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Question: What pressure (in atmospheres) is required to compress 1.00 L of gas at 760 mm Hg pressure to a volu...

What pressure (in atmospheres) is required to compress 1.00 L of gas at 760 mm Hg pressure to a volume of 50.0 mL?

Explanation

Solution

The force applied perpendicular to an object's surface per unit area across which that force is spread is known as pressure. The pressure relative to the ambient pressure is known as gauge pressure (sometimes written gauge pressure).
Pressure is measured in a variety of ways. Some of them are derived from a unit of force divided by a unit of area; for example, the SI unit of pressure, the pascal, is derived from a unit of force divided by a unit of area (Pa)

Complete answer:
Boyle's law is an experimental gas law that states that as the capacity of a container grows, the pressure of a gas tends to drop. The absolute pressure produced by a given mass of an ideal gas is inversely proportional to the volume it fills if the temperature and amount of gas stay fixed within a closed system, according to a modern formulation of Boyle's law.
Boyle's law can be expressed mathematically as: P1VP\propto \dfrac{1}{V}
PV = kPV\text{ }=\text{ }k, or pressure is inversely proportional to volume.
Where P is the pressure of the gas, V is the volume of the gas, and k is a constant, pressure multiplied by volume equals some constant k.
For a given quantity of confined gas, the product of pressure and volume is a constant, according to the equation, and this holds true as long as the temperature remains constant. The law can be effectively stated as P1V1=P2V2{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}} when comparing the same material under two distinct sets of circumstances.
The pressure of the gas drops in proportion to the increase in volume, as shown by this equation. Similarly, when the volume of the gas diminishes, the pressure rises.
P1V1=P2V2P_{1} V_{1}=P_{2} V_{2}, now P1=1P_{1}=1 \cdot atm , and so we hence solve for P2P_{2} using:
P2=P1V1V2=1.00L×1atm0.050L=2 atm{{P}_{2}}=\dfrac{{{P}_{1}}{{V}_{1}}}{{{V}_{2}}}=\dfrac{1.00\cdot L\times 1\cdot atm}{0.050\cdot L}=2\text{ }atm
P2=2 atm\Rightarrow {{P}_{2}}=2\text{ atm}
Most gases behave like ideal gases at moderate pressures and temperatures. The technology of the 17th century could not produce very high pressures or very low temperatures. Hence, the law was not likely to have deviations at the time of publication. As improvements in technology permitted higher pressures and lower temperatures, deviations from the ideal gas behavior became noticeable, and the relationship between pressure and volume can only be accurately described employing real gas theory. The deviation is expressed as the compressibility factor.

Note:
Boyle's law is frequently used to explain how the human body's respiratory system operates. This usually entails describing how the lung capacity may be raised or reduced, resulting in lower or greater air pressure within them (according to Boyle's law). As air flows from high to low pressure, it creates a pressure differential between the air inside the lungs and the ambient air pressure, resulting in either inhalation or exhalation.