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When a chemical reaction takes place, several molecules combine to produce new ...

Oct 3, 2024

Solution by Steps

step 1

To balance the chemical reaction, we need to equate the number of atoms for each element on both sides of the equation. The equation is:

x \text{Pb}(N_3)_2 + y \text{Cr}(MnO_4)_2 \rightarrow p \text{Cr}_2O_3 + q \text{MnO}_2 + r \text{Pb}_3O_4 + s \text{NO}

step 2

Count the number of atoms for each element on both sides. For the left side:

\text{Pb} = x, \text{Cr} = y, \text{Mn} = 2y, \text{N} = 6x, \text{O} = 8y

. For the right side:

\text{Pb} = 3r, \text{Cr} = 2p, \text{Mn} = 2q, \text{N} = s, \text{O} = 3p + 2q + s

step 3

Set up the equations based on the atom counts: 1.

x = 3r

(for Pb) 2.

y = 2p

(for Cr) 3.

2y = 2q

(for Mn) 4.

6x = s

(for N) 5.

8y = 3p + 2q + s

(for O)

step 4

The number of independent equations is 5, and the number of variables

x, y, p, q, r, s

is 6. Therefore, we can select 1 variable arbitrarily

Answer

The balanced chemical reaction has 5 independent equations and 6 variables, allowing for 1 variable to be selected arbitrarily.

Key Concept

Balancing chemical equations involves ensuring the number of atoms for each element is equal on both sides of the reaction.

Explanation

In this case, we derived 5 equations from the atom counts, and since there are 6 variables, we can freely choose one variable, which is essential for solving the system.