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In the United States, barometric pressures are generally reported in inches of mercury (in. Hg). On a beautiful summer day in Chicago, the barometric pressure is 30.45 in. Hg. \((\mathbf{a})\) Convert this pressure to torr. \((\mathbf{b})\) Convert this pressure to atm.

Short Answer

Expert verified
(a) The pressure in torr is 773.43 torr. (b) The pressure in atm is 1.0177 atm.

Step by step solution

01

(a) Convert the pressure to torr.

To convert 30.45 in. Hg to torr, we need to use the first two conversion factors: 1 in. Hg = 25.4 mm Hg 1 torr = 1 mm Hg Step 1: Convert inches of mercury to millimeters of mercury. \( 30.45 \;in. Hg * \frac{25.4\, mm\, Hg}{1\, in. Hg} = 773.43\, mm\, Hg \) Step 2: Convert millimeters of mercury to torr. \( 773.43\, mm\, Hg * \frac{1\, torr}{1\, mm\, Hg} = 773.43\, torr \) So, the pressure in torr is 773.43 torr.
02

(b) Convert the pressure to atm.

To convert 30.45 in. Hg to atm, we will continue from the previously calculated pressure in torr and use the third conversion factor: 1 atm = 760 torr Step 3: Convert torr to atm. \( 773.43\, torr * \frac{1\, atm}{760\, torr} = 1.0177\, atm \) So, the pressure in atm is 1.0177 atm.

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Key Concepts

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

Barometric Pressure
Barometric pressure is a measure of the weight that the atmosphere's column of air exerts on the surface of the Earth. It is a key component in weather forecasting as such air pressure affects weather patterns and conditions. Understanding barometric pressure can help predict changes in the weather, such as when a storm is approaching. Meteorologists typically report it in several different units, each suitable for different situations. Comprehending these units and being able to convert between them is crucial for scientific calculations and studies.
Inches of Mercury
Inches of mercury, denoted as in. Hg, is one of the units commonly used to measure barometric pressure, especially in the United States. The term originated from the traditional way of measuring atmospheric pressure using a mercury barometer. In such devices, atmospheric pressure is indicated by the height to which mercury rises in a glass tube.
This unit remains in common use due to its historical significance and ease of comprehension in daily weather reports. For example, a typical atmospheric pressure at sea level is around 29.92 inches of mercury. Converting from inches of mercury to other units like torr or atm involves a clear understanding of conversion factors which are used to maintain consistency across different pressure measurement systems.
Torr
The torr is another unit of pressure that is often used in scientific contexts, especially in physics and chemistry. Named after the Italian scientist Evangelista Torricelli, who invented the barometer, one torr is equivalent to one millimeter of mercury (mm Hg). Because of this, converting between these two units is straightforward, involving a direct one-to-one ratio.
When converting from inches of mercury to torr, a stepwise process is required: first converting inches to millimeters, and then millimeters to torr. This highlights the need for accuracy in scientific measurements and the importance of using the correct conversion factors to ensure precision.
Atmosphere (atm)
The atmosphere (atm) is a standard unit of pressure defined as being precisely equal to 101,325 Pa (pascals). This unit is very useful for scientific calculations, as it represents the average air pressure at sea level on Earth. Understanding how to convert from other pressure units to atm is important for scientists and engineers alike, as many scientific equations use atm as a baseline for pressure.
Pressure conversions, such as from torr to atm, commonly use the factor that 1 atm equals 760 torr. Mastery of these conversions allows for precise computations across various scientific disciplines. The ability to convert between units of pressure is essential for solving complex problems and understanding the underlying principles of physical science.

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Most popular questions from this chapter

Consider a mixture of two gases, \(A\) and \(B,\) confined in a closed vessel. A quantity of a third gas, \(C,\) is added to the same vessel at the same temperature. How does the addition of gas C affect the following: (a) the partial pressure of gas A, (b) the total pressure in the vessel, (c) the mole fraction of gas B?

A 6.53 -g sample of a mixture of magnesium carbonate and calcium carbonate is treated with excess hydrochloric acid. The resulting reaction produces 1.72 \(\mathrm{L}\) of carbon dioxide gas at \(28^{\circ} \mathrm{C}\) and 743 torr pressure. (a) Write balanced chemical equations for the reactions that occur between hydrochloric acid and each component of the mixture. (b) Calculate the total number of moles of carbon dioxide that forms from these reactions. (c) Assuming that the reactions are complete, calculate the percentage by mass of magnesium carbonate in the mixture.

Rank the following gases from least dense to most dense at 1.00 atm and \(298 \mathrm{K} : \mathrm{SO}_{2}, \mathrm{HBr}, \mathrm{CO}_{2} .\)

Natural gas is very abundant in many Middle Eastern oil fields. However, the costs of shipping the gas to markets in other parts of the world are high because it is necessary to liquefy the gas, which are high because it is necessary to point at atmospheric pressure of \(-164^{\circ} \mathrm{C} .\) One possible strategy is to oxidize the methane to methanol, CH \(_{3} \mathrm{OH}\) , which has a boiling point of \(65^{\circ} \mathrm{C}\) and can therefore be shipped more readily. Suppose that \(10.7 \times 10^{9} \mathrm{ft}^{3}\) of methane at atmospheric pressure and \(25^{\circ} \mathrm{C}\) is oxidized to methanol. (a) What volume of methanol is formed if the density of \(\mathrm{CH}_{3} \mathrm{OH}\) is 0.791 \(\mathrm{g} / \mathrm{mL} ?\) (b) Write balanced chemical equations for the oxidations of methane and methanol to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) Calculate the total enthalpy change for complete combustion of the \(10.7 \times 10^{9} \mathrm{ft}^{3}\) of methane just described and for complete combustion of the equivalent amount of methanol, as calculated in part (a). (c) Methane, when liquefied, has a density of 0.466 \(\mathrm{g} / \mathrm{mL}\) ; the density of methanol at \(25^{\circ} \mathrm{C}\) is 0.791 \(\mathrm{g} / \mathrm{mL} .\) Compare the enthalpy change upon combustion of a unit volume of liquid methane and liquid methanol. From the standpoint of energy production, which substance has the higher enthalpy of combustion per unit volume?

Ammonia and hydrogen chloride react to form solid ammonium chloride: $$\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)$$ Two 2.00 -L flasks at \(25^{\circ} \mathrm{C}\) are connected by a valve, as shown in the drawing. One flask contains 5.00 \(\mathrm{g}\) of \(\mathrm{NH}_{3}(g),\) and the other contains 5.00 \(\mathrm{g}\) of \(\mathrm{HCl}(g) .\) When the valve is opened, the gases react until one is completely consumed. (a) Which gas will remain in the system after the reaction is complete? (b) What will be the final pressure of the system after the reaction is complete? (Neglect the volume of the ammonium chloride formed.) (c) What mass of ammonium chloride will be formed?

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