What is the pressure of the gas in this mercury manometer if h = 83 mm and atmospheric pressure is 769 mmhg?

The total pressure of a gas is equal to the sum of the gauge pressure and the atmospheric pressure. The gauge pressure is the pressure measured in a device. In this case, it will be the pressure measure from the mercury manometer. The atmospheric pressure is the pressure of the surroundings and it is given as 769 mmHg. We need to calculate the gauge pressure from the product of the density of the fluid in the manometer, the gravitational acceleration and the height displacement of the fluid. However, for this case, we need the pressure to be in units of mmHg so the pressure would be just equal to the pressure head in units of mm. We do as follows:

Pg = 83 mmHg
Pa = 769 mmHg
Pt = 83 + 769 = 852 mmHg

10.063g / 10.00 ml = 1.0063 g/ml which rounds off to 4 sig figs as: 1.006 g/ml