An open manometer filled with mercury is connected to a container of hydrogen. The mercury level is 62 mm higher in the arm connected to the hydrogen gas. If atmospheric pressure is 97.7 kPa, what is the pressure of the hydrogen?

To determine the pressure of the hydrogen gas, consider the difference in the mercury levels between the open end and the end connected to the hydrogen.

Given:

Mercury level difference: 62 mm

Atmospheric pressure: 97.7 kPa

In an open manometer, the pressure difference between the two ends is equal to the difference in mercury levels. The pressure at the end connected to the hydrogen can be calculated as:

Pressure of hydrogen = Atmospheric pressure + Pressure difference

The pressure difference can be determined by converting the mercury level difference to pressure units using the density of mercury. The density of mercury is typically around 13,600 kg/m³.

Pressure difference = Density of mercury × g × Height difference

First, convert the height difference from millimeters to meters:

Height difference = 62 mm × (1 m / 1000 mm) = 0.062 m

Substituting the values:

Pressure difference = 13600 kg/m³ × 9.8 m/s² × 0.062 m = 81.152 kPa

Now, calculate the pressure of the hydrogen:

Pressure of hydrogen = 97.7 kPa + 81.152 kPa = 178.852 kPa

Therefore, the pressure of the hydrogen gas is approximately 178.852 kPa.

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