Problem 155 - Chemistry The Science in Context

Question

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

Step-by-Step Solution

Answer

Answer: The blood pressure values of 120 mmHg and 80 mmHg converted to the different units are as follows: - In torr: 120 mmHg = 120 torr (during each heartbeat); 80 mmHg = 80 torr (between heartbeats) - In atm: 120 mmHg ≈ 0.158 atm (during each heartbeat); 80 mmHg ≈ 0.105 atm (between heartbeats) - In bar: 120 mmHg ≈ 0.160 bar (during each heartbeat); 80 mmHg ≈ 0.106 bar (between heartbeats) - In kPa: 120 mmHg ≈ 16 kPa (during each heartbeat); 80 mmHg ≈ 10.6 kPa (between heartbeats)

Step 1: Recall the Conversion Factors

Before we begin converting the blood pressure values, let's recall the conversion factors between the different pressure units involved: 1. 1 mmHg = 1 torr 2. 1 atm = 760 torr 3. 1 atm = 1.01325 bar 4. 1 atm = 101.325 kPa These conversion factors will be used to convert the given blood pressure values to the required units.

Step 2: Convert Blood Pressure to Torr

Since 1 mmHg is equal to 1 torr, the blood pressure values (120 mmHg and 80 mmHg) can be expressed in torr directly: (a) 120 mmHg = 120 torr (during each heartbeat) 80 mmHg = 80 torr (between heartbeats)

Step 3: Convert Blood Pressure to atm

Now, using the conversion factor (1 atm = 760 torr), we convert the blood pressure values from torr to atm: (b) 120 torr * (1 atm / 760 torr) ≈ 0.158 atm (during each heartbeat) 80 torr * (1 atm / 760 torr) ≈ 0.105 atm (between heartbeats)

Step 4: Convert Blood Pressure to bar

Using the conversion factor (1 atm = 1.01325 bar), we can convert the blood pressure values from atm to bar: (c) 0.158 atm * (1.01325 bar / 1 atm) ≈ 0.160 bar (during each heartbeat) 0.105 atm * (1.01325 bar / 1 atm) ≈ 0.106 bar (between heartbeats)

Step 5: Convert Blood Pressure to kPa

Finally, using the conversion factor (1 atm = 101.325 kPa), we convert the blood pressure values from atm to kPa: (d) 0.158 atm * (101.325 kPa / 1 atm) ≈ 16 kPa (during each heartbeat) 0.105 atm * (101.325 kPa / 1 atm) ≈ 10.6 kPa (between heartbeats) Now, we have expressed the blood pressure values in all the required units.

Key Concepts

mmHg to torr

Blood pressure measurements, like the typical '120 over 80' reading encountered in a resting adult, are commonly expressed in millimeters of mercury (mmHg). However, this is not the only unit of measurement for pressure, which leads to the necessity of understanding conversions between different units.

The conversion from mmHg to torr is one of the simplest conversions in the realm of pressure units. This is because 1 mmHg is defined as exactly equivalent to 1 torr. This means that a blood pressure of 120 mmHg systolic (during each heartbeat) and 80 mmHg diastolic (between heartbeats) can be expressed as 120 torr and 80 torr, respectively, without requiring any mathematical calculation. When converting such measurements or comparing data, it's crucial to recognize and utilize this 1:1 relationship between these two units for a seamless transition.

mmHg to atm

The unit 'atmosphere' (atm) is another measure of pressure often used by scientists and is particularly common in the study of gases and atmospheric studies. For those looking to convert mmHg to atm, understanding the conversion factor between these units is key.

Conversion from mmHg to atm requires us to use the conversion factor that 1 atm is equal to 760 mmHg. Therefore, to convert blood pressure from mmHg to atm, divide the mmHg value by 760. For instance, a blood pressure of 120 mmHg during a heartbeat is approximately 0.158 atm when divided by 760, and 80 mmHg between heartbeats is approximately 0.105 atm. It's important to note this conversion in medical contexts, where precise measurements are vital for diagnostics and treatment.

mmHg to bar

When considering industrial and meteorological applications, the bar is a commonly encountered unit of pressure. To convert a blood pressure measurement from mmHg to bar, the relationship between atm and bar must be applied in addition to the previous conversion from mmHg to atm.

The factor used here is that 1 atm equals 1.01325 bar. After calculating the blood pressure in atm using the conversion from mmHg (as previously discussed), you then multiply the resulting atm value by 1.01325 to obtain the pressure in bar. For example, 0.158 atm (which was the conversion result for 120 mmHg) is multiplied by 1.01325 to yield approximately 0.160 bar. It is through these steps that medical measurements can be effectively translated into units required for specialized fields such as engineering or atmospheric science.

mmHg to kPa

In fields ranging from meteorology to engineering, the kilopascal (kPa) is used as a standard unit of pressure. To convert blood pressure from mmHg to kPa, one must be familiar with the conversion between atm to kPa.

The conversion factor is that 1 atm is equivalent to 101.325 kPa. After converting the blood pressure reading from mmHg to atm, the value in atm can then be converted to kPa by multiplying it by 101.325. For example, the systolic blood pressure of 120 mmHg, once converted to 0.158 atm, is further converted to approximately 16 kPa by this multiplication. This conversion is particularly useful in the medical field when using equipment calibrated in kPa or in any other scientific context where kPa is the preferred unit.