Question

Perform the following conversions: (a) \(0.850 \mathrm{~atm}\) to torr, (b) 785 torr to kilopascals, (c) \(655 \mathrm{~mm} \mathrm{Hg}\) to atmospheres, (d) \(1.323 \times 10^{5} \mathrm{~Pa}\) to atmospheres, (e) \(2.50 \mathrm{~atm}\) to bars.

Short answer

(a) \(646~\text{torr}\) (b) \(104.6~\text{kPa}\) (c) \(0.861~\text{atm}\) (d) \(1.306~\text{atm}\) (e) \(2.533~\text{bar}\)

Step-by-step solution

(a) Convert 0.850 atm to torr

To convert atm to torr, we can use the conversion factor: 1 atm = 760 torr. Multiply the given pressure in atm by the conversion factor: \(0.850~\text{atm} \times \frac{760~\text{torr}}{1~\text{atm}}\) This results in: \(0.850 \times 760 = 646~\text{torr}\)

(b) Convert 785 torr to kilopascals

To convert torr to kilopascals (kPa), we use the conversion factor: 1 torr = 0.133322 kPa. Multiply the given pressure in torr by the conversion factor: \(785~\text{torr} \times \frac{0.133322~\text{kPa}}{1~\text{torr}}\) This results in: \(785 \times 0.133322 = 104.6~\text{kPa}\)

(c) Convert 655 mmHg to atmospheres

To convert mmHg to atm, we use the conversion factor: 1 mmHg = 0.0013158 atm. Multiply the given pressure in mmHg by the conversion factor: \(655~\text{mmHg} \times \frac{0.0013158~\text{atm}}{1~\text{mmHg}}\) This results in: \(655 \times 0.0013158 = 0.861~\text{atm}\)

(d) Convert 1.323 x 10^5 Pa to atmospheres

To convert Pascal (Pa) to atm, we can use the conversion factor: 1 Pa = 9.8692 x 10^-6 atm. Multiply the given pressure in Pa by the conversion factor: \(1.323 \times 10^{5}~\text{Pa} \times \frac{9.8692 \times 10^{-6}~\text{atm}}{1~\text{Pa}}\) This results in: \(1.323 \times 10^{5} \times 9.8692 \times 10^{-6} = 1.306~\text{atm}\)

(e) Convert 2.50 atm to bars

To convert atm to bars, we can use the conversion factor: 1 atm = 1.01325 bar. Multiply the given pressure in atm by the conversion factor: \(2.50~\text{atm} \times \frac{1.01325~\text{bar}}{1~\text{atm}}\) This results in: \(2.50 \times 1.01325 = 2.533~\text{bar}\)

Key concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air above us and is measured at a particular location on Earth's surface. It's an important concept in chemistry and environmental science, as it influences chemical reactions and weather patterns.

At sea level, atmospheric pressure is considered to be standard and is commonly used as a reference point. This standard atmosphere (atm) is defined as being precisely equal to 101,325 pascals (Pa). Understanding atmospheric pressure is crucial in chemistry because it affects the boiling points of liquids, gas reactions, and even the way we calculate gas volumes under different pressure conditions.

When solving problems involving atmospheric pressure, it's essential to consider the altitude and local weather conditions as these factors can impact the measured value of atmospheric pressure at a given location.

Pascal

The pascal (Pa) is the SI unit of pressure and is a critical unit of measurement in the field of chemistry and physics. It represents the force of one newton acting perpendicularly onto an area of one square meter.

The concept of pressure is foundational in understanding gas laws and the behavior of fluids. In context, 1 atm is equivalent to 101,325 Pa. Since pascals represent a very small amount of pressure, kilopascals (kPa), which are equal to 1,000 pascals, are often used for more practical measurements in scientific work.

Understanding how to relate pascals to other pressure units like atmospheres, bars, or torr is vital for accurately performing calculations in chemistry and for understanding the impact of pressure in various scientific scenarios.

Torr to Kilopascals Conversion

Converting pressure units from torr to kilopascals (kPa) is a standard practice in science, particularly in the study of gases. Torr is a unit of pressure based on an absolute scale, named after the Italian physicist Evangelista Torricelli. 1 torr is defined as 1/760th of an atmosphere (1 torr = 101,325 Pa / 760).

To convert torr to kPa, you would multiply the pressure value by the conversion factor of 0.133322 kPa/torr. For example, if a pressure is given as 785 torr, the calculation to convert it to kPa would be: \[\begin{equation}785\,\text{torr} \times \frac{0.133322\,\text{kPa}}{1\,\text{torr}} = 104.6\,\text{kPa}.\end{equation}\]This type of conversion is crucial when you need to compare pressure readings obtained using different units or when following international standards that typically use the SI unit system.

mmHg to atm Conversion

The conversion from millimeters of mercury (mmHg) to atmospheres (atm) is common in many scientific calculations, particularly when dealing with pressures close to Earth's surface atmospheric conditions. The unit mmHg is derived from the use of mercury in barometers, where the height of the mercury column reflects atmospheric pressure.

1 mmHg is approximately equal to 0.0013158 atm. So, to convert a pressure reading from mmHg to atm, multiply the mmHg value by 0.0013158. For instance, a pressure of 655 mmHg would be converted to atmospheres as follows: \[\begin{equation}655\,\text{mmHg} \times \frac{0.0013158\,\text{atm}}{1\,\text{mmHg}} = 0.861\,\text{atm}.\end{equation}\]This conversion is fundamental in fields such as meteorology, aviation, and medicine, and understanding it enables students and professionals to accurately interpret and utilize pressure data.