Final answer:
To write equations for the rates of reactions, you use the stoichiometry of the chemical equation and differentiate the concentration with respect to time. In a graph, linear relationships are often represented by y = b + mx, while non-linear relationships require different equations.
Step-by-step explanation:
To write equations that relate the rates of consumption of the reactants and the rates of formation of the products in a chemical reaction, you need to consider the stoichiometry of the reaction. For a balanced chemical equation, the relationship between the rates of consumption and formation is derived from the coefficients of the reactants and products. For example, consider a reaction represented by the equation:
aA + bB → cC + dD
The rate at which A is consumed is given by the equation:
Rate of consumption of A = -1/a (d[A]/dt)
And the rate of formation of C would be:
Rate of formation of C = 1/c (d[C]/dt)
In the context of expressing equations graphically, the linear equation y = b + mx can represent a straight-line relationship between two variables in a graph form. This may be applicable to various concepts in physics and chemistry where a straight-line relationship exists.
For instance, the equation y = (2.0 km/min) t + 0 reflects a direct, linear relationship between distance traveled (y) and time (t) with a slope (m) representing the speed (2.0 km/min) and an intercept (b) of 0. In non-linear relationships such as quadratic or inverse relationships, other forms of equations are used to depict the relationship between variables.