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Chapter 10: Problem 3

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 \(934 \mathrm{kPa}\)

Short Answer

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

Step by step solution

01

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, \(534 \, \text{mm Hg} = 534 \times 0.00133322 \, \text{bar} = 0.711 \text{bar}\).
02

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.
03

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, \(534 \, \text{mm Hg} = 534 \times 0.133322 \, \text{kPa} = 71.2 \, \text{kPa}\).
04

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.
05

Convert bar to kPa for (c)

Convert 1.34 bar to kPa. We know that 1 bar is equal to 100 kPa. Thus, \(1.34 \, \text{bar} = 1.34 \times 100 \, \text{kPa} = 134 \, \text{kPa}\).
06

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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鈥檚 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.

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Most popular questions from this chapter

Silane, \(\operatorname{SiH}_{4}\), reacts with \(\mathrm{O}_{2}\) to give silicon dioxide and water: $$ \mathrm{SiH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{SiO}_{2}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$ A 5.20 -L sample of \(\mathrm{SiH}_{4}\) gas at \(356 \mathrm{mm}\) Hg pressure and \(25^{\circ} \mathrm{C}\) is allowed to react with \(\mathrm{O}_{2}\) gas. What volume of \(\mathrm{O}_{2}\) gas, in liters, is required for complete reaction if the oxygen has a pressure of \(425 \mathrm{mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C} ?\)

A Chlorine gas \(\left(\mathrm{Cl}_{2}\right)\) is used as a disinfectant in municipal water supplies, although chlorine dioxide \(\left(\mathrm{ClO}_{2}\right)\) and ozone are becoming more widely used. \(\mathrm{ClO}_{2}\) is a better choice than \(\mathrm{Cl}_{2}\) in this application because it leads to fewer chlorinated by-products, which are themselves pollutants. (a) How many valence electrons are in \(\mathrm{ClO}_{2} ?\) (b) The chlorite ion, \(\mathrm{ClO}_{2}^{-},\) is obtained by reducing \(\mathrm{ClO}_{2}\). Draw a possible electron dot structure for \(\mathrm{ClO}_{2}^{-} .\) (Cl is the central atom.) (c) What is the hybridization of the central Cl atom in \(\mathrm{ClO}_{2}^{-}\) ? What is the shape of the ion? (d) Which species has the larger bond angle, \(\mathrm{O}_{3}\) or \(\mathrm{ClO}_{2}^{-} ?\) Explain briefly. (e) Chlorine dioxide, \(\mathrm{ClO}_{2},\) a yellow-green gas, can be made by the reaction of chlorine with sodium chlorite: $$2 \mathrm{NaClO}_{2}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NaCl}(\mathrm{s})+2 \mathrm{ClO}_{2}(\mathrm{g})$$ Assume you react \(15.6 \mathrm{g}\) of \(\mathrm{NaClO}_{2}\) with chlorine gas, which has a pressure of \(1050 \mathrm{mm} \mathrm{Hg}\) in a 1.45-L flask at \(22^{\circ} \mathrm{C}\). What mass of \(\mathrm{ClO}_{2}\) can be produced?

A 1.0 -L flask contains 10.0 g each of \(\mathrm{O}_{2}\) and \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) (a) Which gas has the greater partial pressure, \(\mathrm{O}_{2}\) or \(\mathrm{CO}_{2}\), or are they the same? (b) Which molecules have the greater rms speed, or are they the same? (c) Which molecules have the greater average kinetic energy, or are they the same?

5\. A self-contained underwater breathing apparatus (SCUBA) uses canisters containing potassium superoxide. The superoxide consumes the \(\mathrm{CO}_{2}\) exhaled by a person and replaces it with oxygen. $$ 4 \mathrm{KO}_{2}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{K}_{2} \mathrm{CO}_{3}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) $$ What mass of \(\mathrm{KO}_{2}\), in grams, is required to react with \(8.90 \mathrm{L}\) of \(\mathrm{CO}_{2}\) at \(22.0^{\circ} \mathrm{C}\) and \(767 \mathrm{mm} \mathrm{Hg} ?\)

A flask is first evacuated so that it contains no gas at all. Then, \(2.2 \mathrm{g}\) of \(\mathrm{CO}_{2}\) is introduced into the flask. On warming to \(22^{\circ} \mathrm{C},\) the gas exerts a pressure of \(318 \mathrm{mm}\) Hg. What is the volume of the flask?
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