Parallel irreversible elementary reactions: X → Y with k1 and X → Z with k2. What is the rate of disappearance of species X?

Introduction / Context:
Parallel reactions are common when a reactant can follow multiple competing pathways. Knowing the overall consumption rate of the common reactant is essential for reactor sizing and selectivity analysis.

Given Data / Assumptions:

• Two elementary and irreversible channels: X → Y with rate r1 = k1 * CX and X → Z with rate r2 = k2 * CX.
• Isothermal, well mixed conditions; concentration of X is CX (denoted CA in options).
• No other consumption or production routes for X.

Concept / Approach:
For parallel first order steps in the same reactant, the total consumption rate is the sum of the individual rates because each pathway removes the same reactant molecules independently. Superposition applies to rates when pathways do not interact kinetically.

Step-by-Step Solution:
Write r_total = r1 + r2.Substitute r1 = k1 * CX and r2 = k2 * CX.Hence r_total = (k1 + k2) * CX.

Verification / Alternative check:
Dimension check: k1 and k2 have units of time^(-1) for first order; multiplying by concentration gives concentration per time, which matches the disappearance rate dimension.

Why Other Options Are Wrong:
Halving either constant or their sum has no basis; the pathways act simultaneously and independently, so the rates add without a factor of one half.

Common Pitfalls:
Confusing series reactions with parallel reactions or forgetting that selectivity depends on the ratio k1/k2, while the disappearance rate depends on k1 + k2.

Final Answer:
CA * (K1 + K2)