A student conducts an experiment to determine the order of reaction for the oxidation of a purple dye. The reaction is determined to be first-order and the half- life is 420 seconds. What is the rate constant, k? k = [?] x 10 [?] S-1 exponent (yellow) coefficient (green) Enter

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**Title: Determination of Rate Constant of a First-Order Reaction**

**Introduction:**
In this experiment, a student is tasked with identifying the reaction order of the oxidation of a purple dye. The reaction is determined to be first-order, and the half-life observed is 420 seconds. 

**Objective:**
To calculate the rate constant \( k \) for the first-order reaction using the given half-life.

**Problem Statement:**
A student conducts an experiment to determine the order of reaction for the oxidation of a purple dye. The reaction is determined to be first-order and the half-life is 420 seconds. What is the rate constant, \( k \)?

**Formula:**
The rate constant \( k \) for a first-order reaction can be calculated using the formula:
\[ k = \frac{\ln(2)}{t_{1/2}} \]

where:
- \( \ln(2) \) is the natural logarithm of 2 (approximately 0.693).
- \( t_{1/2} \) is the half-life of the reaction.

**Calculation:**
Given that the half-life \( t_{1/2} \) is 420 seconds, we can substitute this value into the formula.

\[ k = \frac{0.693}{420 \text{ s}} \]

**Rate Constant:**
After performing the calculation, the rate constant \( k \) is determined to be approximately: 
\[ k = 1.65 \times 10^{-3} \text{ s}^{-1} \]

**Interactive Element:**
Below this problem description, there may be an interactive element on the educational website where students can input their calculated values:

\[ k = \]
\[ [ \text{Enter your coefficient (green)} ] \times 10^{ [ \text{Enter your exponent (yellow)} ]} \text{ s}^{-1} \]
\[ \text{Enter} \]

**Conclusion:**
Understanding the rate constant of a reaction provides insight into the reaction kinetics and how the concentration of reactants decreases over time. This experiment helps students to practically apply the integrated rate law for first-order reactions and reinforces the concept of half-life in the context of chemical kinetics.
Transcribed Image Text:**Title: Determination of Rate Constant of a First-Order Reaction** **Introduction:** In this experiment, a student is tasked with identifying the reaction order of the oxidation of a purple dye. The reaction is determined to be first-order, and the half-life observed is 420 seconds. **Objective:** To calculate the rate constant \( k \) for the first-order reaction using the given half-life. **Problem Statement:** A student conducts an experiment to determine the order of reaction for the oxidation of a purple dye. The reaction is determined to be first-order and the half-life is 420 seconds. What is the rate constant, \( k \)? **Formula:** The rate constant \( k \) for a first-order reaction can be calculated using the formula: \[ k = \frac{\ln(2)}{t_{1/2}} \] where: - \( \ln(2) \) is the natural logarithm of 2 (approximately 0.693). - \( t_{1/2} \) is the half-life of the reaction. **Calculation:** Given that the half-life \( t_{1/2} \) is 420 seconds, we can substitute this value into the formula. \[ k = \frac{0.693}{420 \text{ s}} \] **Rate Constant:** After performing the calculation, the rate constant \( k \) is determined to be approximately: \[ k = 1.65 \times 10^{-3} \text{ s}^{-1} \] **Interactive Element:** Below this problem description, there may be an interactive element on the educational website where students can input their calculated values: \[ k = \] \[ [ \text{Enter your coefficient (green)} ] \times 10^{ [ \text{Enter your exponent (yellow)} ]} \text{ s}^{-1} \] \[ \text{Enter} \] **Conclusion:** Understanding the rate constant of a reaction provides insight into the reaction kinetics and how the concentration of reactants decreases over time. This experiment helps students to practically apply the integrated rate law for first-order reactions and reinforces the concept of half-life in the context of chemical kinetics.
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