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Musings on Ideal Gas Law PV=nRT

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billnotgatez:
1m³ = 1000.0L
now the light shines on my head

billnotgatez:
This is a rewrite of a previous post with better formatting

Please correct me if these thoughts have errors ---

When analyzing some Ideal Gas problems you can treat them as an ideal gas in situation 1 and situation 2.

Given the general Ideal Gas Law formula

[tex]    PV=nRT   [/tex]

Both situations can be represented mathematically by

[tex]    Situation 1 ~ \Longrightarrow ~~   (P_1  \times  V_1) = (n_1  \times  R  \times  T_1)   [/tex]

[tex]    Situation 2 ~ \Longrightarrow ~~   (P_2  \times  V_2) = (n_2  \times  R  \times  T_2)   [/tex]

It follows mathematically

[tex]    Situation 1 ~ \Longrightarrow ~~   (R)  =  \frac{(P_1  \times  V_1) }{ (n_1  \times  T_1)}   [/tex]

[tex]    Situation 2 ~ \Longrightarrow ~~   (R)  =  \frac{(P_2  \times  V_2) }{ (n_2  \times  T_2)}  [/tex]

Since R is the same in both situations (it is a constant)

[tex]     \frac{(P_1  \times  V_1) }{ (n_1  \times  T_1)} =  \frac{(P_2  \times  V_2) }{ (n_2  \times  T_2)}   [/tex]

Algebraically this can be converted to (cross-multiplying)

[tex]   (P_1  \times  V_1  \times  n_2  \times  T_2) = (P_2  \times  V_2  \times  n_1  \times  T_1)   [/tex]

Therefore rearranging the variables

[tex]    (P_2) =  \frac{(P_1  \times  V_1  \times  n_2  \times T_2) }{ (V_2  \times  n_1  \times  T_1)}   [/tex]

Or

[tex]    (V_2) =  \frac{ (P_1  \times  V_1  \times  n_2  \times  T_2) }{ (P_2  \times  n_1  \times  T_1)}   [/tex]

Or

[tex]    (T_2) = \frac { (P_2  \times  V_2  \times  n_1  \times  T_1) }{ (P_1  \times  V_1  \times  n_2)}   [/tex]

Or

[tex]    (n2) =   \frac{(P_2  \times  V_2  \times  n_1  \times  T_1) }{ (P_1  \times  V_1  \times  T_2)}   [/tex]

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