Question

Gases are different from solids and liquids. In a sample of gas, the molecules are far apart. The gas molecules also move around and collide with each other as well as with the walls of the container. These collisions generate pressure. The pressure of a gas can be measured in different units. One convenient unit of measure is called the atmosphere (atm) because it is based on atmospheric pressure. At sea level, the average pressure is 1 atm. As you get higher in altitude, the pressure steadily drops until you leave the atmosphere, where the pressure is very close to 0 atm.

The table below shows the different commonly used units of measuring gas pressure. Use this table in the pressure unitec:

$$ \begin{array}{|l|c|c|} \hline {\text { Unit }} & \text { Abbreviation } & \begin{array}{c} 1 \mathrm{~atm} \\ \text { equivalent } \end{array} \\ \hline \text { atmosphere } & \text { atm } & \begin{array}{c} 1.00 \mathrm{~atm} \\ \text { (exact) } \end{array} \\ \hline \begin{array}{l} \text { millimeters of } \\ \text { mercury } \end{array} & \mathrm{mmHg} & 760 \mathrm{mmHg} \\ \hline \text { torr } & \text { torr } & 760 \text { torr } \\ \hline \text { inches of mercury } & \text { in. } \mathrm{Hg} & 29.9 \text { in. } \mathrm{Hg} \\ \hline \begin{array}{l} \text { pounds per square } \\ \text { inch (psi) } \end{array} & \mathrm{lb} / \mathrm{in}^{2} & 14.7 \mathrm{lb} / \mathrm{in}^{2} \\ \hline \text { pascal } & \mathrm{Pa} & 101,325 \mathrm{~Pa} \\ \hline \end{array} $$

Part A

Convert \(0.700\) atm of pressure to its equivalent in millimeters of mercury.

Express the pressure numerically in millimeters of mercury.

Part B

The pressure in car tires is often measured in pounds per square inch (Ib/in. \(^{2}\) ), with the recommended pressure being in the range of 25 to \(45 \mathrm{lb} / \mathrm{in} .^{2} .\) Suppose a tire has a pressure of \(30.0 \mathrm{lb} / \mathrm{in} .^{2} .\) Convert \(30.0 \mathrm{lb} / \mathrm{in} .^{2}\) to its equivalent in atmospheres.

Express the pressure numerically in atmospheres.

High-pressure liquid chromatography (HPLC) is a method used in chemistry and biochemistry to purify chemical substances. The pressures used in this procedure range from around 500 kilopascals \((500,000 \mathrm{~Pa})\) to about \(60,000 \mathrm{kPa}(60,000,000 \mathrm{~Pa}) .\) It is often convenient to know the pressure in torr. If an HPLC procedure is running at a pressure of \(4.70 \times 10^{8} \mathrm{~Pa}\), what is its running pressure in torr?

Express the pressure numerically in torr.

Answer 1

Part A

1 atm = 760 mm Hg

Using Unitary method of calculation,

=> 0.700 atm = 0.700*760 mm Hg = 532 mm Hg

Part B

1 atm = 14.7 lb/ in2

Using Unitary method of calculation,

=> 1 lb/ in2 = 1/14.7 atm = 0.068 atm

=> 30 lb/ in2 = (30)*(0.068) atm = 2.04 atm

Part C

101,325 Pa = 760 torr

Using Unitary method of calculation,

=> 1 Pa = 7.5×10-3 torr

=> 4.70×108 Pa = 4.70×108 ×7.5×10-3 torr = 3.525×106 torr