What is the pressure (in mmHg) of the gas inside the apparatus below if the atmospheric pressure is Patm=748 mmHg, h1=40 mmHg, and h2=67 mmHg?

I don't see any apparatus below.

To find the pressure of the gas inside the apparatus, we will use the concept of hydrostatic pressure and apply Pascal's law.

The hydrostatic pressure at any given height within a fluid is given by the formula:

P = Patm + ρgh

where:
P is the pressure at the height,
Patm is the atmospheric pressure,
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the height from the surface.

In this case, the atmospheric pressure (Patm) is given as 748 mmHg. The height of the fluid column above the gas in the apparatus is (h2 - h1), which is (67 mmHg - 40 mmHg) = 27 mmHg. It is important to note that the pressure in the apparatus is caused by the weight of the fluid column above it.

To find the density (ρ) of the fluid, we can consult a table or use the value of a standard liquid, such as water. The density of water is approximately 1 g/cm^3 or 1000 kg/m^3.

Then, we need to convert the units for the density and height to a consistent system. Converting the density from kg/m^3 to g/cm^3, we have:

ρ = 1000 g/m^3 = 1 g/cm^3

Now, converting the height from mmHg to cm, we have:

h = (h2 - h1) cm = (67 mmHg - 40 mmHg) cm = 27 cm

Substituting the values into the formula, we get:

P = Patm + ρgh
P = 748 mmHg + (1 g/cm^3 * 27 cm * 9.81 m/s^2) (converting cm to m)
P = 748 mmHg + 265.47 mmHg

Calculating the expression, we have:

P = 1013.47 mmHg

Therefore, the pressure of the gas inside the apparatus is approximately 1013.47 mmHg.