Problem 10 - Chemistry The Molecular Science

Question

Gas pressures can be expressed in units of \(\mathrm{mmHg}\), atm, torr, and kPa. Convert these pressure values. (a) \(720 . \mathrm{mmHg}\) to atm (b) 1.25 atm to \(\mathrm{mmHg}\) (c) \(542 . \mathrm{mmHg}\) to torr (d) \(740 . \mathrm{mmHg}\) to \(\mathrm{kPa}\) (e) \(700 . \mathrm{kPa}\) to \(\mathrm{atm}\)

Step-by-Step Solution

Answer

(a) 0.947 atm; (b) 950 mmHg; (c) 542 torr; (d) 98.651 kPa; (e) 6.907 atm.

Step 1: Convert mmHg to atm

To convert from mmHg to atm, use the conversion factor: \(1 \text{ atm} = 760 \text{ mmHg}\). For (a) \(720 \text{ mmHg}\): \[\frac{720 \text{ mmHg}}{760 \text{ mmHg/atm}} = 0.9474 \text{ atm}\].

Step 2: Convert atm to mmHg

To convert from atm to mmHg, use the conversion factor: \(1 \text{ atm} = 760 \text{ mmHg}\). For (b) \(1.25 \text{ atm}\): \[1.25 \text{ atm} \times 760 \text{ mmHg/atm} = 950 \text{ mmHg}\].

Step 3: Convert mmHg to torr

Since mmHg and torr are equivalent, \(1 \text{ mmHg} = 1 \text{ torr}\). For (c) \(542 \text{ mmHg}\): \[542 \text{ torr} = 542 \text{ mmHg}\].

Step 4: Convert mmHg to kPa

To convert from mmHg to kPa, use the conversion factor: \(1 \text{ atm} = 101.325 \text{ kPa}\) and \(1 \text{ atm} = 760 \text{ mmHg}\). First, convert mmHg to atm and then atm to kPa.For (d) \(740 \text{ mmHg}\):\[\frac{740 \text{ mmHg}}{760 \text{ mmHg/atm}} = 0.9737 \text{ atm}\]Then convert to kPa:\[0.9737 \text{ atm} \times 101.325 \text{ kPa/atm} = 98.651 \text{ kPa}\].

Step 5: Convert kPa to atm

To convert from kPa to atm, use the conversion factor: \(1 \text{ atm} = 101.325 \text{ kPa}\).For (e) \(700 \text{ kPa}\):\[\frac{700 \text{ kPa}}{101.325 \text{ kPa/atm}} = 6.907 \text{ atm}\].

Key Concepts

Gas Pressure

Gas pressure is a measurement that indicates the force exerted by gas particles within a container. This pressure results from gas molecules colliding with the walls of their container, and these collisions are what enable us to measure and express gas pressure. It is a vital concept in chemistry and physics as it helps us understand how gases behave under different conditions.
Pressure is typically expressed in various units, each serving a unique purpose based on context, ease of use, or historical reasons. Understanding how to convert between these units is essential for interpreting scientific data and communicating results effectively.

mmHg

The term 'mmHg' stands for millimeters of mercury. It is one of the standard units of pressure measurement often encountered in medical settings for measuring blood pressure, as well as in laboratories and scientific experiments.
The use of mercury arises from the traditional barometer wherein mercury's height in a glass tube indicates the atmospheric pressure. One millimeter of mercury is equivalent to the pressure exerted by a column of mercury one millimeter high under standard conditions. This translates to about 0.1333 kPa or 0.001316 atm.

Atmospheres (atm)

Atmosphere, abbreviated as atm, is a unit of pressure that is based on the Earth's atmosphere at sea level. It provides a simple reference point for pressure comparisons and is widely used in diverse scientific disciplines.
By definition, 1 atm is equivalent to 101.325 kPa, 760 mmHg, or 760 torr. Due to its straightforward relationship with these other units, atm is particularly useful when discussing and converting gas pressures in many scientific contexts.

Torr

Torr is another pressure unit named after Evangelista Torricelli, the inventor of the barometer. It is equivalent to 1 mmHg and, therefore, interchangeable with mmHg in practical situations.
This equivalence means that when converting pressures involving torrs and mmHg, the numeric value remains the same, facilitating quick and easy calculations without complex conversions. This feature makes torr a convenient and practical option in many laboratory and scientific applications.

Kilopascals (kPa)

Kilopascal, abbreviated as kPa, is a metric unit of pressure commonly used worldwide in both laboratories and industry. It forms part of the International System of Units (SI), making it a universal unit of measurement for scientific work.
A kilopascal equals 1,000 pascals where one pascal represents the pressure of one newton per square meter. In terms of other pressure units, 101.325 kPa is equivalent to 1 atm and 760 mmHg. This precise conversion is crucial in calculations involving pressure to ensure consistency and accuracy across different unit systems.