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Chapter 10: Problem 21

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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Most popular questions from this chapter

A piece of dry ice (solid carbon dioxide) with a mass of 5.50 \(\mathrm{g}\) is placed in a 10.0 -L vessel that already contains air at 705 torr and \(24^{\circ} \mathrm{C}\) . After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant CO\(_{2}\) gas, and the total pressure in the container at \(24^{\circ} \mathrm{C} ?\)

Which of the following statements best explains why nitrogen gas at STP is less dense than Xe gas at STP? \begin{equation}\begin{array}{l}{\text { (a) Because Xe is a noble gas, there is less tendency for the Xe }} \\ {\text { atoms to repel one another, so they pack more densely in }} \\ {\text { the gaseous state. }} \\ {\text { (b) Xe atoms have a higher mass than } \mathrm{N}_{2} \text { molecules. Because }} \\ {\text { both gases at STP have the same number of molecules per }} \\ {\text { unit volume, the Xe gas must be denser. }}\\\\{\text { (c) The Xe atoms are larger than } \mathrm{N}_{2} \text { molecules and thus take }} \\ {\text { up a larger fraction of the space occupied by the gas. }} \\\ {\text { (d) Because the Xe atoms are much more massive than the }} \\\ {\mathrm{N}_{2} \text { molecules, they move more slowly and thus exert }} \\\ {\text { less upward force on the gas container and make the gas }} \\ {\text { appear denser. }}\end{array}\end{equation}

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Suppose that a woman weighing 130 \(\mathrm{lb}\) and wearing high- heeled shoes momentarily places all her weight on the heel of one foot. If the area of the heel is \(0.50 \mathrm{in.}^{2},\) calculate the pressure exerted on the underlying surface in (a) pounds per square inch, (b) kilopascals, and (c) atmospheres.

The planet Jupiter has a surface temperature of 140 \(\mathrm{K}\) and a mass 318 times that of Earth. Mercury (the planet) has a surface temperature between 600 \(\mathrm{K}\) and 700 \(\mathrm{K}\) and a mass 0.05 times that of Earth. On which planet is the atmosphere more likely to obey the ideal-gas law? Explain.
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