From your knowledge of X and Y in the equation (as well as the rate in a given experiment from your graph) calculate k from your data

From your knowledge of X and Y in the equation (as well as the rate in a given experiment from your graph) calculate k from your data. Rate= K[I^-]^x [S2O8^2-]^y
Using the pictures of the trials given, I need help answering this question.

1.From your knowledge of X and Y in the equation (as well as the rate in a given experiment from your graph) calculate k from your data.
Rate= K[I^-]^x [S2O8^2-]^y

3 4 5 6 7 Time (s) between appearances of color 147(5) 180 (5) 203 (5) 199 (5) Aliquot no. 1 2 3 4 5 6 7 Time (s) between appearances of color Cumulative times (s) 147 0 327 (5) 530 (5) 724 (5) 927 (5) 1134 (5) 1400 (5) Solution 1 4,7 x Solution 2,0XS -203 (52 -207 (5) 266 (5) Solution 4. Initial [Sâ‚‚0g2-] = 0.10 M; initial [I] = 0.025 M. Time experiment started g Cumulative times (s) Total moles of 2- Sâ‚‚O² consumed 2.0×104 4.0×104 6.0×104 3. What effect does changing the [Sâ‚‚O82] have on the reaction? Increases by about 2 8.0×10-4 10.×10-4 12×10-4 14×104 4. Write the rate law for this reaction that is consistent with your data. Rate = K[[ ] [â‚�â‚‚â‚‚] Calculations 1. Rate of reaction, A[Sâ‚‚O2-]/At, as calculated from graphs (that is, from slopes of lines): -6 Solution 3.0 X105 Solution 4 Total moles of 2- Sâ‚‚O² consumed 2.0×10 4 4.0×10-4 6.0×10-4 8.0×10-4 10.×104 12×10-4 14×10-4 2. What effect does doubling the concentration of I have on the rate of this reaction? abat Jolle Decreases by about 2 skond 31 de onsdag

The Correct Answer and Explanation is :

To calculate the rate constant ( k ) in the rate law for the reaction, we need to use the given rate law and the data from the trials.

Step-by-Step Process:

  1. Write the Rate Law:
    The general rate law is given by:
    [
    \text{Rate} = k [I^-]^x [S_2O_8^{2-}]^y
    ]
    Here, ( x ) and ( y ) are the reaction orders with respect to ( [I^-] ) and ( [S_2O_8^{2-}] ), respectively. These can be determined experimentally, likely from previous steps.
  2. Determine the Exponents ( x ) and ( y ):
    From the problem setup, it is likely that you are given or have determined the values of ( x ) and ( y ) (reaction orders). In the problem, you may need to use the changes in concentrations and corresponding changes in rates to determine ( x ) and ( y ). For example, doubling the concentration of ( I^- ) or ( S_2O_8^{2-} ) and observing how the rate changes helps you find these exponents.
  3. Calculate the Rate Constant ( k ):
    Once the values of ( x ) and ( y ) are known, select one set of trial data where you know the initial concentrations of ( [I^-] ) and ( [S_2O_8^{2-}] ), as well as the corresponding rate. Use these values in the rate law formula to solve for ( k ). For example, using data from Trial 1:
    [
    \text{Rate}_1 = k [I^-]^x [S_2O_8^{2-}]^y
    ]
    Rearranging to solve for ( k ):
    [
    k = \frac{\text{Rate}_1}{[I^-]^x [S_2O_8^{2-}]^y}
    ]
    Substitute the values from the trial data (rate, concentrations) to find ( k ).
  4. Interpretation of Data:
  • Effect of Changing ( [S_2O_8^{2-}] ): Doubling the concentration of ( S_2O_8^{2-} ) increases the reaction rate, suggesting that the reaction order with respect to ( S_2O_8^{2-} ) (i.e., ( y )) is positive. From the graph, you can observe how the rate changes with increasing ( [S_2O_8^{2-}] ) and use this information to confirm ( y ).
  • Effect of Changing ( [I^-] ): Doubling the concentration of ( I^- ) likely increases the reaction rate, so the order with respect to ( I^- ) (i.e., ( x )) is also positive. You can confirm this by examining how the rate changes with ( [I^-] ).
  1. Rate Law Consistency:
    Finally, verify that the calculated rate constant ( k ) is consistent across all trials. If it is, your rate law and exponents ( x ) and ( y ) are correct.

Final Answer:

The rate constant ( k ) can be calculated from the rate law using the concentrations and the reaction rate from a chosen trial. Make sure to determine the correct reaction orders ( x ) and ( y ) by analyzing how the rate changes with changes in concentration. After finding ( k ), you can confirm it using data from multiple trials.

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