A mixture containing only caco3 and mgco3 was heated to a constant weight , if mass of residue is 51.6%if original mass. Calculate the value of z where z=2*%of caco3

To solve the problem, we need to understand the thermal decomposition of calcium carbonate (CaCO3) and magnesium carbonate (MgCO3). When these carbonates are heated, they decompose into their respective oxides and carbon dioxide gas. The reactions can be summarized as follows:

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

Given that the mass of the residue after heating is 51.6% of the original mass, we can set up the problem using the following steps:

Step 1: Define Variables

Let the original mass of the mixture be represented as 100 grams. Therefore, the mass of the residue after heating is:

Residue Mass = 51.6% of Original Mass = 0.516 × 100 g = 51.6 g

Step 2: Establish the Mass Relationships

Let x be the mass of CaCO3 in the original mixture and y be the mass of MgCO3. Thus, we have:

x + y = 100 g

When heated, the mass of the residue will consist of the oxides formed from both carbonates:

• From CaCO3, the mass of CaO produced is: x × (40 / 100) = 0.4x (since the molar mass of CaO is 40 g/mol and that of CaCO3 is 100 g/mol).
• From MgCO3, the mass of MgO produced is: y × (40 / 84) = 0.4762y (the molar mass of MgO is 40 g/mol and that of MgCO3 is 84 g/mol).

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

Residue Mass = 0.4x + 0.4762y

Step 3: Set Up the Equation

We know that the mass of the residue is 51.6 g, so we can set up the equation:

0.4x + 0.4762y = 51.6

Step 4: Substitute and Solve

Now, we can substitute y from the first equation into the second equation:

y = 100 - x

Substituting this into the residue equation gives:

0.4x + 0.4762(100 - x) = 51.6

Expanding this, we get:

0.4x + 47.62 - 0.4762x = 51.6

Combining like terms results in:

-0.0762x + 47.62 = 51.6

Rearranging gives:

-0.0762x = 51.6 - 47.62

-0.0762x = 3.98

Solving for x yields:

x = 3.98 / -0.0762 ≈ 52.2 g

Step 5: Calculate the Percentage of CaCO3

Now that we have the mass of CaCO3, we can find the percentage:

% of CaCO3 = (x / 100) × 100 = 52.2%

Step 6: Determine the Value of z

Finally, we can calculate z, where z = 2 × % of CaCO3:

z = 2 × 52.2 = 104.4

In summary, the value of z is 104.4.