# A #7 L# container holds #12 # 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 #350^oK# to #175 ^oK#. By how much does the pressure change?

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The pressure change in this scenario can be calculated using the ideal gas law and the concept of stoichiometry for the reaction between gases A and B. Since three molecules of gas B bind to one molecule of gas A, the total number of gas molecules decreases after the reaction. The ideal gas law equation relating pressure, volume, moles, and temperature is:

[ PV = nRT ]

Where:

- ( P ) is pressure
- ( V ) is volume (7 L)
- ( n ) is the number of moles
- ( R ) is the ideal gas constant
- ( T ) is temperature (in Kelvin)

The reaction will reduce the number of gas molecules, affecting the total number of moles in the container. Therefore, the pressure change can be calculated using the ideal gas law before and after the reaction, considering the temperature change as well. The ideal gas law can be rearranged to solve for pressure:

[ P = \frac{nRT}{V} ]

Given that ( n_A = 12 ) mol and ( n_B = 18 ) mol initially, and the temperature changes from 350 K to 175 K, we can calculate the initial and final pressures using the ideal gas law. Then, the pressure change can be determined.

[ P_1 = \frac{(12 + 18) \times R \times 350}{7} ]

[ P_2 = \frac{(12 + 18) \times R \times 175}{7} ]

[ \Delta P = P_2 - P_1 ]

Where ( \Delta P ) is the pressure change.

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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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