Chapter 5: Q5.15P (page 227)

The gravitational force exerted by an object is given by F= mg,where Fis the force in Newtons, mis the mass in kilograms, and gis the acceleration due to gravity (9.81 m/s²).
(a) Use the definition of the pascal to calculate the mass (in kg) of the atmosphere above 1 m² of ocean.
(b) Osmium (Z= 76) is a transition metal in Group 8B(8) and has the highest density of any element (22.6 g/mL). If an osmium column is 1 m² in area, how high must it be for its pressure to equal atmospheric pressure? [Use the answer from part (a) in your calculation.]

Short Answer

Expert verified

The mass of the atmosphere is $1.09 \times 10^{4} kg$ .
The height of the column is $0.457 m$ .

Step by step solution

Determination of mass

1 Pascal is the pressure exerted on a surface when a force of 1 Newton acts on a surface area of 1m².

$Pressure = \frac{Force}{Area}$

$1 Pa = \frac{1 N}{1 m^{2}}$

According to the given data, F = mg

Where,

F = force

m = mass

g = acceleration due to gravity

1 atm = $1.01325 \times 10^{5} Pa$

Now, the mass of the atmosphere is,

$\begin{array}{rcl} 1.01325 \times 10^{5} Pa & = & \frac{mg}{area} \\ 1.01325 \times 10^{5} Pa & = & \frac{m \times 9.8 {m/s}^{2}}{1 m^{2}} \\ m & = & 1.09 \times 10^{4} kg \end{array}$

Thus, the mass of the atmosphere is $1.09 \times 10^{4} kg$ .

Determination of height of the column

The relation between density and pressure is,

$P = p g h$

Where,

data-custom-editor="chemistry" $ρ = density g = acceleration due to gravity h = height$

Now, the height of the column is,

data-custom-editor="chemistry" $h = \frac{P}{pg} = \frac{1.01325 \times 10^{5} Pa}{22.6 g/ml× 9.81 {m/s}^{2}} h = 0.457 m$

Thus, the height of the column is $0.457 m$

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Determination of mass

Determination of height of the column

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