Final answer:
To find the final volume of a sample of argon gas after heating and pressure change, the combined gas law is used, and the units are converted to SI units. Applying the formula P1V1/T1 = P2V2/T2 and solving for the final volume yields an answer of approximately 12.47 L.
Step-by-step explanation:
To determine the final volume of the argon sample when it is heated from 12 °C to 62 °C and the pressure changes from 570 mmHg to 150 kPa, we will use the combined gas law, which relates the pressure, volume, and temperature of a gas. The combined gas law is given by the equation:
P1V1/T1 = P2V2/T2
First, we need to convert all the units to appropriate SI units: Kelvin for temperature, and Pascals for pressure. To convert degrees Celsius to Kelvin, add 273.15. To convert mmHg to pascals, use the conversion factor 1 mmHg = 133.322 Pa.
The initial and final conditions are:
- Initial temperature T1 = 12 °C + 273.15 = 285.15 K
- Initial pressure P1 = 570 mmHg * 133.322 = 76003.14 Pa
- Final temperature T2 = 62 °C + 273.15 = 335.15 K
- Final pressure P2 = 150 kPa = 150,000 Pa
Using the combined gas law to solve for V2:
V2 = V1 * P1/P2 * T2/T1
V2 = 7.5 L * 76003.14/150,000 * 335.15/285.15
V2 ≈ 12.47 L
The final volume of the argon gas when heated to 62 °C and a pressure of 150 kPa is approximately 12.47 L.