Question

Convert each of the pressures described below to atm: (a) At the peak of Mt. Everest, atmospheric pressure is only \(2.75 \times 10^{2} \mathrm{mmHg}\) (b) A cyclist fills her bike tires to 86 psi. (c) The surface of Venus has an atmospheric pressure of \(9.15 \times 10^{6} \mathrm{~Pa}\) (d) At \(100 \mathrm{ft}\) below sea level, a scuba diver experiences a pressure of \(2.54 \times 10^{4}\) torr.

Short answer

(a) 0.361 atm. (b) 5.85 atm. (c) 90.3 atm. (d) 33.4 atm.

Step-by-step solution

Understand the Conversion Factors

To convert different pressure units to atmospheres (atm), use the following conversion factors:1 atm = 760 mmHg1 atm = 14.696 psi1 atm = 101325 Pa1 atm = 760 torr

Convert mmHg to atm (part a)

Given pressure: \(2.75 \times 10^{2} \text{ mmHg}\)Using the conversion factor: \(1 \text{ atm} = 760 \text{ mmHg}\)\(\text{Pressure in atm} = \frac{2.75 \times 10^{2} \text{ mmHg}}{760 \text{ mmHg/atm}} = 0.361 \text{ atm}\)

Convert psi to atm (part b)

Given pressure: 86 psiUsing the conversion factor: \(1 \text{ atm} = 14.696 \text{ psi}\)\(\text{Pressure in atm} = \frac{86 \text{ psi}}{14.696 \text{ psi/atm}} = 5.85 \text{ atm}\)

Convert Pa to atm (part c)

Given pressure: \(9.15 \times 10^{6} \text{ Pa}\)Using the conversion factor: \(1 \text{ atm} = 101325 \text{ Pa}\)\(\text{Pressure in atm} = \frac{9.15 \times 10^{6} \text{ Pa}}{101325 \text{ Pa/atm}} = 90.3 \text{ atm}\)

Convert torr to atm (part d)

Given pressure: \(2.54 \times 10^{4} \text{ torr}\)Using the conversion factor: \(1 \text{ atm} = 760 \text{ torr}\)\(\text{Pressure in atm} = \frac{2.54 \times 10^{4} \text{ torr}}{760 \text{ torr/atm}} = 33.4 \text{ atm}\)

Key concepts

pressure units

When working with pressures in chemistry, you'll come across various units. The most common ones are atmospheres (atm), millimeters of mercury (mmHg), pounds per square inch (psi), pascals (Pa), and torr. Each unit measures pressure, which is the force exerted on a given area. Different environments and situations use different units, so it’s crucial to know how to convert between them.
For instance:

• 1 atm is the standard pressure at sea level.
• Millimeters of mercury (mmHg) are commonly used in weather and medical settings.
• Pounds per square inch (psi) often appear in tire pressure measurements.
• Pascals (Pa) are the SI unit for pressure and are used in many scientific calculations.
• Torr is closely related to mmHg and is used in high vacuum physics.

atmospheric pressure

Atmospheric pressure refers to the pressure exerted by the weight of the Earth's atmosphere. At sea level, this pressure is defined as 1 atmosphere (atm).
However, atmospheric pressure changes with altitude. For instance, at the peak of Mt. Everest, the atmosphere is much thinner, resulting in a pressure of only around 0.361 atm. Conversely, at lower elevations or underwater, the pressure increases as more mass is present above the point of measurement.
Understanding atmospheric pressure is important in various fields, especially in meteorology, aviation, and even scuba diving, because it affects weather patterns, flight dynamics, and underwater buoyancy.

conversion factors

Conversion factors are used to change a measurement from one unit to another. It's vital to have the correct conversion factors and understand how to use them.
For pressure, some essential conversion factors are:

• 1 atm = 760 mmHg
• 1 atm = 14.696 psi
• 1 atm = 101325 Pa
• 1 atm = 760 torr

To convert between units, divide or multiply by these factors. For example, to convert 86 psi to atm, you divide 86 by 14.696, giving you 5.85 atm. Practice with different scenarios helps solidify the understanding of these conversions.

chemistry calculations

In chemistry, proper calculations ensure accurate results and analysis. Pressure conversions are a fundamental part of many chemistry problems. They are used in gas laws, reactions in different conditions, and even in producing desired concentrations.
In calculations, always:

• Identify the given unit and the unit to convert to.
• Use the correct conversion factor.
• Perform the division or multiplication carefully.

For instance, converting the surface pressure of Venus (9.15 x 10^6 Pa) to atm involves dividing by 101325 Pa/atm, resulting in 90.3 atm.
Such conversions show the real-world applications of chemistry calculations, from planetary studies to understanding everyday phenomena like tire pressure.