What pressure (in atm) is exerted by a column of mercury 1.10 m high? The density of mercury is 13.5951 g/cm3.
A sample consisting of 1.00 mol Ar is expanded isothermally at 0°C from 22.4 dm3 to 44.8 dm3 (a) reversibly, (b) against a constant external pressure equal to the final pressure of the gas, and (c) freely (against zero external pressure). For the three
asked on June 22, 2015
To determine the pressure exerted by a column of mercury, we can use the formula:
Pressure = (density of mercury) x (acceleration due to gravity) x (height of the column)
First, let's convert the given height of the column into meters:
1.10 m
Next, let's convert the density of mercury from grams per cubic centimeter (g/cm3) to kilograms per cubic meter (kg/m3):
Density of mercury = 13.5951 g/cm3 = 13,595.1 kg/m3
Now, let's substitute the values into the formula to calculate the pressure:
Pressure = (13,595.1 kg/m3) x (9.8 m/s2) x (1.10 m)
Calculating this expression:
Pressure = 167,192.034 N/m2
However, we need to convert the unit from pascals (N/m2) to atmospheres (atm). Since 1 atm is equal to 101,325 N/m2, we can divide the pressure by this conversion factor:
Pressure = 167,192.034 N/m2 ÷ 101,325 N/m2
Using a calculator, we find:
Pressure ≈ 1.651203 atm
Therefore, the pressure exerted by the column of mercury is approximately 1.65 atm.
To find the pressure exerted by a column of mercury, we can use the formula:
Pressure = density × gravitational acceleration × height
First, we need to convert the density of mercury from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³). Since there are 1000 g in a kg and 100 cm in a meter, we can convert the units as follows:
Density (kg/m³) = Density (g/cm³) × (1000 g / 1 kg) × (1 cm / 0.01 m)^3
Now we can substitute the given density of mercury into the equation:
Density (kg/m³) = 13.5951 g/cm³ × (1000 g / 1 kg) × (1 cm / 0.01 m)^3
Calculating this expression will give us the density of mercury in kg/m³.
Next, we need to determine the gravitational acceleration. The standard value for the acceleration due to gravity is approximately 9.8 m/s².
Finally, we can substitute the known values into the formula:
Pressure = density × gravitational acceleration × height
Height (m) = 1.10 m (given)
Now we can calculate the pressure:
Pressure = density × gravitational acceleration × height
Remember to convert the density to kg/m³ and use the correct value for gravitational acceleration.
By following these steps and plugging in the numbers, you should be able to calculate the pressure exerted by the column of mercury in atm.