(II) A storage tank at STP contains 28.5 kg of nitrogen (N2) . (a) What is the volume of the tan

(II) A storage tank at STP contains 28.5 kg of nitrogen (N2)...

Key Concepts

Mole-Mass Conversion

Converting between mass and moles is critical in gas calculations because the ideal gas law uses the amount of substance (n) in moles. This conversion is done using the molar mass of the gas, which enables the determination of the number of moles from a given mass, linking the macroscopic (mass) and microscopic (molecular quantity) views of a substance.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental equation in thermodynamics that relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas using the gas constant (R). It is used to determine one variable when the others are known, making it essential for calculations involving the behavior of gases under various conditions.

Standard Temperature and Pressure (STP)

STP refers to a set of reference conditions for gases, typically 0°C (273.15 K) and 1 atm of pressure. These conditions are used to simplify calculations and comparisons for gas volumes and behaviors, providing a baseline to understand how gases behave under standardized conditions.

Transcript

00:01 A storage tank at standard temperature and pressure contains 28 .5 kilograms of nitrogen.

00:07 Firstly, what is the volume of the tank? what is the pressure if an additional 25 kilograms of nitrogen is added without changing the pressure? right.

00:18 So we're going to start from two equations.

00:20 So the first equation is standard gas law.

00:22 So p pressure times volume is equal to a number of moles times gas constant times the temperature.

00:30 Chat.

00:33 And we are also going to relate the number of moles to the mass.

00:39 So number of moles times a standard atomic weight is equal to the mass.

00:46 And by substituting, so if we call this equation one, and equation two, by substituting equation two into equation one, we can say that, and rearranging because we want the volume to be the subject of the equation.

01:02 So we get that volume is equal to mass times the gas constant times the temperature over the standard atomic weight and multiplied by the pressure.

01:18 We're going to call this equation three.

01:22 So we have the mass is given by 28 .5.

01:28 So let's work out what we've got.

01:30 So m equals 28 .5.

01:32 So from the question, although i prefer working in standard international units because that enables consistency.

01:43 So we're going to work in grams because that's a standard unit.

01:47 So 2 .85 times 10 to the 4 because then we don't make mistakes when we're in si units and it's much easier to make a mistake if you're working in different units and then your units don't match up.

02:02 So you're off and off by factors of 10 and that's bad because then you don't get the marks and that kind of sucks.

02:09 The gas constant is given by standard 8 .31 and that's joules.

02:17 So this is grams, joules per kelvin per mole.

02:23 And this one.

02:26 Temperature is given by 273 kelvin or 0 degrees celsius.

02:33 T equals 273 kelvin and pressure is a pressure and so yeah pressure standard is so it's 1 .013 times 10 to the 5 pascals p a and and the standard atomic weight of a nitrogen molecule so nitrogen hangs around in dimers and 2.

03:04 So it's 2 times the standard atomic weight of a nitrogen molecule, which is 14 to 14 .0 to 3 significant figures.

03:13 So we have a is equal to 28 grams per mole.

03:26 And substituting all of these into this equation here.

03:31 So substituting these five into this equation, plugging it into calculation.

03:35 We have, but the volume is equal to, let me just double check this on a calculator is equal to 22 .8 meters cubed.

03:52 And so for part b, we do our trick where we divide through the two equations to get a relationship.

04:03 So i'm just going to start a new wide.

04:06 Board for this...

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