Verify your calculations for the rate. Are you reporting your data with the correct number of significant figures?
| Concentration of iodide anion solution (mM) | 20.1 | 20.1 |
| :------------------------------------------ | :---- | :---- |
| Concentration of thiosulfate anion solution (mM) | 176.0 | 176.0 |
| Concentration of hydrogen peroxide solution (mM) | 20.0 | |
| Temperature of iodide anion solution (${ }^{\circ} C$ ) | 10.0 | |
| Volume used of iodide anion solution ($I ^{-}$)(mL) | 1.0 | |
| Volume used of hydrogen peroxide solution ($H _2 O _2$ )( $m _{1+1} y _{11}$ and $y _1$. | 8.8 | |
| Time (s) | | |
| Observations | | |
| Initial concentration of iodide anion in the reaction (mM) | 47.6 | |
| Initial concentration of thiosulfate anion in the reaction (mM) | 0.96 | |
Answer (2)
The rate of the reaction can be calculated as 0.11 mM/s using the formula, given the significant figures from the concentrations and time involved. Both initial concentration values have 2 significant figures, which is consistent with the calculated rate. Therefore, the reported rate should be stated as 0.11 mM/s with the correct significant figures.
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Calculate the rate of the reaction: R a t e = 8.8 s 0.96 mM = 0.109090909... mM/s
Determine the number of significant figures: Both 0.96 and 8.8 have two significant figures.
Round the calculated rate to two significant figures: R a t e ≈ 0.11 mM/s
The rate should be reported with two significant figures.
0.11 mM/s
Explanation
Problem Analysis We are asked to verify the calculations for the rate of a reaction and to check if the data is reported with the correct number of significant figures. We are given the initial concentration of thiosulfate anion as 0.96 mM and the time as 8.8 s. The rate is calculated as the change in concentration divided by the change in time.
Rate Calculation The rate of the reaction can be calculated using the formula: R a t e = Change in Time Change in Concentration = Δ t Δ [ S 2 O 3 2 − ] In this case, the change in concentration of thiosulfate is 0.96 mM, and the time is 8.8 s. Therefore, R a t e = 8.8 s 0.96 mM
Numerical Result Calculating the rate: R a t e = 8.8 0.96 = 0.109090909... mM/s
Significant Figures Now, let's consider significant figures. The initial concentration of thiosulfate (0.96 mM) has two significant figures, and the time (8.8 s) also has two significant figures. Therefore, the rate should be reported with two significant figures. Rounding the calculated rate (0.109090909... mM/s) to two significant figures gives us 0.11 mM/s.
Verification Comparing the calculated rate with the reported rate: The calculated rate, rounded to the correct number of significant figures, is 0.11 mM/s. The problem statement does not explicitly state the calculated rate, so we can only verify if the number of significant figures is correct. Since both given values have two significant figures, the answer should also have two significant figures.
Final Answer The rate of the reaction is calculated to be 0.11 mM/s, considering the significant figures. Therefore, the rate should be reported with two significant figures.
Examples
Understanding reaction rates is crucial in many real-world applications. For instance, in pharmaceutical development, knowing the rate at which a drug degrades helps determine its shelf life and efficacy. Similarly, in environmental science, reaction rates are used to model the breakdown of pollutants in the atmosphere or water. By accurately calculating and reporting reaction rates, scientists and engineers can make informed decisions and predictions in various fields.
