Mass Composition Of A Mixture Of KClO_{3}, KHCO_{3}, K_{2}CO_{3} And KCl

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Mass Composition Of A Mixture Of KClO_{3}, KHCO_{3}, K_{2}CO_{3} And KCl

A mixture containing KClO_{3}, KHCO_{3}, K_{2}CO_{3} and KCl was heated. CO_{2}, O_{2} and H_{2}O gases were produced as follows:

2KClO_{3}(s) -------> 2KCl(s) + 3O_{2}(g)

2KHCO_{3}(s) -------> K_{2}O(s) + H_{2}O(g) + 2CO_{2}(g)

K_{2}CO_{3}(s) -------> K_{2}O(s) + CO_{2}(g)

The KCl does not react under the conditions of the reaction. If 100 g of the mixture produces 1.80 g of H_{2}O, 13.20 g of CO_{2} and 4.0 g of O_{2}, what was the mass composition of the original mixture if the mixture decomposed completely?

**The strings**:
S_{7}P_{1}A_{15} (containership-mass).

S_{7}P_{6}A_{66} (grouping/interaction- chemical)
**The math**:

Both Pj Problem are of Interest, however, Pj Problem of type *grouping/interactio* (chemical) is in focus.

Decomposition Of KClO_{3}:

Molar mas of O_{2} = 16 x 2 = 32 g

So, 4 g of O_{2} = 4/32 = 0.125 mol of O_{2}

3 mols of O_{2} is produced from 2 moles of KClO_{3} decomposition

So, 0.125 mol of oxygen is produced from (2x0.125)/3 = 0.083 mol of KClO_{3}

Molar mass of KClO_{3} = 39 + 36 + 48 = 123 g

So, mass of 0.083 mol of KClO_{3} = (0.083 x 123) = 10.25 g.

Decomposition of KHCO_{3}:

Molar mass of H_{2}O = 1x2 + 16 = 18

So, 1.80 g of H_{2}O = 1.80/18 = 0.1 mol of H_{2}O

1 mole of H_{2}O is produced by 2 moles of KHCO_{3}

So, 0.1 mol of H_{2}O is produced from 0.2 mol of KHCO_{3}

Molar mass of KHCO_{3} = 39 + 1 + 12 + 48 = 100 g

So, mass of 0.2 mol of KHCO_{3} = 0.2 x 100 = 20 g.

CO_{2} is also produced:

20 g of KHCO_{3} = 20/100 = 0.2 mol

2 moles of KHCO_{3} produced 2 moles of CO_{2}

So, 0.2 mol KHCO_{3} produced 0.2 mol of CO_{2}

Molar mass of CO_{2} = 12 +32 = 44

So, mass of CO_{2} produced = (0.2 x 44) = 8.8 g

Decomposition of K_{2}CO_{3}:

13.20 - 8.8 = 4.4 g = mass of CO_{2} produced

Molar mass of CO_{2} = 12 + 32 = 44

So, mol of CO_{2} produced = 4.4/44 = 0.1 mol

1 mole of K_{2}CO_{3} produced 1 mole of CO_{2}

So, 0.1 mol of K_{2}CO_{3} produced 0.1 mol of CO_{2}

Molar mass of K_{2}CO_{3} = 2x39 + 12 + 3x16 = 78 + 12 + 48 = 138

So, mass of 0.1 mol of K_{2}CO_{3} = (0.1x138) = 13.8 g

mass of KCl = 100 -(10.25 + 20 + 13.8) = 100 - 44 = 56 g

Mass composition of mixture is as follows:

10.25 g KClCO_{3}, 20 g KHCO_{3}

13.8 g K_{2}CO_{3}, 56 g KCl.

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