The temperature of a sample of CH4 at a fixed volume is changed, causing a change in pressure from 44911.44 torr to 6.5 atm. If its new temperature is 688 °C, what was its original temperature in degrees Celsius?

To solve this problem, we can use the Gay-Lussac's law which states that the pressure of a gas is directly proportional to its temperature if the volume and the amount of gas are kept constant. The formula for Gay-Lussac's law is P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.

Step 1: Convert all units to the same system. In this case, we'll convert the pressure from atm to torr since the initial pressure is given in torr. 1 atm = 760 torr, so 6.5 atm = 6.5 * 760 = 4940 torr.

Step 2: Convert the temperatures from Celsius to Kelvin since the temperatures in the Gay-Lussac's law are absolute. The formula to convert Celsius to Kelvin is K = °C + 273.15. So, T2 = 688 °C + 273.15 = 961.15 K.

Step 3: Substitute the values into the Gay-Lussac's law and solve for T1.

44911.44 torr / T1 = 4940 torr / 961.15 K

Cross multiply to solve for T1:

T1 = 44911.44 torr * 961.15 K / 4940 torr = 8765.15 K

Step 4: Convert T1 from Kelvin back to Celsius:

T1 = 8765.15 K - 273.15 = 8492 °C

So, the original temperature of the sample was approximately 8492 °C.