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Ch.5 - Gases
All textbooksTro 4th EditionCh.5 - GasesProblem 112
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Chapter 5, Problem 112

Twenty-five milliliters of liquid nitrogen (density = 0.807 g/mL) is poured into a cylindrical container with a radius of 10.0 cm and a length of 20.0 cm. The container initially contains only air at a pressure of 760.0 mmHg (atmospheric pressure) and a temperature of 298 K. If the liquid nitrogen completely vaporizes, what is the total force (in lb) on the interior of the container at 298 K?

Verified step by step guidance
1
Calculate the mass of liquid nitrogen using its volume and density: \( \text{mass} = \text{volume} \times \text{density} \).
Convert the mass of nitrogen to moles using its molar mass (28.02 g/mol for \( N_2 \)).
Use the ideal gas law \( PV = nRT \) to find the pressure exerted by the vaporized nitrogen. Here, \( n \) is the number of moles, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.
Calculate the total pressure inside the container by adding the initial atmospheric pressure to the pressure exerted by the nitrogen gas.
Determine the total force on the interior of the container using the formula \( F = P \times A \), where \( A \) is the surface area of the interior of the cylindrical container. Convert the force from Newtons to pounds (1 N = 0.224809 lb).
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