Question

Consider the reaction: $$ 8 \mathrm{H}_{2} \mathrm{~S}(g)+4 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{S}_{8}(g) $$ Complete the table. $$ \begin{array}{lllll} \Delta\left[\mathrm{H}_{2} S\right] / \Delta t & \Delta\left[\mathrm{O}_{2}\right] / \Delta t & \Delta\left[\mathrm{H}_{2} \mathrm{O}\right] / \Delta t & \Delta\left[\mathrm{S}_{8}\right] / \Delta t & \text { Rate } \\ -0.080 \mathrm{M} / \mathrm{s} & & & & \\ \hline \end{array} $$

Short answer

The change in concentrations per time are \( \Delta[O2] / \Delta t = -0.040 \, M/s \), \( \Delta[H2O] / \Delta t = 0.080 \, M/s \) and \( \Delta[S8] / \Delta t = 0.010 \, M/s \) with the reaction rate being \( 0.080 \, M/s \) in terms of the consumption of H2S.

Step-by-step solution

Determine the change in concentration of O2

The stoichiometric ratio between H2S and O2 is 8 : 4. Use this ratio to find the rate of change of O2: if \( \Delta[H2S] / \Delta t = -0.080 \, M/s \) then \( \Delta[O2] / \Delta t = \frac{4}{8} \cdot \Delta[H2S] / \Delta t \)

Calculate the change in concentration of O2

Perform the calculation \( \Delta[O2] / \Delta t = \frac{4}{8} \cdot (-0.080 \, M/s) = -0.040 \, M/s \) as the rate of change of O2 concentration.

Determine the change in concentration of H2O

The stoichiometric ratio between H2S and H2O is 1:1. So the rate of change of H2O concentration will be equal in magnitude and opposite in sign to the rate of change of H2S concentration: \( \Delta[H2O] / \Delta t = - \Delta[H2S] / \Delta t = 0.080 \, M/s \).

Determine the change in concentration of S8

The stoichiometric ratio between H2S and S8 is 8:1. For every 8 moles of H2S consumed, 1 mole of S8 is formed. So \( \Delta[S8] / \Delta t = \frac{1}{8} \cdot \Delta[H2S] / \Delta t \) in terms of magnitude and with a positive sign, since S8 is being produced.

Calculate the change in concentration of S8

Perform the calculation \( \Delta[S8] / \Delta t = \frac{1}{8} \cdot (-0.080 \, M/s) = -0.010 \, M/s \). However, since S8 is being produced, we take the absolute value, \( \Delta[S8] / \Delta t = 0.010 \, M/s \) as the rate of change of S8 concentration.

Write the rate of the reaction

The rate of the reaction can be expressed using any of the reactants or products. Typically, the rate is expressed in terms of the consumption of a reactant, so we can use H2S: \( Rate = - \Delta[H2S] / \Delta t = 0.080 \, M/s \) since reaction rates are expressed as positive values.

Key concepts

Understanding Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the quantitative relationship between reactants and products in a chemical reaction. It's like a recipe that tells you how much of each ingredient you need to create a certain product.

For a balanced chemical equation, stoichiometry provides the proportions of each substance involved. For example, in the reaction given at the start, $$8 \text{H}_2\text{S}(g) + 4 \text{O}_2(g) \longrightarrow 8 \text{H}_2\text{O}(g) + \text{S}_8(g)$$the stoichiometric ratios tell us that 8 moles of hydrogen sulfide react with 4 moles of oxygen to produce 8 moles of water and 1 mole of sulfur. These ratios are crucial when calculating how concentration changes impact each species in the reaction over time.

By understanding the stoichiometry of a reaction, students can predict the amounts of reactants consumed and products formed, which is particularly useful in laboratory settings and industrial applications where precise quantities are necessary for reactions to occur successfully.

Concentration Change Over Time

Monitoring the concentration change over time is essential in understanding the progress of a chemical reaction. As a reaction proceeds, reactants are converted into products, causing their concentrations to change at rates that can be measured.

To quantify this, chemists use the rate of change in concentration, expressed as moles per liter per second (M/s). In the solution provided, you can see that the change in concentration of hydrogen sulfide (H2S) is given, and using stoichiometry, the changes in the other substances are calculated.

It's important to note that in a reaction, the concentration of reactants typically decreases over time, while the concentration of products increases. This is reflected in the sign of the concentration change: a negative sign for reactants (indicating a decrease) and a positive sign for products (indicating an increase). The ability to determine and understand these changes helps chemists control and optimize reactions.

Rate of Reaction

The rate of a reaction is a measure of how quickly reactants are converted into products. It's an essential part of understanding chemical kinetics, which is the study of reaction rates and mechanisms. A higher reaction rate means that the substances react quickly, while a lower rate indicates a slower reaction.

In our case, the rate of reaction is reported as a positive value, which commonly represents the speed at which a reactant is consumed or a product is formed. The rate can be determined by monitoring the concentration change of any one reactant or product over time. However, when comparing rates using different substances, it's important to take into account their stoichiometric coefficients from the balanced chemical equation.

Enhancing the rate of reaction can be achieved through different means, such as increasing the temperature, utilizing catalysts, or changing reactant concentrations. Understanding how to control reaction rates is vital in many fields, from manufacturing to environmental science, where fast and efficient reactions may be necessary.