(II) What is the pressure inside a 38.0 -L container holding 105.0 kg of argon gas at 20.0^∘ C ?

Name: Problem 39, Chapter 17: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2019-09-01T13:46:38-08:00
Duration: 5 min 9 s
Channel: Jordan Moore
Description: (II) What is the pressure inside a 38.0 -L container holding 105.0 kg of argon gas at 20.0^∘ C ?

(II) What is the pressure inside a 38.0 -L container holding...

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a fundamental equation in thermodynamics that relates the pressure (P), volume (V), the number of moles (n) of a gas, temperature (T), and the universal gas constant (R). It is used to determine one variable when the others are known, making it essential in calculations involving gaseous systems under the assumption that the gas behaves ideally.

Conversion of Mass to Moles

In problems involving gases, it is often necessary to convert the mass of the gas to moles using its molar mass. This conversion allows the use of the Ideal Gas Law, which is based on the amount of substance in moles rather than mass.

Temperature Conversion to Kelvin

Since the Ideal Gas Law requires the temperature to be in an absolute scale, converting temperature from degrees Celsius to Kelvin is crucial. This conversion is done by adding 273.15 to the Celsius temperature, ensuring that calculations are performed with the correct temperature units.

Unit Consistency

Maintaining consistent units across all variables (pressure, volume, temperature, and number of moles) is fundamental when applying the Ideal Gas Law. This often involves converting volumes to liters, pressures to atmospheres or pascals, and using the appropriate value of the gas constant depending on the chosen units.

Transcript

00:01 What is the pressure inside a 38 .0 litre container holding 105 kilograms of argon gas at 20 degrees celsius? right.

00:12 Okay, so we're going to begin from two equations.

00:15 So idle gas law.

00:16 P pressure times volume is equal to n.

00:21 A number of moles, gas constant, which is 8 .3 .1, and temperature.

00:27 So pv equals nrt.

00:30 We're going to call that equation 1.

00:33 And our other equation relates the number of moles to mass.

00:38 So mass is equal to number of moles times the standard atomic weight of the material.

00:52 And because we want to find pressure, pressure is our unknown.

00:55 We're going to make pressure.

00:56 We're going to call this equation 2, and we're going to make pressure the the subject of the equation, and we're also going to substitute in equation to equation 1.

01:08 So n equals m over ar, and we're going to substitute out n with m over ar here.

01:14 And doing that, we get to pressure is equal to m mass times the gas constant times the temperature, divided by volume times the gas constant.

01:32 And i like to stick to standard international units because that means that i don't make mistakes when i'm putting this all through a calculator.

01:41 So the mass is given as m in this case is equal to 1 .05 times 10 to the 5 grams.

01:54 R is equal to 8 .31.

02:01 And our units in this case are given by joules per kelvin per mole.

02:14 Temperature is at 20 degrees.

02:17 So in terms of kelvin, that's equal to 219.

02:20 So 273, which is absolute 0, which is 0 degrees celsius plus 20.

02:26 So 293 kelvin.

02:32 And our volume is given by, is given by, so we're going to give this in terms of meters cube because that's a standard international unit is in meters, is equal to...

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