Final answer:
To balance the chemical equation CH₄(g) + Br₂(g) ⇌ CBr₄(g) + HBr(g), we balance one element at a time, leading to the balanced equation CH₄(g) + 4 Br₂(g) ⇌ CBr₄(g) + 4 HBr(g) with coefficients, in order, of 1, 4, 1, 4.
Step-by-step explanation:
To balance the equation CH₄(g) + Br₂(g) ⇌ CBr₄(g) + HBr(g), we first count the number of atoms of each element on both sides of the equation. We start by balancing more complex molecules before single-element molecules, typically leaving hydrogen and oxygen to be balanced last.
Looking at our equation, we see that the carbon (C) atoms balance, with one on each side. However, the hydrogen (H) atoms do not balance, with four hydrogens on the reactant side and only one hydrogen on the product side. To balance hydrogen, we add a coefficient of 4 in front of HBr, giving us 4 hydrogen atoms on the product side. Now we need to balance the bromine (Br) atoms. There is one bromine atom in the CBr₄ molecule and four in the 4 HBr molecules, adding up to a total of 8 bromine atoms on the product side. To balance this, we can put a coefficient of 4 in front of Br₂, resulting in 8 bromine atoms on the reactant side also.
The balanced equation is: CH₄(g) + 4 Br₂(g) ⇌ CBr₄(g) + 4 HBr(g). The coefficients in order are 1, 4, 1, 4. This balanced equation now adheres to the law of conservation of mass, as there are equal numbers of each atom type on both sides of the equation.