Problem 1 - Chemistry and Chemical Reactivity

Question

The pressure of a gas is \(440 \mathrm{mm}\) Hg. Express this pressure in units of (a) atmospheres, (b) bars, and (c) kilopascals.

Step-by-Step Solution

Answer

(a) 0.5789 atm, (b) 0.5867 bars, (c) 58.667 kPa.

Step 1: Understanding the Conversion Factors

The pressure value is given as \(440 \mathrm{mm} \) Hg. We need to convert it into three different units: atmospheres, bars, and kilopascals. The conversion factors are:1. \( 1 \text{ atm} = 760 \mathrm{mm} \) Hg2. \( 1 \text{ bar} = 750.062 \mathrm{mm} \) Hg3. \( 1 \text{ kPa} = 7.50062 \mathrm{mm} \) Hg.

Step 2: Convert to Atmospheres

To convert \(440 \mathrm{mm} \) Hg to atmospheres, we use the conversion factor for atmospheres. The formula is:\[ \text{Pressure in atm} = \frac{440 \mathrm{mm} \text{ Hg}}{760 \mathrm{mm} \text{ Hg/atm}} \]Calculating this gives:\[ \text{Pressure in atm} \approx 0.5789 \text{ atm} \]

Step 3: Convert to Bars

To convert \(440 \mathrm{mm} \) Hg to bars, use the conversion factor for bars. The formula is:\[ \text{Pressure in bars} = \frac{440 \mathrm{mm} \text{ Hg}}{750.062 \mathrm{mm} \text{ Hg/bar}} \]Performing the calculation results in:\[ \text{Pressure in bars} \approx 0.5867 \text{ bars} \]

Step 4: Convert to Kilopascals

To find the pressure in kilopascals, apply the conversion factor for kilopascals:\[ \text{Pressure in kPa} = \frac{440 \mathrm{mm} \text{ Hg}}{7.50062 \mathrm{mm} \text{ Hg/kPa}} \]This calculation provides:\[ \text{Pressure in kPa} \approx 58.667 \text{ kPa} \]

Key Concepts

Understanding Atmospheres

The term 'atmosphere' (atm) is a widely used unit of pressure in both science and engineering. It was originally defined as the pressure exerted by the Earth's atmosphere at sea level. This unit simplifies the complexities of measuring atmospheric pressure in real-world applications.

An important point to remember is that 1 atmosphere is equal to 760 mm Hg, as indicated by the conversion factors in the original solution provided. This gives us a straightforward way to convert pressure values from millimeters of mercury (mm Hg) to atmospheres.

• It provides a simple conversion calculation: divide the mm Hg value by 760.
• This is particularly useful when dealing with gases, as it allows for easy comparisons with standard atmospheric conditions.

Understanding this conversion is fundamental to effectively expressing pressure in atmospheres and helps students enhance their understanding of atmospheric pressure as it relates to weather, altitude, and various scientific experiments.

Exploring Bars

The bar is another unit of pressure, commonly used in many scientific disciplines and industries. One bar is slightly less than the atmospheric pressure at sea level.

The practice of using bars is especially popular in meteorology and weather forecasting, where it is crucial to represent large changes in atmospheric pressure accurately.

• 1 bar is equal to 750.062 mm Hg, offering a slightly different representation than atmospheres.
• Bars are convenient for indicating pressures much higher or lower than normal atmospheric pressure.

The ability to convert between mm Hg and bars allows for greater versatility in scientific calculations and helps learners to become proficient in translating real-world events into measurable data.

Demystifying Kilopascals

Kilopascals (kPa) are part of the metric system's unit for pressure measurement and are frequently used in engineering, physics, meteorology, and other fields. Understanding kilopascals provides an essential foundation for scientific literacy, especially in countries where the metric system prevails.

One of the key aspects of kilopascals is their relation to the standard atmosphere:

• 1 kPa is equivalent to 7.50062 mm Hg.
• The use of kilopascals is widespread in fields like meteorology, where precise atmospheric pressure readings are necessary.

Converting pressure values from mm Hg to kPa ensures that measurements adhere to the International System of Units (SI), promoting uniformity and clarity in scientific communication. This helps in achieving accurate, standardized documentation of pressure-related phenomena.