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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. \(\mathrm{Hg}\). (a) Convert this pressure to torr. (b) Convert this pressure to atm.

Short Answer

Expert verified
(a) To convert the given pressure of 30.45 in. Hg to torr, we first convert inches of mercury to millimeters of mercury using the conversion factor 1 in. Hg = 25.4 mm Hg: \(30.45 \,\text{in. Hg} \times \frac{25.4 \,\text{mm Hg}}{1\, \text{in. Hg}} = 772.83\, \text{mm Hg}\) Since 1 torr is equal to 1 mm Hg, the pressure in torr is the same as the pressure in millimeters of mercury: 772.83 torr. (b) To convert the pressure from torr to atm, we use the conversion factor 1 atm = 760 torr: \(772.83 \, \text{torr} \times \frac{1\, \text{atm}}{760\, \text{torr}} \approx 1.017\, \text{atm}\) So, the barometric pressure is approximately 1.017 atm.

Step by step solution

01

(Step 1: Write down the given information.)

The given barometric pressure in Chicago on a beautiful summer day is 30.45 in. Hg.
02

(Step 2: Convert inches of mercury to millimeters of mercury)

In order to convert inches of mercury to millimeters of mercury, we'll use the conversion factor 1 in. Hg = 25.4 mm Hg: \(30.45 \,\text{in. Hg} \times \frac{25.4 \,\text{mm Hg}}{1\, \text{in. Hg}}\) Now, perform the multiplication: \(30.45 \times 25.4 = 772.83\, \text{mm Hg}\) So, the pressure in millimeters of mercury is 772.83 mm Hg.
03

(Step 3: Convert millimeters of mercury to torr)

Since 1 torr is equal to 1 mm Hg, the pressure in torr is the same as the pressure in millimeters of mercury: 772.83 mm Hg = 772.83 torr So, the pressure in torr is 772.83 torr.
04

(Step 4: Convert torr to atmospheres)

Now we will use the conversion factor between torr and atmospheres (1 atm = 760 torr) to convert the pressure from torr to atm: \(772.83 \, \text{torr} \times \frac{1\, \text{atm}}{760\, \text{torr}}\) Now, perform the multiplication: \(\frac{772.83}{760} \approx 1.017\, \text{atm}\) So, the pressure in atmospheres is approximately 1.017 atm. In summary: (a) The barometric pressure in torr is 772.83 torr. (b) The barometric pressure in atm is approximately 1.017 atm.

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