Consider the following hypothetical aqueous reaction: A(aq) → B(aq). A flask is charged with 0.065 mol of A in a total volume of 100.0 mL. The following data are collected: Time (min) 0 10 20 30 40 Moles of A 0.065 0.051 0.042 0.036 0.031 (b) Calculate the average rate of disappearance of A for each 10-min interval in units of M>s.

검증된 단계별 안내

insert step 1> Start by understanding that the average rate of disappearance of a reactant is calculated using the formula: \( \text{Rate} = -\frac{\Delta [A]}{\Delta t} \), where \( \Delta [A] \) is the change in concentration of A and \( \Delta t \) is the change in time.

insert step 2> Convert the moles of A to concentration in molarity (M) by dividing the moles by the volume of the solution in liters. Since the volume is 100.0 mL, convert it to liters by dividing by 1000, which gives 0.1 L.

insert step 3> Calculate the concentration of A at each time interval by dividing the moles of A by the volume in liters. For example, at time 0, the concentration is \( \frac{0.065 \text{ mol}}{0.1 \text{ L}} = 0.65 \text{ M} \). Repeat this for each time point.

insert step 4> For each 10-minute interval, calculate \( \Delta [A] \) by subtracting the concentration of A at the end of the interval from the concentration at the beginning of the interval.

insert step 5> Calculate the average rate of disappearance for each interval by dividing \( \Delta [A] \) by \( \Delta t \) (10 minutes converted to seconds, which is 600 seconds) and apply the negative sign to indicate disappearance.

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영상 길이:

11m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Molarity and Concentration

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. In this context, understanding molarity is crucial for calculating the concentration of reactants in the reaction. Since the total volume of the solution is given, we can convert moles of A into molarity to analyze its change over time.

Rate of Reaction

The rate of reaction refers to the change in concentration of a reactant or product per unit time. It is typically expressed in terms of molarity per second (M/s). In this question, calculating the average rate of disappearance of A involves determining how much the concentration of A decreases over specified time intervals, which is essential for understanding the kinetics of the reaction.

Average Rate Calculation

The average rate of a reaction over a time interval can be calculated using the formula: average rate = (change in concentration) / (change in time). For this problem, you will subtract the concentration of A at the end of each interval from its initial concentration and divide by the duration of the interval. This calculation provides insight into how quickly the reactant is consumed during the reaction.