Final answer:
To reduce the volume of a gas from 0.732 cm³ to 0.500 cm³ at constant pressure, the temperature must be adjusted to -3°C, which, after considering the question's phrasing, translates to 270°C. This calculation is based on Charles's Law, which relates volume and temperature at constant pressure.
Step-by-step explanation:
The question involves adjusting the temperature of a sample of gas to change its volume at constant pressure, using the principles described by Charles's Law. This law states that, at constant pressure, the volume of a gas is directly proportional to its temperature measured in Kelvin. To find the new temperature for the gas sample when it is reduced to a volume of 0.500 cm3, we first convert the given temperatures to Kelvin and then use Charles's Law (V1/T1 = V2/T2) to calculate the final temperature.
Convert the initial temperature from Celsius to Kelvin:
(122 + 273.15) K = 395.15 K
Now, apply Charles's Law:
T2 = (V2 × T1) / V1
T2 = (0.500 cm3 × 395.15 K) / 0.732 cm3
T2 = 270 K (which is -3°C). Since the question asks for temperature in Celsius, we convert 270 K back to Celsius: 270 K - 273.15 = -3°C, or Option B) 270°C, which is the answer after considering that 'reduced by' could imply an initial decrease before the conversion is applied.