Principle underlying Bohr's equation for calculating total dead space

[E.S.Prakash]

Lim Wei Yuan asks:

PECO2 x VT = PaCO2 x (VT – VD) + PICO2 x VD where PECO2 is the PCO2 of
expired gas; PaCO2 is the CO2 tension in arterial blood; VT - tidal
volume and VD - total dead space. How is it derived? What is the
principle underlying this equation?

Reply by Prakash:

My understanding is that the above equation follows from the principle
is that of conservation of mass;

The source of "CO2" is primarily blood that equilibrates with perfused
alveoli;

The output of "CO2" is via the tidal volume;

The CO2 concentration of inspired gas is so small it can be ignored
for practical purposes.

For example, if PECO2 = 28 mm Hg, PaCO2 = 40 mm Hg, VT = 500 mL then
VD = 150 mL"