The addition reaction A + B = C takes place in the gas phase. Assuming that V liters of a mixture A + B containing a% A

The addition reaction A + B = C takes place in the gas phase. Assuming that V liters of a mixture A + B containing a% A (by volume) were introduced into the reaction, and that the reaction proceeds quantitatively, derive the formula for calculating the composition of the final mixture (in percent by volume). Discuss your options.

ϕ is the volume fraction of gas in the mixture; ϕ = (V / V mixture) * 100%;
100% = 1.
Initial mixture:
ϕ (A) = 0.01 * a,
ϕ (B) = (1 -0.01 * a)
V (A) = 0.01 * a * V l;
V (B) = (1-0.01 * a) * V l;
Excess A in the original mixture:
V (C) = V- 0.01 * a * V l;
V (A) = 0.01 * a * V – (V * (1 – 0.01 * a)) = 0.02 * a * V -V l;
V (total final mixture) = V – 0.01 * a * V + 0.02 * a * V – V = 0.01 * a * V l;
ϕ (C) = (V – 0.01 * a * V) / 0.01 * a * V;
ϕ (A) = (0.02 * a * V – V) / 0.01 * a * V.
Excess B in the original mixture:
V (C) = 0.01 * a * V l;
V (B) = V * (1 – 0.01 * a) – 0.01 * a * V = V – 0.02 * a * V l;
V (total volume of the final mixture) = 0.01 * a * V + V – 0.02 * a * V = V – 0.01 * a * V l;
ϕ (C) = 0.01 * a * V / (V – 0.01 * a * V);
ϕ (B) = V – 0.02 * a * V / (V – 0.01 * a * V).