For the reaction 2 A(g) + B(g)->3 C(g), a. determine the expression for the rate of the reaction in terms of the change in concentration of each of the reactants and products. b. when A is decreasing at a rate of 0.100 M>s, how fast is B decreasing? How fast is C increasing?

Reaction stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is grounded in the balanced chemical equation, which ensures that atoms are conserved during the reaction.

For instance, the equation \(2 A(g) + B(g) \rightarrow 3 C(g)\) suggests that 2 moles of A react with 1 mole of B to produce 3 moles of C. This ratio must be maintained to ensure the reaction proceeds according to the equation. If we alter the amounts, the reaction may not complete fully or might result in leftover reactants.

Understanding stoichiometry is crucial because it dictates the proportions needed for a reaction to proceed optimally. This means, for educational purposes, we need to focus on the coefficients in the balanced equation, as these will tell us how the rates of consumption of the reactants and the rate of formation of the products are interrelated.

The rate of reaction expression relates the speed at which reactants are consumed and products are formed. It is a central concept in chemical kinetics, representing how quickly a chemical reaction occurs. To write the rate expression from the balanced equation, one must consider the stoichiometric coefficients, which are represented by the numbers in front of each chemical species in the balanced equation.

In our example \(2 A(g) + B(g) \rightarrow 3 C(g)\), the expression for the rate of the reaction would be \(\text{Rate} = -\frac{\Delta \lbrack A\rbrack}{2\Delta t} = -\frac{\Delta \lbrack B\rbrack}{\Delta t} = \frac{\Delta \lbrack C\rbrack}{3\Delta t}\) where \([\Delta X\rbrack\) represents the concentration change of substance X over time \(\Delta t\). Negative signs indicate consumption of reactants, while the absence of a negative sign indicates the formation of a product. Remember, rates of consumption are directly tied to reactant stoichiometry, and students should take note of the negative sign which is often a source of confusion but underscores the directionality of the reaction.

Concentration change over time is the rate at which the concentration of a substance in a reaction mixture increases or decreases as the reaction proceeds. It can be measured in mol/L/s or M/s, with negative values signifying a decrease and positive values an increase.

In our textbook exercise, when \(A\) is decreasing at \(0.100\text{ M/s}\), this is a quantitative measure of its consumption. By understanding the stoichiometry and ratios of the balanced equation, we can determine how the other substances are affected. Since \(B\) decreases at half the rate of \(A\) (due to stoichiometry, for every 2 moles of \(A\) consumed, 1 mole of \(B\) is consumed), its rate is \(0.050\text{ M/s}\). Similarly, the increase of \(C\) is one and a half times the rate of \(A\'s\) decrease, equating to \(0.150\text{ M/s}\).

This concept is crucial in predicting how fast a reactant is used up or a product is formed, which can influence practical applications such as determining the time required to complete a reaction, optimizing industrial processes, or calculating yield.