I need to write a balanced equation for this problem and am having difficulty doing so.

The question is this: use the mole ratio of CuO produced per mole of malachite to write a balanced equation for the malachite decomposition reaction. Assume that CO2 is also a product of the decomposition.
Here are my numbers
moles of CuO produced 141.57
moles of malachite in 1g 221.12
ratio of moles of CuO produced per moles of malachite decomposed 79.55

Are these experimentally determined values? I have a hard time believing 1 g malachite contains 221.12 moles. I might believe that 1 mole of malachite contains 221.12 g malachite.

To write a balanced equation for the malachite decomposition reaction, we need to determine the chemical formula for malachite and identify the products formed during decomposition.

Malachite is a carbonate mineral with the chemical formula Cu2CO3(OH)2.

The decomposition of malachite can be represented as follows:
Cu2CO3(OH)2 → CuO + CO2 + H2O

From the given information, we know that the ratio of moles of CuO produced per mole of malachite decomposed is 79.55. This means that for every mole of malachite decomposed, 79.55 moles of CuO are produced.

To balance the equation, we need to ensure that the number of atoms on both sides of the equation is the same.

To determine the coefficients in front of each compound, we can start by balancing the copper (Cu) atoms. In malachite, there are two Cu atoms, while in CuO, there is only one Cu atom. To balance the number of Cu atoms, we will put a 2 in front of CuO.

Next, we can balance the carbon (C) atoms. In malachite, there is one C atom, while in CO2 there is one as well. Therefore, no coefficient is needed for CO2.

Then, we balance the oxygen (O) atoms. In malachite, there are six O atoms (two from CO3 and four from OH), while in CuO there is only one O atom. Therefore, we need to put a 3 in front of CuO to balance the O atoms.

Finally, we balance the hydrogen (H) atoms. In malachite, there are four H atoms, while in H2O there are two. We put a coefficient of 2 in front of H2O to balance the H atoms.

The balanced equation for the malachite decomposition reaction is:
2Cu2CO3(OH)2 → 2CuO + CO2 + 2H2O