Question

When a mercury manometer is connected to a gas main, the mercury stands $40.0 \mathrm{cm}$ higher in the tube that is open to the air than in the tube connected to the gas main. A barometer at the same location reads $74.0 \mathrm{cm}\( Hg. Determine the absolute pressure of the gas in \)\mathrm{cm}$ Hg.

Short answer

Answer: The absolute pressure of the gas is 114.0 cm Hg.

Step-by-step solution

Find the pressure difference using the mercury manometer reading

The mercury manometer reading tells us that the level of mercury is 40.0 cm higher in the tube open to the air than the one connected to the gas main. This difference in height corresponds to the pressure difference between the gas and the atmosphere. Since the height difference is given in cm, we don't need to convert the units. Therefore, the pressure difference is 40.0 cm Hg.

Find the atmospheric pressure using the barometer reading

We are given the barometric reading, which tells us the atmospheric pressure at the location. The barometer reads 74.0 cm Hg. This is the atmospheric pressure at that specific location.

Calculate the absolute pressure of the gas

Now that we have both the pressure difference between the gas and the atmosphere (40.0 cm Hg) and the atmospheric pressure (74.0 cm Hg), we can calculate the absolute pressure of the gas. To do this, we need to add the pressure difference to the atmospheric pressure: Absolute pressure of the gas = Atmospheric pressure + Pressure difference Absolute pressure of the gas = 74.0 cm Hg + 40.0 cm Hg

Write the final answer

Now, we just need to perform the final calculation to find the absolute pressure of the gas: Absolute pressure of the gas = 114.0 cm Hg So, the absolute pressure of the gas is 114.0 cm Hg.