium carbonate to calcium oxide and magnesium carbonate to magnesium oxide are 1:1, the moles of calcium oxide and magnesium oxide formed will be the same as the moles of the oxide residue.

3. Calculate the moles of calcium carbonate and magnesium carbonate:
- Since calcium carbonate has a molecular weight ratio of 1:1 with calcium oxide, and magnesium carbonate has a molecular weight ratio of 1:1 with magnesium oxide, the moles of calcium carbonate and magnesium carbonate will also be the same as the moles of the oxide residue.

4. Calculate the weight of calcium carbonate:
- Multiply the moles of calcium carbonate by the molar mass of calcium carbonate (100.09 g/mol) to find the weight of calcium carbonate contained in the unknown sample.

5. Calculate the percent, by weight, of calcium carbonate:
- Divide the weight of calcium carbonate by the initial weight of the unknown sample (5.424 g) and multiply by 100 to get the percent, by weight, of calcium carbonate in the unknown.

Here are the calculations:

1. Moles of oxide residue = (2.791 g / 56.08 g/mol) + (2.791 g / 40.31 g/mol) = 0.07 mol + 0.07 mol = 0.14 mol

2. Moles of calcium oxide = 0.14 mol
Moles of magnesium oxide = 0.14 mol

3. Moles of calcium carbonate = 0.14 mol
Moles of magnesium carbonate = 0.14 mol

4. Weight of calcium carbonate = 0.14 mol * 100.09 g/mol = 14.01 g

5. Percent, by weight, of calcium carbonate = (14.01 g / 5.424 g) * 100% = 257.67%

Please note that the calculated percent of calcium carbonate is more than 100%, which suggests an error in the calculations or experimental data.