Twenty-five milliliters of liquid nitrogen ( density = 0.807 g / mL ) is poured into a cylindri

Twenty-five milliliters of liquid nitrogen ( density = 0.807...

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

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is fundamental for relating the pressure, volume, temperature, and amount (in moles) of a gas. It allows one to predict changes in any of these variables provided the others are known, which is critical in determining the final pressure after a phase change in a confined space.

Phase Transition and Vaporization

Phase transition refers to the process of a substance changing from one state (liquid) to another (gas). Understanding vaporization is vital when computing the new gas volume and pressure in a container, as it involves energy changes and significant expansion.

Pressure and Force Relationship

Pressure is defined as the force per unit area exerted by a fluid. This concept is used to calculate the total force acting on the interior walls of a container by multiplying the internal pressure by the area over which the pressure is applied.

Density and Mass Calculation

Density links the mass of a substance to its volume and is used to convert a given volume into mass. This conversion is essential when determining the number of moles of a liquid based on its density, which can then be inserted into the ideal gas law for further calculations.

Unit Conversion

Unit conversion is critical in solving physics and chemistry problems, particularly when the problem spans different measurement systems. Converting units, such as volume, pressure, or force, ensures that all values are consistent and that the final answer is expressed in the desired measurement system.

Transcript

00:01 Question 11224 for this question: the voting that we do is to calculate the volume of celinda pi aspa, and that would be 3.142 times.

00:39 Radius is 10 centimeters and then the length is top 20 and that gives 2 s 2 s.

00:53 4 centimeter, i o 624 liso.

01:04 We know that often the 5 men liquid ammonia is added to export.

01:18 The volume of air will be.

01:25 This far do the following of linderman 25, and that is 62 at 9, the letter of 6.259 theta.

01:50 This is 6.2 per leta.

01:58 Now we need to find after we have the container.

02:03 We have a nitrogen point, so i want to calculate the mole of her and molemo of and it container column of air will be 6.2 power in later, and we are told that the pressure is limitation.

02:44 Is co atmosphere and the temperature is 298 to 90 is 298 square, so we use the attigeto calculate the mole of air 6.259, liver, divided by 0.08, more square tins 298 and the petengives in 0.2561 molar of a now.

03:57 I need to calculate more of nitration of nitro and a container we have 25.

04:17 We are told that the squares .8 plus 7 gram per me, and so we already have the mass of apout.

04:32 We also know that 28 camfitn know neither give to this mona mass.

04:45 Will be 14 times, 2 is 28.

04:50 Meat is positive, mole of it oggetti state dogteams .8 to 528, and that we that i theropont 05 mo so pressure is set it by mixture of nitrate stan by make sure of nitrogen and air.

05:54 You use p v equals a p, so is going to be total pressure because it's going to the going to be exprest by both nitrogen and air...

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