1.5 gm mixture of CaCO3 and MgCO3 was heated in a vessel and the weight of the residue was found 0.8 gm, then find the percentage composition of CaCO3 ?

To determine the percentage composition of calcium carbonate (CaCO3) in the mixture, we can use the information provided about the initial weight of the mixture and the weight of the residue after heating. When CaCO3 and magnesium carbonate (MgCO3) are heated, they decompose into their respective oxides and carbon dioxide gas. The reactions can be summarized as follows:

Understanding the Reactions

When heated, the carbonates decompose as follows:

• CaCO3 → CaO + CO2 (g)
• MgCO3 → MgO + CO2 (g)

In both reactions, carbon dioxide is released as a gas, which means the weight of the residue will be less than the initial weight of the mixture. The residue consists of the oxides of calcium and magnesium.

Setting Up the Problem

Let’s denote:

• x = mass of CaCO3 in the mixture
• y = mass of MgCO3 in the mixture

From the problem, we know:

• x + y = 1.5 g (total mass of the mixture)
• Weight of the residue after heating = 0.8 g

Calculating the Mass of the Residue

The mass of the residue can be calculated based on the masses of the oxides formed:

• Mass of CaO formed from x grams of CaCO3 = x - (x * (44/100)) = x * (56/100)
• Mass of MgO formed from y grams of MgCO3 = y - (y * (44/100)) = y * (56/100)

Thus, the total mass of the residue can be expressed as:

Residue = (x * 56/100) + (y * 56/100) = 0.8 g

Factoring out 56/100 gives us:

0.56(x + y) = 0.8 g

Substituting Known Values

Since we know that x + y = 1.5 g, we can substitute this into the equation:

0.56(1.5) = 0.8 g

Calculating this gives:

0.84 = 0.8 g

This indicates that we need to adjust our approach since the equation does not hold true. Let's express y in terms of x using the first equation:

y = 1.5 - x

Now substituting y in the residue equation:

0.56(x) + 0.56(1.5 - x) = 0.8

0.56x + 0.84 - 0.56x = 0.8

0.84 - 0.8 = 0.56x

0.04 = 0.56x

Thus, x = 0.04 / 0.56 = 0.0714 g (approximately)

Finding the Mass of MgCO3

Now substituting back to find y:

y = 1.5 - 0.0714 = 1.4286 g (approximately)

Calculating the Percentage Composition

Now that we have the masses of both components, we can find the percentage composition of CaCO3 in the original mixture:

Percentage of CaCO3 = (mass of CaCO3 / total mass of mixture) * 100

Percentage of CaCO3 = (0.0714 / 1.5) * 100 ≈ 4.76%

Final Thoughts

Therefore, the percentage composition of calcium carbonate in the original mixture is approximately 4.76%. This method illustrates how chemical reactions and stoichiometry can be applied to solve real-world problems in chemistry.