Question

Convert the following pressures into atmospheres. a. \(105.2 \mathrm{kPa}\) c. \(752 \mathrm{mm} \mathrm{Hg}\) b. \(75.2 \mathrm{cm} \mathrm{Hg}\) d. 767 torr

Short answer

The pressures in atmospheres are: a. 1.038 atm, c. 0.989 atm, b. 0.989 atm, and d. 1.009 atm.

Step-by-step solution

1. Convert 105.2 kPa to atm

First, let's use the conversion factor between kPa and atm. We know that \(1 \mathrm{atm} = 101.325 \mathrm{kPa}\), so to convert 105.2 kPa to atm, we have: Pressure in atm = \(\frac{105.2 \mathrm{kPa}}{1 \mathrm{atm} / 101.325 \mathrm{kPa}}\) Pressure in atm = 1.038 atm

2. Convert 752 mm Hg to atm

Next, we use the conversion factor between mm Hg and atm. We know that \(1 \mathrm{atm} = 760 \mathrm{mmHg}\), so to convert 752 mm Hg to atm, we have: Pressure in atm = \(\frac{752 \mathrm{mmHg}}{1 \mathrm{atm} / 760 \mathrm{mmHg}}\) Pressure in atm = 0.989 atm

3. Convert 75.2 cm Hg to atm

Now, let's use the conversion factor between cm Hg and atm. We know that \(1 \mathrm{atm} = 76 \mathrm{cmHg}\), so to convert 75.2 cm Hg to atm, we have: Pressure in atm = \(\frac{75.2 \mathrm{cmHg}}{1 \mathrm{atm} / 76 \mathrm{cmHg}}\) Pressure in atm = 0.989 atm

4. Convert 767 torr to atm

Finally, we use the conversion factor between torr and atm. We know that \(1 \mathrm{atm} = 760 \mathrm{torr}\), so to convert 767 torr to atm, we have: Pressure in atm = \(\frac{767 \mathrm{torr}}{1 \mathrm{atm} / 760 \mathrm{torr}}\) Pressure in atm = 1.009 atm That's it! The pressures in atmospheres are: a. 1.038 atm, c. 0.989 atm, b. 0.989 atm, and d. 1.009 atm.

Key concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the atmosphere above any given point. It is an essential concept in chemistry because it affects how gases behave under different conditions. When we talk about atmospheric pressure, we often use the term "standard pressure," which equals 1 atmosphere (atm) or 101.325 kilopascals (kPa). This value is based on the average sea-level atmospheric pressure. Understanding atmospheric pressure is crucial when performing pressure conversions in chemistry, as it sets the baseline for comparing other pressure units.

Pressure Units

Pressure, in the context of chemistry, is described as the force applied perpendicular to the surface of an object, divided by the area over which that force is distributed. It is measured in several units, each reflecting different measurement systems or historical practices. - The most common units include atmospheres (atm), pascals (Pa), kilopascals (kPa), millimeters of mercury (mmHg), centimeters of mercury (cmHg), and torr. - An atmosphere (atm) is a unit that represents the air pressure at sea level on Earth. - Kilopascals (kPa) and pascals (Pa) are metric units commonly used in scientific contexts. - Millimeters of mercury (mmHg) and torr are units commonly used in barometry. Understanding the relationships between these units allows for the effective conversion from one to another, ensuring proper communication and calculation of pressure in various scientific applications.

Unit Conversion

Unit conversion is a crucial part of working with measurements in chemistry. It involves changing one unit of measure to another, using known conversion factors. To convert between pressure units, you must understand the conversion relationships between them. For example: - 1 atm is equivalent to 101.325 kPa, 760 mmHg, or 760 torr. - Conversions require dividing the given pressure value by the conversion factor or multiplying, depending on the units involved. These conversions ensure that values are in a consistent format, allowing for comparison, calculation, and communication across different systems. Often, you'll find it useful to set up a fraction where the desired units remain, while the initial units cancel out.

kPa to atm

Converting kilopascals (kPa) to atmospheres (atm) is straightforward when you use the right conversion factor. Since 1 atm equals 101.325 kPa, you divide the value in kPa by 101.325 to find the pressure in atm. **Example**: - If you have 105.2 kPa and want to convert to atm: Pressure in atm = \( \frac{105.2 \text{ kPa}}{101.325 \text{ kPa/atm}} \) This calculation results in approximately 1.038 atm.This conversion is frequent in chemical calculations, allowing you to express pressures in terms of the atmosphere, a universally understood unit.

torr to atm

To convert from torr to atmospheres (atm), you simply use the relationship where 1 atm equals 760 torr. This conversion factor helps determine how many atm you have for any given torr pressure. **Example**:- For a pressure of 767 torr: Pressure in atm = \( \frac{767 \text{ torr}}{760 \text{ torr/atm}} \)This calculation results in approximately 1.009 atm.Understanding this conversion is useful for working with instruments like barometers, which frequently measure pressure in torr. The ease of converting allows chemists to work interchangeably between different pressure units in their analyses.