Calculate the instantaneous rate of the reaction at 30 s
Understand the Problem
The question is asking us to calculate the instantaneous rate of a chemical reaction at a specific time, which in this case is 30 seconds. This typically involves examining the concentration of reactants or products at that time, and possibly requires knowledge of the reaction's rate law or a provided concentration-time data set.
Answer
The instantaneous rate at $t = 30$ seconds can be approximated using concentrations at $t = 29$ and $t = 31$ seconds.
Answer for screen readers
The instantaneous rate at 30 seconds is estimated using the average of nearby concentrations.
Steps to Solve
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Identify the Data Determine the concentration of the reactant or product at the specific time, which is 30 seconds. If you have a table or graph of concentration over time, find the value corresponding to 30 seconds.
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Determine Nearby Concentrations To find the instantaneous rate, you will often need concentrations at time $t = 30$ seconds and at a nearby time, such as $t = 29$ seconds and $t = 31$ seconds, to calculate the slope of the tangent line.
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Calculate the Average Rate If you have concentrations from the previous step, calculate the average rate of change between those two nearby times. The formula for average rate is:
$$ \text{Average Rate} = \frac{C(t+1) - C(t-1)}{t+1 - (t-1)} $$
where $C(t)$ is the concentration at time $t$.
- Estimate the Instantaneous Rate To estimate the instantaneous rate at $t = 30$ seconds, use the average rate calculated above as a close estimate, or apply calculus by finding the derivative of the concentration function if available.
The instantaneous rate at 30 seconds is estimated using the average of nearby concentrations.
More Information
Instantaneous rates are important in kinetics as they reflect how quickly a reaction is happening at a specific moment in time. Knowing the instantaneous rate can help predict how changes in conditions could alter the reaction progress.
Tips
- Assuming that the instantaneous rate can be calculated using only one concentration value instead of nearby values.
- Failing to use the correct time intervals that are very close to the desired time.
