Problem 124 - Chemistry: An Atoms-Focused Approach

Question

Blood Pressure A typical blood pressure in a resting adult is "120 over 80," meaning 120 \(\mathrm{mmHg}\) with each beat of the heart and 80 mm Hg of pressure between heartbeats. Express these pressures in the following units: (a) torr; (b) atm; (c) bar; (d) kPa.

Step-by-Step Solution

Answer

Question: Convert the blood pressure values 120 mmHg (pressure with each heartbeat) and 80 mmHg (pressure between heartbeats) to the following units: (a) torr, (b) atm, (c) bar, and (d) kPa. Answer: (a) 120 torr and 80 torr (b) 0.1579 atm and 0.1053 atm (c) 0.1599 bar and 0.1066 bar (d) 15.99 kPa and 10.66 kPa

Step 1: Convert mmHg to torr

As 1 mmHg is equal to 1 torr, we don't actually need to do any calculations for this conversion: 120 mmHg = 120 torr (pressure with each heartbeat) 80 mmHg = 80 torr (pressure between heartbeats)

Step 2: Convert mmHg to atm

Now we'll convert the pressures from mmHg to atm using the conversion factor 1 atm = 760 torr (or mmHg): 120 mmHg * (1 atm / 760 mmHg) = 0.1579 atm (pressure with each heartbeat) 80 mmHg * (1 atm / 760 mmHg) = 0.1053 atm (pressure between heartbeats)

Step 3: Convert mmHg to bar

First, we need to convert the pressures from mmHg to kPa, and then to bar, using the conversion factors 1 atm = 760 torr and 1 bar = 100 kPa: 120 mmHg * (1 atm / 760 mmHg) * (101.325 kPa / 1 atm) = 15.99 kPa (pressure with each heartbeat) 80 mmHg * (1 atm / 760 mmHg) * (101.325 kPa / 1 atm) = 10.66 kPa (pressure between heartbeats) Now, we'll convert the kPa values to bar: 15.99 kPa * (1 bar / 100 kPa) = 0.1599 bar (pressure with each heartbeat) 10.66 kPa * (1 bar / 100 kPa) = 0.1066 bar (pressure between heartbeats)

Step 4: Convert mmHg to kPa

Finally, to convert the pressures directly from mmHg to kPa, we'll use the conversion factor 1 atm = 760 torr and 101.325 kPa / 1 atm: 120 mmHg * (1 atm / 760 mmHg) * (101.325 kPa / 1 atm) = 15.99 kPa (pressure with each heartbeat) 80 mmHg * (1 atm / 760 mmHg) * (101.325 kPa / 1 atm) = 10.66 kPa (pressure between heartbeats) So, the blood pressure values expressed in the various units are: (a) 120 torr and 80 torr (b) 0.1579 atm and 0.1053 atm (c) 0.1599 bar and 0.1066 bar (d) 15.99 kPa and 10.66 kPa

Key Concepts

mmHg

Blood pressure is often measured in millimeters of mercury, abbreviated as mmHg. This unit is used to express pressure as the height of a column of mercury. The measurement technique dates back to when mercury was used in barometers because it is liquid at room temperature and dense. Blood pressure readings like 120/80 mmHg are common and easy to interpret when thinking about blood pressure. The numbers reflect systolic pressure (when the heart beats) and diastolic pressure (when the heart rests).

• 1 mmHg equals approximately 133.322 pascals.
• It is a convenient unit as it can directly relate to standard medical equipment readings.

These measurements are crucial in diagnosing and treating hypertension and other cardiovascular conditions.

torr

The unit torr is often used interchangeably with mmHg because they are equivalent. Named after Evangelista Torricelli, an Italian physicist who invented the barometer, torr has become a part of the international vocabulary for pressure. The simplicity of conversion between mmHg and torr—being a one-to-one relationship—means no complex calculations are necessary when switching from mmHg to torr.

• 1 mmHg = 1 torr
• Used predominantly in scientific research involving vacuum pressures and some meteorological settings.

atmosphere (atm)

An atmosphere, abbreviated as atm, is another common unit of pressure. It is defined as being equivalent to the average atmospheric pressure at sea level. This makes it practical for comparing readings in scientific and engineering contexts. You can convert mmHg to atm using the relationship that 1 atm equals 760 mmHg. To convert, divide the mmHg value by 760. For example, 120 mmHg translates to 0.1579 atm.

• 1 atm = 760 mmHg
• Useful for understanding how body pressure compares to atmospheric pressure.

bar

The bar is a unit of pressure that is used internationally but is not part of the International System of Units (SI). However, it is accepted by them. The bar is slightly less than the atmosphere in magnitude but offers a convenient way to express pressure based on powers of ten. To convert measurements in mmHg to bar, first convert mmHg to kPa, and then kPa to bar (as 1 bar = 100 kPa). This conversion process simplifies calculation in fields such as meteorology and industrial applications.

• 1 bar = 100,000 pascals
• 1 atm = approximately 1.01325 bar
• Convenient for using in weather forecasting and tire pressure readings.

kilopascal (kPa)

The kilopascal is a unit of pressure that enhances precision with lower magnitude numbers. The SI unit of pressure is the pascal (Pa), but kilopascals (kPa) are more commonly used when measuring pressure in contexts that involve higher numbers, like meteorology and engineering. To convert mmHg to kPa, use the conversion factor where 1 atm equals 101.325 kPa. Therefore, each mmHg is a fraction of kPa. Dividing mmHg by the ratio that 101.325 kPa is to 760 mmHg gives the kPa value.

• 1 atm = 101.325 kPa
• Useful for detailed and precise measurements in scientific fields.