Physics Applied to Diving 4.- Avogadro's Law

Avogadro's law shows the relationship between the volume of a gas and the amount of substance in the Ideal Gas Model. In SCUBA diving this law gives reason to why when you fill your BCD it's volume is proportional to how much air you get in.

This law enunciates that: "At the same temperature and pressure the molar volume of all ideal gases is the same." [1]

The mathematical way to show this law is:

V=n*k

Where V is the volume of the gas, n is the amount of substance of the gas and k is a constant value. This law tells us that a certain amount of gaseos substance occupies a certain amount of space regarding of the molecule species. Remember we aren't speaking about the size of the molecules, but how much space do they need to maintain the temperature and the pressure constant. The number of molecules is measure in moles where each mole corresponds to 6.022 * 10²³ molecules (Avogadro's Number).

Calculations

In order to calculate the volume of a gas from an amount of gas substance only using this law, you need a reference state. Imagine you have a reference state "1" where the volume is V₁ and the amount of substance is n₁, then you change the smount of substance to a known value we call n₂. This new state where the amount of substance is n₂ will have a different unknown volume value that we call V₂. To calculate the value of V₂, we must do the procedure shown next.

V_1/n₁ = k

V_2/n₂ = k

Knowing that k is a constant, meaning it doesn't change value, it has the same value in both cases which gives us:

V_1/n₁ = k = V_2/n₂

V_1/n₁ = V_2/n₂

The equation shown above is useful to calculate V_1,n₁, V₂or n₂ with the proper clearance whenever we have 3 of the 4 variables. In this case because we want to calculate V₂we do the next clearance.

V₂/n₂= V₁/n₁

(V₂*n₂)/n₂= (n₂*V₁)/n₁

V₂= (n₂*V₁)/n₁

Example 1.-

If a volume of gas of 10 liters has 0.4 moles of substance, what will be the volume of the gas if you have 2 moles of gas?

What we know:

V₁ = 10 L

n₁ = 0.4 mol

V₂ =?

n₂ = 2 mol

To find the volume we are looking for, we must do some clearance, so:

V₁/n₁ = V₂/n₂

(n₂*V₁)/n₁ = (n₂*V₂)/n₂

(n₂*V₁)/n₁ = V₂

V₂ = (2 mol * 10 L) / 0.4 mol = 50 L

So, the volume of the gas goes from 10 L to 50 L.

[1] Nicholas W. Tschoegl, Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, First Edition, 2000, page 77

March 30, 2020 Tags : All , Book , Physics Applied to Diving

Monday, March 30, 2020

Physics Applied to Diving 4.- Avogadro's Law