Problem 3 - Chemistry and Chemical Reactivity

Question

Indicate which represents the higher pressure in each of the following pairs: (a) \(534 \mathrm{mm}\) Hg or 0.754 bar (b) \(534 \mathrm{mm}\) Hg or \(650 \mathrm{kPa}\) (c) 1.34 bar or \(934 \mathrm{kPa}\)

Step-by-Step Solution

Answer

(a) 0.754 bar, (b) 650 kPa, (c) 934 kPa.

Step 1: Convert mm Hg to bar for (a)

First, convert 534 mm Hg to bar. We know that 1 mm Hg is approximately 0.00133322 bar. Thus, \(534 \, \text{mm Hg} = 534 \times 0.00133322 \, \text{bar} = 0.711 \text{bar}\).

Step 2: Compare Pressures for (a)

Now, compare 0.711 bar and 0.754 bar. Since 0.754 bar is greater than 0.711 bar, 0.754 bar represents the higher pressure.

Step 3: Convert mm Hg to kPa for (b)

Convert 534 mm Hg to kPa. We know that 1 mm Hg is approximately 0.133322 kPa. Thus, \(534 \, \text{mm Hg} = 534 \times 0.133322 \, \text{kPa} = 71.2 \, \text{kPa}\).

Step 4: Compare Pressures for (b)

Compare 71.2 kPa with 650 kPa. 650 kPa is obviously greater than 71.2 kPa. Therefore, 650 kPa represents the higher pressure.

Step 5: Convert bar to kPa for (c)

Convert 1.34 bar to kPa. We know that 1 bar is equal to 100 kPa. Thus, \(1.34 \, \text{bar} = 1.34 \times 100 \, \text{kPa} = 134 \, \text{kPa}\).

Step 6: Compare Pressures for (c)

Now, compare 134 kPa and 934 kPa. Since 934 kPa is greater than 134 kPa, 934 kPa represents the higher pressure.

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air in the atmosphere on a surface. This pressure is essential to understand because it influences many phenomena in our everyday lives. At sea level, atmospheric pressure is approximately 101.3 kPa or 1 atm, which is equivalent to 760 mm Hg.

Atmospheric pressure varies depending on geographical location and altitude. For example:

• At higher altitudes, such as on a mountain, atmospheric pressure is lower because the column of air above is shorter.
• At sea level, atmospheric pressure is higher because the air column above is taller.

Understanding atmospheric pressure is crucial when comparing pressures in problems involving different units such as mm Hg, bar, and kPa. It allows for a standard reference point for these comparisons.

Bar to kPa Conversion

Conversion between bar and kPa is a common task in pressure-related calculations. A bar and kPa are both units of pressure, but they are used in different contexts.

• 1 bar is equal to 100 kPa.
• To convert bar to kPa, simply multiply the number of bar by 100.
• To convert kPa to bar, divide the number of kPa by 100.

This conversion is straightforward and helps in comparing pressure values. For instance, when a question requires you to find out which pressure is higher, converting both measurements to the same unit can simplify the comparison.

Consistently using kPa can be particularly useful in scientific calculations because it is a standard unit in the International System of Units (SI), which facilitates consistency and accuracy in measurements.

Pressure Comparison

When comparing pressures, it's essential to ensure that all pressures are converted to the same unit, making it easier to see which is higher or lower. Here’s how you can make comparisons:

• First, identify and list the pressures in their given units.
• Convert all pressures to a common unit, such as kPa or bar, using the appropriate conversion factors.
• After conversion, simply compare the numeric values to determine which is greater or lesser.

In practical applications, comparing pressures involves understanding the context of each pressure level, such as in engineering processes, meteorology, and various scientific experiments. Moreover, this skill is vital in real-life scenarios like checking tire pressure or studying weather patterns.

By mastering the skill of pressure conversion and comparison, you can enhance your ability to solve a wide range of problems in both academic and practical situations.