Final answer:
To convert an equation to the natural base, use the identity bn = en(lnb), which translates the base to e (approximately 2.7183) by using the properties of logarithms and exponentials.
Step-by-step explanation:
To convert an equation with a base other than the natural base (e) into terms of the natural base, you can use the identity bn = en(lnb). This identity expresses base b raised to the power n as the natural exponential function raised to the product of n and the natural logarithm of b.
This conversion uses the important mathematical relationship that logarithms of different bases can be converted using change of base formulas.
For instance, considering an equation M = b to the power n, you can rewrite this as M = en(lnb) by first taking the natural log of both sides (ln) to get nlnb and then raising both sides as powers of e. This effectively translates the equation into terms of the natural base, e, which is approximately equal to 2.7183.
In the context of chemistry, the pKb and pKa values relate to the strength of bases and acids, respectively. For weak bases, the relationship between Kb and the Ka of its conjugate acid is given by Ka × Kb = 1.0 × 10^-14.