Final answer:
To find the final temperature of the compressed gas, the combined gas law is used, where pressure and temperature are directly proportional when volume is constant. After converting to the appropriate units and using the formula P1/T1 = P2/T2, the final temperature is calculated to be 51.9°C, which is not listed in the provided options.
Step-by-step explanation:
The question involves using the combined gas law, which relates pressure, temperature, and volume of a gas. Given that a gas at 31.0°C is compressed from 1.45 atm to 1175 mmHg, to find the final temperature after compression, we can use the combined gas law formula: P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature. It's important to first convert temperatures to Kelvin and pressures to the same units before doing any calculations.
First, convert the initial temperature from °C to K: T1 = 31.0 + 273.15 = 304.15 K. Then, convert 1.45 atm to mmHg: 1.45 atm × 760 mmHg/atm = 1102 mmHg. Now, we can set up the equation like this:
1102 mmHg / 304.15 K = 1175 mmHg / T2
By solving for T2, we get: T2 = (1175 mmHg × 304.15 K) / 1102 mmHg ≈ 325.05 K
Now, convert the final temperature back to °C: T2 = 325.05 K - 273.15 = 51.9°C. Since this temperature is not one of the provided options, the student may have made a mistake in the options or in their initial conversion. None of the options A) 31.0°C B) 0.62°C C) 1198.8°C D) 75.9°C match the calculated temperature of 51.9°C.