A #5 L# container holds #15 # mol and #8 # mol of gasses A and B, respectively. Every four of molecules of gas B bind to three molecule of gas A and the reaction changes the temperature from #250^oK# to #370 ^oK#. By how much does the pressure change?
The final pressure is 1.4 times whatever the initial pressure was.
The ratio of the temperature change in oK is equal to the ratio of the change in the total number of moles of gas in the container times the inverse ratio of the pressures, assuming ideal gas behavior where n = PV/RT and a constant volume.
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To solve this problem, we need to first determine the number of molecules of gas A and B that are involved in the reaction. Given that there are 15 moles of gas A and 8 moles of gas B, we can use Avogadro's number to find the total number of molecules for each gas.
Then, we can calculate the initial and final pressures of the gas using the ideal gas law, (PV = nRT), where (P) is pressure, (V) is volume, (n) is the number of moles of gas, (R) is the ideal gas constant, and (T) is temperature in Kelvin.
After finding the initial and final pressures, we can subtract the initial pressure from the final pressure to determine the change in pressure.
Let's proceed with the calculations:

Calculate the number of molecules of gas A and B:
 Number of molecules of gas A: (15 , \text{moles} \times 6.022 \times 10^{23} , \text{molecules/mol})
 Number of molecules of gas B: (8 , \text{moles} \times 6.022 \times 10^{23} , \text{molecules/mol})

Determine the number of molecules of B that react with A:
 Since every 4 molecules of B react with 3 molecules of A, the number of molecules of B that react with A is: (\frac{8 , \text{moles} \times 6.022 \times 10^{23} , \text{molecules/mol}}{4} = 1.5055 \times 10^{24} , \text{molecules of B})

Calculate the total number of molecules remaining after the reaction:
 Number of molecules of A remaining: (15 , \text{moles} \times 6.022 \times 10^{23} , \text{molecules/mol}  3 \times 1.5055 \times 10^{24} , \text{molecules of A})
 Number of molecules of B remaining: (8 , \text{moles} \times 6.022 \times 10^{23} , \text{molecules/mol}  4 \times 1.5055 \times 10^{24} , \text{molecules of B})

Calculate the initial and final pressures using the ideal gas law:
 Initial pressure: (P_1 = \frac{nRT}{V}) at (T = 250 , \text{K})
 Final pressure: (P_2 = \frac{nRT}{V}) at (T = 370 , \text{K})

Calculate the change in pressure:
 Change in pressure: (P_2  P_1)
Performing these calculations will give us the change in pressure.
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When evaluating a onesided 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 onesided 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 onesided 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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 A #5 L# container holds #7 # mol and #4 # mol of gasses A and B, respectively. Groups of four of molecules of gas B bind to three molecule of gas A and the reaction changes the temperature from #250^oK# to #370 ^oK#. By how much does the pressure change?
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