Question

The volume of a microbial culture is observed to increase according to the formula (V(cm³) = eʰ) where (h) is time in seconds.

(a) Calculate the expression for (V(in.³)) in terms of (h).
(b) Both the exponential function and its argument must be dimensionless. The given equation seems to violate both of these rules, and yet the equation is valid. Explain this paradox. (Hint: Observe the result of part (a).

A concentration (C (mol/L)) varies with time (min) according to the equation (C = 3.00 exp (-2000) (incomplete)

Answer 1

The expression for V(in.³) can be calculated by converting the volume from cm³ to in³. The given equation appears to violate the rules of dimensionality, but it can be resolved by converting the units appropriately.

Step-by-step explanation:

(a) To calculate the expression for V(in.³) in terms of h, we need to convert the volume from cm³ to in³. Since 1 in = 2.54 cm, we can use this conversion factor to convert the volume:

V(in.³) = V(cm³) / (2.54³)

Substituting the given equation, we have:

V(in.³) = (eʰ) / (2.54³)

(b) The exponential function and its argument are usually dimensionless. However, in this case, we have the volume expressed in cm³. The paradox is resolved by converting the volume from cm³ to in³, as shown in part (a), which results in a valid equation.