Question

For the reaction, \(2 A+B \longrightarrow 3 C\), it was found that the rate of disappearance of \(B\) was \(0.30 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\). What were the rates of disappearance of \(A\) and the rate of appearance of \(C\) ?

Short answer

The rate of disappearance of \(A\) is \(0.60 \, \mathrm{mol} \, \mathrm{L}^{-1} \, \mathrm{s}^{-1}\) and the rate of appearance of \(C\) is \(0.90 \, \mathrm{mol} \, \mathrm{L}^{-1} \, \mathrm{s}^{-1}\).

Step-by-step solution

Understanding the stoichiometry of the reaction

The given chemical reaction is \(2 A + B \longrightarrow 3 C\). According to the stoichiometry of the reaction, two moles of \(A\) react with one mole of \(B\) to produce three moles of \(C\).

Calculating the rate of disappearance of \(A\)

The rate of disappearance of \(B\) is given as \(0.30 \, \mathrm{mol} \, \mathrm{L}^{-1} \, \mathrm{s}^{-1}\). For every mole of \(B\) that disappears, two moles of \(A\) will disappear, since the stoichiometric coefficient of \(A\) is twice that of \(B\). To find the rate of disappearance of \(A\), we multiply the rate of disappearance of \(B\) by 2: \[ \text{Rate of disappearance of } A = 2 \times 0.30 \, \mathrm{mol} \, \mathrm{L}^{-1} \, \mathrm{s}^{-1} \]

Calculating the rate of appearance of \(C\)

Similarly, for every mole of \(B\) that disappears, three moles of \(C\) are produced. To find the rate of appearance of \(C\), we multiply the rate of disappearance of \(B\) by 3: \[ \text{Rate of appearance of } C = 3 \times 0.30 \, \mathrm{mol} \, \mathrm{L}^{-1} \, \mathrm{s}^{-1} \]

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Therefore, the amount of each element must be the same in the products as it is in the reactants.

This relationship is represented by a balanced chemical equation, which indicates the proportions of reactants and products involved. For example, in the reaction \(2 A + B \longrightarrow 3 C\), the coefficients 2, 1, and 3 tell us the ratio of moles of each substance that react or are formed. Understanding these ratios is crucial when calculating the rates of disappearance and appearance of substances in a chemical reaction.

In practice, stoichiometry allows us to predict how much of a product will form from a certain amount of reactants or how much of a reactant is needed to create a desired amount of product. It is a fundamental concept for anyone studying or working in the field of chemistry, as it is applied in everything from laboratory experiments to industrial processes.

Rate of Disappearance

The 'rate of disappearance' in a chemical reaction refers to the speed at which a reactant is consumed as the reaction proceeds. It is an important aspect when studying reaction kinetics, which is the study of the rates of chemical processes.

To determine the rate of disappearance of a reactant, you must measure how much of the substance is used up over a certain period. This rate is typically expressed in units of concentration per unit time, such as mol/L/s. In our example reaction \(2 A + B \longrightarrow 3 C\), when we say that the rate of disappearance of \(B\) is \(0.30 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\), it means that 0.30 moles of \(B\) are used up every second in each liter of the reaction mixture.

The rate of disappearance is essential for calculating other reaction rates and designing reactions with desired speeds. This concept is not only vital in academic studies but is also applied extensively in various industries where controlling the speed of a reaction can affect the quality and yield of a product.

Rate of Appearance

Conversely to the rate of disappearance, the 'rate of appearance' measures how quickly a product forms in a chemical reaction. This rate is crucial for understanding and controlling chemical processes because it helps us determine how long it will take for a product to reach a certain concentration.

The rate of appearance is also expressed in concentration per unit time, like mol/L/s. For every mole of a reactant that disappears in the time of the reaction, a specific number of moles of a product will appear, according to the stoichiometry of the reaction. In our example \(2 A + B \longrightarrow 3 C\), for each mole of \(B\) that disappears, three moles of \(C\) appear.

Using the provided rate of disappearance for \(B\), and knowing that three moles of \(C\) are formed for each mole of \(B\) that reacts, we can calculate the rate of appearance for \(C\). Such calculations are important for determining the productivity of a chemical reaction and for scaling reactions up from a laboratory to an industrial scale, where accurate yields are essential.