Consider the reaction: 2 H2O2(aq) → 2 H2O(l) + O2(g). The graph shows the concentration of H2O2 as a function of time. Use the graph to calculate each quantity: a. the average rate of the reaction between 10 and 20 seconds, b. the instantaneous rate of the reaction at 30 seconds.

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1. <insert step 1: Identify the relevant data from the graph for the time intervals specified. For part (a), note the concentration of H2O2 at 10 seconds and at 20 seconds. For part (b), note the concentration of H2O2 at 30 seconds.>
2. <insert step 2: For part (a), calculate the change in concentration of H2O2 over the time interval from 10 to 20 seconds. This is done by subtracting the concentration at 20 seconds from the concentration at 10 seconds.>
3. <insert step 3: For part (a), calculate the average rate of the reaction by dividing the change in concentration by the change in time (20 seconds - 10 seconds). The average rate is given by the formula: \( \text{Average rate} = -\frac{\Delta [\text{H}_2\text{O}_2]}{\Delta t} \).>
4. <insert step 4: For part (b), to find the instantaneous rate at 30 seconds, determine the slope of the tangent to the curve at 30 seconds. This can be done by drawing a tangent line at 30 seconds and calculating its slope, which is \( -\frac{d[\text{H}_2\text{O}_2]}{dt} \).>
5. <insert step 5: Interpret the results: The average rate gives an overall rate of reaction over a time interval, while the instantaneous rate provides the rate at a specific moment in time.>