Final answer:
To find the final pressure after heating an ideal gas at constant volume and then increasing the gas amount by 50%, apply Charles's law for the temperature change and the ideal gas law for the increase in gas quantity. The final pressure is calculated by multiplying the initial pressure by the temperature ratio and then increasing it by 50%.
Step-by-step explanation:
The question asks to calculate the final pressure of an ideal gas after two processes: heating at a constant volume and increasing the quantity of the gas by 50% at constant volume and temperature. To find the new pressure after heating, we can apply Charles's law which states that at constant volume, the pressure of a gas is directly proportional to its temperature in Kelvin. As the temperature is increased from 30°C (303.15 K) to 131°C (404.15 K), the pressure also increases. The initial pressure of 9 atm will change in the same ratio as the temperature change, which can be calculated as (404.15 K / 303.15 K) * 9 atm.
After calculating the new pressure after the temperature change, we consist the volume and increase the amount of gas by 50% at the same temperature. This corresponds to adding more moles of gas while keeping the volume and temperature the same. According to the ideal gas law PV = nRT, if the amount of gas (n) increases by 50%, the pressure (P) must also increase by 50% since V, R, and T remain constant. Therefore, the final pressure is 1.5 times the pressure found after the temperature change.