Determine the pressure of the gas given that atmospheric pressure is 102000pa and density of mercury is 13.6g/cm?

To determine the pressure of the gas, we can use the equation for hydrostatic pressure:

P = ρgh

Where:
P = pressure of the gas
ρ = density of mercury = 13.6 g/cm^3
g = acceleration due to gravity = 9.81 m/s^2
h = height of the mercury column in meters

First, we need to convert the density of mercury from g/cm^3 to kg/m^3:
13.6 g/cm^3 = 13600 kg/m^3

Next, we need to convert the atmospheric pressure from Pa to mmHg (since the density of mercury is given in g/cm^3):
1 atm = 760 mmHg
102000 Pa = 102000/133.322 mmHg = 765.3 mmHg

Now, we can calculate the height of the mercury column using the equation:
P = ρgh
765.3 mmHg = 13600 kg/m^3 * 9.81 m/s^2 * h
h = 765.3 mmHg / (13600 kg/m^3 * 9.81 m/s^2)
h ≈ 0.056 m

Finally, we can calculate the pressure of the gas using the equation:
P = ρgh
P = 13600 kg/m^3 * 9.81 m/s^2 * 0.056 m
P ≈ 7500 Pa

Therefore, the pressure of the gas is approximately 7500 Pa.