# A #7 L# container holds #7 # mol and #18 # mol of gasses A and B, respectively. Every three of molecules of gas B bind to one molecule of gas A and the reaction changes the temperature from #320^oK# to #240 ^oK#. By how much does the pressure change?

The pressure decreases by

Determine the amount of gas in moles both before and after the reaction is the key to solving this puzzle.

The pressure in each situation and, consequently, the pressure change can then be determined using the ideal gas equation.

The total number of moles we have before the gases react is 7 + 18 = 25.

The equation can be expressed as:

Thus, after the reaction, the total moles are 6 + 1 = 7.

Seven final moles in total.

Using the ideal gas equation, we obtain:

First:

Lastly:

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To find the change in pressure, we can use the combined gas law, which states:

P1V1/T1 = P2V2/T2

Where: P1 = initial pressure V1 = initial volume T1 = initial temperature P2 = final pressure V2 = final volume T2 = final temperature

Given: Initial volume (V1) = 7 L Initial moles of gas A (nA) = 7 mol Initial moles of gas B (nB) = 18 mol Initial temperature (T1) = 320 K Final temperature (T2) = 240 K

Using the ideal gas law, we can find the initial pressure (P1) and final pressure (P2):

P1 = (nA + nB) * R * T1 / V1 P2 = (nA + nB) * R * T2 / V1

Where: R = ideal gas constant (8.314 J/(mol*K))

Substitute the given values into the equations to find P1 and P2, then calculate the difference between the final and initial pressures:

ΔP = P2 - P1

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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