Problem 14 - Chemistry

Question

The atmospheric pressure at the summit of Denali (formerly known as Mt. McKinley) is \(606 \mathrm{mmHg}\) on a certain day. What is the pressure in atm and in kPa?

Step-by-Step Solution

Answer

The pressure at the summit of Denali is 0.797 atm and 80.791 kPa.

Step 1: Conversion to Atmospheres

Firstly, convert the pressure from mmHg to atm. Use the conversion factor, 1 atm = 760 mmHg. So, divide the given pressure by 760 to get the answer.

Step 2: Calculation in Atmospheres

Calculate the atmospheric pressure in atm by dividing the given pressure (606 mmHg) by the conversion factor 760 mmHg/atm. Therefore, \(P_{atm} = \frac{606 \, mmHg}{760 \, mmHg/atm} = 0.797 \, atm\)

Step 3: Conversion to Kilopascals

Next, convert the atmospheric pressure from mmHg to kPa. Use the conversion factor, 1 mmHg = 0.133322 kPa. Multiply the given pressure by this conversion factor to find the pressure in kPa.

Step 4: Calculation in Kilopascals

Calculate the pressure in kPa as follows: \(P_{kPa} = 606 \, mmHg \times 0.133322 \, kPa/mmHg = 80.791 \, kPa\).

Key Concepts

Understanding mmHg to atm Conversion

The conversion from millimeters of mercury (mmHg) to standard atmospheres (atm) is a crucial skill in scientific disciplines, particularly when dealing with pressure measurements. This process is important because pressure is commonly measured in mmHg, especially in meteorological and medical contexts, but standard atmospheric pressure is a basis for reference in many scientific fields.

To convert mmHg to atm, we employ a universally recognized conversion factor: 1 atm is equivalent to 760 mmHg. Therefore, to perform the conversion, you divide the pressure value in mmHg by 760.
For instance, in the situation of Denali's atmospheric pressure being 606 mmHg, the calculation in atm would be: \[\begin{equation}P_{\text{atm}} = \frac{606 \, \text{mmHg}}{760 \, \text{mmHg/atm}} = 0.797 \, \text{atm}\end{equation}\]By understanding this conversion, students can easily relate various pressure readings to a standard reference, enhancing comprehension of phenomena such as atmospheric changes with altitude.

Basics of Pressure Unit Conversion

Pressure unit conversions are a fundamental aspect of scientific calculations, and comprehending these is crucial for scientists and students alike. Pressure can be expressed in many different units, including mmHg, atm, pascal (Pa), and kilopascals (kPa).

The key to mastering these conversions lies in knowing the equivalence values between units:

• 1 atm = 760 mmHg
• 1 atm = 101.325 kPa
• 1 mmHg = 0.133322 kPa

These equivalences allow you to change from one unit to another through multiplication or division. For instance, if you need to convert atm to kPa, you would multiply the value in atm by 101.325 kPa/atm. This process is inversely applicable when converting kPa to atm by dividing the pressure in kPa by 101.325.

Kilopascals Calculation from mmHg

Calculating pressure in kilopascals (kPa) from millimeters of mercury (mmHg) provides a bridge between commonly used pressure measurements in different contexts. Conversions to kPa are essential because kPa is often used in engineering, physics, and weather reports as part of the International System of Units (SI).

To convert mmHg to kPa, the conversion factor 1 mmHg equals 0.133322 kPa is used. Here's how you perform the conversion:\[\begin{equation}P_{\text{kPa}} = \text{pressure in mmHg} \times 0.133322 \, \text{kPa/mmHg}\end{equation}\]Applying this to the case study provided, the pressure in kPa on Denali's summit is:\[\begin{equation}P_{\text{kPa}} = 606 \, \text{mmHg} \times 0.133322 \, \text{kPa/mmHg} = 80.791 \, \text{kPa}\end{equation}\]With this conversion, students can interpret and compare pressure readings across various scientific reports and studies, reinforcing their understanding of the relationships between different units of pressure.