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Chapter 11: Problem 1

An "empty" \(0.500\) -gallon milk carton sits in a room where the temperature is \(25.20^{\circ} \mathrm{C}\). The barometric pressure is exactly 1 atm. (a) What is the Kelvin temperature of the air inside the carton? (b) What is the pressure in millimeters of mercury of the air inside the carton? (c) What is the volume in liters of the air inside the carton? (1 gallon \(=3.78 \mathrm{~L}\) )

Short Answer

Expert verified
(a) The Kelvin temperature of the air inside the carton is \(298.35\ \mathrm{K}\); (b) the pressure in millimeters of mercury is \(760\ \mathrm{mmHg}\); (c) the volume in liters of the air inside the carton is approximately \(1.89\ \mathrm{L}\).

Step by step solution

01

(a) Convert temperature from Celsius to Kelvin

To convert the temperature from Celsius to Kelvin, we can use the following formula: \[T_{K} = T_{C} + 273.15\] Where \(T_{K}\) is the temperature in Kelvin, and \(T_{C}\) is the temperature in Celsius. Given \(T_{C} = 25.20^{\circ} \mathrm{C}\), we have: \[T_{K} = 25.20 + 273.15\] Now calculate the temperature in Kelvin: \[T_{K} = 298.35\ \mathrm{K}\]
02

(b) Convert pressure from atm to mmHg

To convert pressure from atm to mmHg (millimeters of mercury), we can use the following conversion factor: 1 atm = 760 mmHg Given the pressure is exactly 1 atm, we have: \[P_{mmHg} = 1 \cdot 760\] Now, calculate the pressure in mmHg: \[P_{mmHg} = 760 \ \mathrm{mmHg}\]
03

(c) Convert volume from gallons to liters

To convert the volume from gallons to liters, we can use the following conversion factor: 1 gallon = 3.78 L Given the volume of the carton is 0.500-gallon, we have: \[V_{L} = 0.500 \cdot 3.78\] Now, calculate the volume in liters: \[V_{L} \approx 1.89 \ \mathrm{L}\] So, the answers are (a) the Kelvin temperature of the air inside the carton is 298.35 K; (b) the pressure in millimeters of mercury is 760 mmHg; (c) the volume in liters of the air inside the carton is approximately 1.89 L.

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Most popular questions from this chapter

Arrange these gases, all at STP, in order of increasing density: \(\mathrm{CO}_{2}, \mathrm{H}_{2}, \mathrm{O}_{2}, \mathrm{CH}_{4}, \mathrm{He}\).

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