Ammonia is essential to so many industries that, on a molar...

Ammonia is essential to so many industries that, on a molar basis, it is the most heavily produced substance in the world. Calculate $P_{\mathrm{IGL}}$ and $P_{\mathrm{VDW}}(\text { in atm })$ of 51.1 $\mathrm{g}$ of ammonia in a $3.000-L$ container at $0^{\circ} \mathrm{C}$ and $400 .^{\circ} \mathrm{C},$ the industrial temperature. (See Table 5.4 for the values of the van der Waals constants.)

Key Concepts

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry and physics represented as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is the absolute temperature in Kelvin. This law describes the relationship between these variables for a hypothetical ideal gas, assuming that the gas molecules do not interact and occupy negligible volume.

Van der Waals Equation

The van der Waals equation is an adjusted form of the ideal gas law that accounts for the finite size of gas molecules and the intermolecular forces acting between them. It introduces two constants, a and b, which correct the pressure and volume terms respectively, resulting in the equation [P + a(n/V)²](V - nb) = nRT. This equation provides a more accurate model for real gases, particularly under conditions of high pressure and low temperature.

Mole Concept

The mole concept is fundamental in chemistry for relating the mass of a substance to the number of particles it contains. By dividing the mass of a substance by its molar mass, one can determine the number of moles present. This conversion is crucial when applying both the ideal gas law and the van der Waals equation, as these equations require the quantity of substance in moles.

Temperature Conversion

Temperature conversion, particularly from degrees Celsius to Kelvin, is essential in gas law calculations since the ideal gas law and its modifications require the temperature to be expressed in an absolute scale. The conversion is done by adding 273.15 to the Celsius temperature, ensuring that all thermodynamic equations are used with the correct temperature units.

Transcript

00:01 This problem, we're trying to figure out the pressure of ammonia under certain conditions.

00:08 Just write ammonia up here.

00:11 We're trying to look at the ideal gas law versus the vanderwals equation.

00:16 The ideal gas law is pb equals nrt, a very simple equation.

00:24 And vanderwalls essentially builds on that.

00:27 We get p plus n squared a over v squared, v minus n b equals n r t the vanderwells adjusts the pressure term to include a term for inter -particle interactions and v minus nb this term has to do with adjusting the volume to account for the volume of the particles because then in the ill gas we assume doesn't really have mass nor volume so looking at the info that we have.

01:14 We know the mass of the ammonia.

01:17 We know volume, temperature.

01:18 We have two temperatures.

01:20 We actually have to solve it for both.

01:23 And we know r, which is just a constant.

01:28 So first thing we want to do is mass doesn't help us here.

01:30 We mean moles.

01:33 So if you look it up, molar mass of ammonia should be 17 .03 grams per mole.

01:46 If you solve that, you'll find the n equals almost exactly three.

01:56 So now let's look back at these equations.

01:58 First, let's just adjust them so we are solving for pressure.

02:04 So p equals nrt over v.

02:09 So then adjusting this, we get p plus n squared a over v squared equals nrt over v.

02:23 Minus n b and solving one more time by subtracting that term make it p equals n r t or v minus n b my this n squared a over v squared so we're almost ready to solve everything but there are a few more things we need first of all we can't actually solve these equations using degrees celsius you actually have to convert them to kelvin, which is luckily a very easy conversion.

03:01 So this actually becomes 273 kelvin, because all you have to do is add 273...

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