Problem 140 - Chemistry: An Atoms-Focused Approach

Question

In the presence of \(\mathrm{O}_{2}\) NO reacts with sulfur-containing proteins to form S-nitrosothiols, such as \(\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{SNO} .\) This compound decomposes to form a disulfide and \(\mathrm{NO}\) $$2 \mathrm{C}_{6} \mathrm{H}_{13} \mathrm{SNO}(a q) \rightarrow 2 \mathrm{NO}(g)+\mathrm{C}_{12} \mathrm{H}_{26} \mathrm{S}_{2}(a q)$$ The following data were collected for the decomposition reaction at \(69^{\circ} \mathrm{C}\) $$\begin{array}{cc}\text { Time (min) } & {\left[\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{SNO}\right](\mathrm{M})} \\\0 & 1.05 \times 10^{-3} \\\\\hline 10 & 9.84 \times 10^{-4} \\\\\hline 20 & 9.22 \times 10^{-4} \\\\\hline 30 & 8.64 \times 10^{-4} \\\\\hline 60 & 7.11 \times 10^{-4} \\\\\hline\end{array}$$ Calculate the value of the first-order rate constant for the reaction.

Step-by-Step Solution

Answer

Question: Calculate the first-order rate constant for the decomposition of S-nitrosothiols using the given initial concentration of 1.05 x 10^-3 M and final concentration of 8.64 x 10^-4 M after 30 minutes. Answer: The first-order rate constant for the decomposition of S-nitrosothiols is 6.40 × 10^-3 min^-1.

Step 1: Choose the two data points to use

We will use the time intervals 0 and 30 min, with the respective concentrations of \([\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{SNO}]_{0} = 1.05 \times 10^{-3}\,\mathrm{M}\) and \([\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{SNO}] = 8.64 \times 10^{-4}\,\mathrm{M}\).

Step 2: Calculate the rate constant (\(k\))

Plug in the values of initial and final concentration along with time into the equation to calculate \(k\): $$k = \frac{\ln \frac{1.05 \times 10^{-3}}{8.64 \times 10^{-4}}}{30 \ min}$$ $$k = \frac{\ln (1.2148)}{30 \ min}$$ $$k = \frac{0.192}{30 \ min}$$ $$k = 6.40 × 10^{-3}\, \mathrm{min^{-1}}$$ The value of the first-order rate constant for the decomposition reaction is \(k = 6.40 × 10^{-3}\, \mathrm{min^{-1}}\).

Key Concepts

Rate Constant

The rate constant, often denoted by the symbol \( k \), is a fundamental parameter in the study of chemical kinetics. It provides a quantitative measure of the speed at which a chemical reaction proceeds. In the case of first-order reactions, the rate constant is particularly important because it allows us to understand the dependence of reaction rate on the concentration of a single reactant.

For the reaction in question—S-nitrosothiol decomposition—the rate constant helps us quantify how quickly the compound decomposes into its products at a given temperature. The formula to find the rate constant \( k \) for a first-order reaction is:

• \( k = \frac{\ln \left( \frac{[A]_0}{[A]} \right)}{t} \)

Here, \([A]_0\) is the initial concentration, \([A]\) is the concentration at time \( t \), and \( t \) is the time interval. By inserting our known concentration values and time into this equation, we find the rate constant to be \( k = 6.40 \times 10^{-3} \text{ min}^{-1} \).

Understanding the rate constant helps us predict how long it takes for reactants to convert to products, which is immensely useful in both laboratory and industrial settings.

Chemical Kinetics

Chemical kinetics is the branch of chemistry that investigates the rates of chemical reactions and the factors affecting them. It explores how different variables, like concentration, temperature, and pressure, influence the speed of reactions.

For first-order reactions like S-nitrosothiol decomposition, kinetics focuses on how the rate of reaction depends on the concentration of one reactant. This simplicity enables accurate predictions about reaction progress over time.

In the specific case of chemical kinetics involving S-nitrosothiols, one key feature is that changes in the concentration of the compound over time follow a predictable logarithmic pattern. This is because the rate of reaction is directly proportional to the concentration of the reactant at any given moment.

Measuring the rate constant, as we computed earlier, helps to describe the kinetics of these reactions under specific conditions. This understanding can be extended to model complex biological processes where S-nitrosothiol plays a role, allowing chemists to manipulate conditions to achieve desired reaction speeds.

S-nitrosothiol Decomposition

S-nitrosothiols are a group of compounds formed when nitric oxide (NO) reacts with thiol groups in proteins. These compounds have significant biological relevance, particularly because of their ability to modulate various signaling pathways in the body.

The decomposition of S-nitrosothiols, such as \(\text{C}_6 \text{H}_{13} \text{SNO}\), is a crucial reaction that regenerates nitric oxide—an important cellular signaling molecule—and forms disulfides. The reaction can be represented as:

• \(2 \text{C}_6 \text{H}_{13} \text{SNO} (aq) \rightarrow 2 \text{NO} (g) + \text{C}_{12} \text{H}_{26} \text{S}_2 (aq)\)

This decomposition reaction is significant not only because of its chemical interest but also due to its implications in physiological processes.

Studying such decomposition reactions helps scientists understand how the balance of S-nitrosothiols affects cellular functions. It also provides insights into designing therapeutic strategies targeting nitric oxide pathways, highlighting its broader impact beyond the laboratory.