The rate law for the reaction NO2(g) + CO(g) NO(g) + CO2(g) is Rate = k[NO2]2[CO]0. Which of the following reaction mixtures will have the fastest rate at a given temperature?
The correct answer and explanation is:
To determine which reaction mixture will have the fastest rate, we must examine how the rate law depends on the concentrations of the reactants.
Given Rate Law:
Rate=k[NO2]2[CO]0\text{Rate} = k[\text{NO}_2]^2[\text{CO}]^0
This tells us:
- The rate is second order with respect to NO₂ (it appears squared).
- The rate is zero order with respect to CO, meaning CO’s concentration does not affect the reaction rate.
- The rate constant k is constant at a given temperature.
Interpretation:
Since [CO]0=1[\text{CO}]^0 = 1, the rate simplifies to: Rate=k[NO2]2\text{Rate} = k[\text{NO}_2]^2
Therefore, the rate only depends on the concentration of NO₂. Increasing or decreasing [CO] will not change the rate.
Correct Answer:
The mixture with the highest concentration of NO₂ will have the fastest rate, regardless of the CO concentration.
Explanation (300 words):
The rate law for the reaction NO₂(g) + CO(g) → NO(g) + CO₂(g) is given as: Rate=k[NO2]2[CO]0\text{Rate} = k[\text{NO}_2]^2[\text{CO}]^0
This expression describes how the speed of the reaction is influenced by the concentrations of the reactants. The exponent on each concentration term shows the order with respect to that substance. In this case, the reaction is second-order with respect to NO₂, meaning that if the concentration of NO₂ is doubled, the rate of the reaction increases by a factor of 22=42^2 = 4. Conversely, the reaction is zero-order with respect to CO, which means the concentration of CO has no effect on the reaction rate.
This zero-order behavior occurs when CO is in excess or not involved in the rate-determining step. The reaction mechanism likely includes an initial slow step involving NO₂ alone, which governs the overall reaction speed.
Because the rate is directly proportional to [NO2]2[\text{NO}_2]^2, the fastest rate will occur in the reaction mixture that has the highest concentration of NO₂. For example, if you’re given several choices of mixtures with varying concentrations of NO₂ and CO, you should select the one with the highest [NO₂]. Even if CO is completely absent or doubled in other choices, it will not change the rate due to its zero-order impact.
Understanding how rate laws work is essential in chemical kinetics, as it helps chemists optimize reaction conditions to speed up or control chemical processes effectively.