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Chapter 10: Problem 31

The rate constant of a reaction depends on (a) extent of reaction (b) time of reaction (c) temperature (d) initial concentration of the reactants

Short Answer

Expert verified
Temperature affects the rate constant; thus, the answer is (c) temperature.

Step by step solution

01

Understanding the Rate Constant

The rate constant is a part of the rate law equation for a chemical reaction, usually represented by the symbol 'k'. It is specific to a particular reaction at a given temperature.
02

Factors Affecting the Rate Constant

The rate constant can be affected by the temperature. An increase in temperature usually increases the rate constant, according to the Arrhenius equation. This is because higher temperatures provide more energy to overcome the activation energy barrier.
03

Evaluating Other Factors

The extent of reaction, time, and initial concentration of the reactants do not directly affect the rate constant. These factors influence the rate of reaction but do not change the rate constant itself, since it is independent of concentration and extent of reaction.
04

Conclusion

Based on the analysis, the rate constant of a reaction is dependent on temperature, making option (c) the correct answer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Arrhenius Equation
The Arrhenius equation is crucial in understanding how temperature affects the rate constant of a chemical reaction. It mathematically illustrates the relationship between the rate constant \( k \) and temperature \( T \). The equation is expressed as:\[ k = A \cdot e^{-\frac{E_a}{RT}} \]where:
  • \( k \) is the rate constant.
  • \( A \) is the pre-exponential factor, a constant specific to each chemical reaction.
  • \( E_a \) is the activation energy, the minimum energy needed for the reaction to occur.
  • \( R \) is the universal gas constant.
  • \( T \) is the temperature in Kelvin.
The Arrhenius equation shows that \( k \) changes exponentially with temperature. As the temperature rises, molecules gain energy, increasing the chance of successful collisions that can lead to a reaction. Understanding this equation helps in predicting how fast a reaction will proceed under different temperatures.
Chemical Reactions
Chemical reactions involve the transformation of reactants into products, typically involving the breaking and making of chemical bonds. These processes can vary greatly in speed, from rapid, explosive reactions to those that occur so slowly they seem imperceptible.The rate of a chemical reaction is influenced by several factors, including:
  • The nature of the reactants: Different substances react at different rates.
  • The presence of a catalyst: Catalysts can significantly speed up reactions without being consumed.
  • Concentration of reactants: A higher concentration usually means more frequent collisions leading to faster reactions.
  • Temperature: As explained by the Arrhenius equation, higher temperatures increase reaction rates.
Each reaction is characterized by a rate law, which is an equation that relates the rate of reaction to the concentration of its reactants, often involving the rate constant \( k \). Understanding these factors is key in the study and application of chemical reactions in both laboratory and industrial settings.
Temperature Effect on Reactions
Temperature has a profound impact on the rates of chemical reactions. It's one of the primary factors influencing the rate constant, as heightened temperatures typically increase reaction rates. Here's why temperature has such an effect:
  • Increased molecular energy: With higher kinetic energy, molecules move faster and collide more frequently.
  • Overcoming activation energy: Higher temperatures provide energy to overcome the activation energy barrier, facilitating more successful reactions.
  • Exponentially increased rate constant: As per the Arrhenius equation, the rate constant increases exponentially as temperature rises. This means even a small temperature increase can lead to a significant rise in reaction rates.
Thus, controlling temperature is crucial in industrial processes to optimize reaction rates and efficiency. By doing so, chemists and engineers can ensure reactions proceed at a desired rate, balancing speed with safety and cost-effectiveness.

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Most popular questions from this chapter

In a chemical reaction two reactants take part. The rate of reaction is directly proportional to the concentration of one of them and inversely proportional to the concentration of the other. The order of reaction is (a) 0 (b) 1 (c) 2 (d) 4

The rate constant, the activation energy and the Arrhenius parameter of a chemical reaction at \(25^{\circ} \mathrm{C}\) are \(3.0 \times 10^{-4} \mathrm{~s}^{-1}, 104.4 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(6 \times 10^{14} \mathrm{~s}^{-1}\) respectively. The value of the rate constant as \(\mathrm{T} \longrightarrow \infty\) is (a) \(2.0 \times 10^{18} \mathrm{~s}^{-1}\) (b) \(6.0 \times 10^{14} \mathrm{~s}^{-1}\) (c) infinity (d) \(3.6 \times 10^{30} \mathrm{~s}^{-1}\)

In the first-order reaction, half of the reaction is com pleted in 100 seconds. The time for \(99 \%\) reaction to occur will be (a) \(664.64 \mathrm{~s}\) (b) \(646.6 \mathrm{~s}\) (c) \(660.9 \mathrm{~s}\) (d) \(654.5 \mathrm{~s}\)

The reaction \(\mathrm{A} \longrightarrow \mathrm{B}\) follows first order kinetics. The time taken for \(0.8\) mole of \(\mathrm{A}\) to produce \(0.6\) mole of is 1 hour. What is the time taken for conversion of \(0.9\) mole of A to produce \(0.675\) mole of \(\mathrm{B} ?\) (a) 2 hour (b) 1 hour (c) \(0.5\) hour (d) \(0.25\) hour

When the temperature of a reaction increases from \(27^{\circ} \mathrm{C}\) to \(37^{\circ} \mathrm{C}\), the rate increases by \(2.5\) times, the activation energy in the temperature range is (a) \(70.8 \mathrm{~kJ}\) (b) \(7.08 \mathrm{~kJ}\) (c) \(35.8 \mathrm{~kJ}\) (d) \(14.85 \mathrm{~kJ}\)
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