A chemical reaction for the production of C and D by the reaction of A and B is shown below:
3 A+ 4 B⟶C+ 2 D
Assuming the un-normalized rate of production of D is r, write an expression for dnAdt in terms of r
To find the expression for dnAdt in terms of r, we need to use the stoichiometry of the chemical reaction. In this case, the stoichiometric coefficient of A is 3, which means that for every 3 moles of A reacted, we get 1 mole of C and 2 moles of D produced.
Based on the stoichiometry, we can express the rate of production of C and D in terms of the rate of consumption of A as follows:
Rate of production of C = (1/3) * dnAdt
Rate of production of D = (2/3) * dnAdt
Since the rate of production of D is given as r, we can write:
(2/3) * dnAdt = r
Now we can rearrange the equation to solve for dnAdt:
dnAdt = (3/2) * r
Therefore, the expression for dnAdt in terms of r is given by:
dnAdt = (3/2) * r