A sample of gas at 35degree Celsius and 1 atm occupies a volume of 37.5L. At what temp should the gas be kept, if it required to reduce the volume to 3.0 litre at the same pressure?

Question

A sample of gas at 35degree Celsius  and 1 atm occupies a volume of 37.5L. At what temp should the gas be kept, if it required to reduce the volume to 3.0 litre at the same    pressure?

Jeremiah Adams · Accepted Answer

The gas should be kept at -248 degrees C.

Apply Charles Law to determine the direct relationship between temperature and volume in degrees Kelvin (assuming constant pressure and molecular count). # V_1/T_1 = V_2/T_2# # V_1 = 37.5l# # T_1 = 35 + 273 = 308# degrees K # V_2 = 3.0l# # T_2 = unknown These values can be substituted into the equation to get # 37.5/308 = 3.0/ T_2# multiplying across gives # T_2 = 308 xx 3.0/37.5# Which gives # T_2 = 24.6 degrees K To find degrees C, subtract 273. # 24.6 -273 = -248# degrees C. ( to three significant digits.)

Cooper Anderson · Answer

undefined Using the combined gas law equation, rearranging to solve for the final temperature, and plugging in the given values:

$T_f = \frac{P_iV_iT_i}{P_fV_f}$

$T_f = \frac{(1 \, \text{atm})(37.5 \, \text{L})(308 \, \text{K})}{(1 \, \text{atm})(3.0 \, \text{L})}$

$T_f \approx 1152 \, \text{K}$

So, the gas should be kept at approximately 1152 Kelvin to reduce the volume to 3.0 liters at the same pressure.