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enokoner
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Homework Statement
A mixture of two gases, A and B, exists at pressure p1, volume V, and temperature T1. Gas A is subsequently removed from the mixture in a constant-volume process. The remaining gas B is found to have a pressure p2, volume V, and temperature T2. Express the ratio of the number of moles of gas B to the number of moles of gas A in the terms of p1, p2, T1 and T2.
a. [itex] \frac{p_2 T_1}{p_1 T_2 - p_2 T_1}[/itex]
b. [itex] \frac{p_2 T_1^{2}}{T_2(p_1 T_2 - p_2T_1)}[/itex]
*Options c and d were not written because they contained specific gas constants which do not pertain to molar equations.
Homework Equations
Ideal Gas: [itex]pV = N \overline{R}T[/itex]
Dalton's Law: [itex] p = \sum p_i [/itex]
The Attempt at a Solution
Universal gas constant crosses out. Volume stays constant and also crosses out.
∴ [itex] \frac{N_B}{N_A}= \frac{p_B T_A}{T_B p_A} [/itex]
Relating pA and pB to p1
[itex] p_1= p_A + p_B [/itex]
and to p2
[itex] p_2 = p_B [/itex]
Also, [itex] T_A = T_1 \ T_B = T_2 [/itex]
∴ [itex] \frac{N_B}{N_A}= \frac{p_2 T_1}{T_2(p_2 - p_1)}[/itex]
This is not an option. I have a feeling its because I assumed [itex] p_2 = p_B [/itex]. That assumption doesn't feel right. I don't know how else to relate these two. Thank you for considering this.