An ideal gas is contained in a cylinder with a volume of 5.0 102 mL at a temperature of 30.°C and a pressure of 710. torr. The gas is then compressed to a volume of 27 mL, and the temperature is raised to 800.°C. What is the new pressure of the gas?
Change temps to kelvins
P2V2/T2=P1V1/T1
solve for P2
im confused on what numbers need to be plugged into the equation
Then write them down in columns
P1.....V1......P2.......V2....T1.....T2
then substitute into the equation.
okay so its (710)(500)/(303)=p2(27)/1073
then i multiply?
Yes, solve for P2. You multiply AND divide to do that.
To determine the new pressure of the gas, you can use the combined gas law equation, which relates the initial and final conditions of a gas sample.
The combined gas law equation is given as:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (710. torr)
V1 = initial volume (5.0 * 10^2 mL)
T1 = initial temperature (30.°C + 273.15) converted to Kelvin (303.15 K)
P2 = final pressure (unknown)
V2 = final volume (27 mL)
T2 = final temperature (800.°C + 273.15) converted to Kelvin (1073.15 K)
Now, let's substitute the given values into the equation:
(710. torr * 5.0 * 10^2 mL) / (303.15 K) = (P2 * 27 mL) / (1073.15 K)
Solving for P2 (final pressure):
P2 = [(710. torr * 5.0 * 10^2 mL) / (303.15 K)] * [(1073.15 K) / (27 mL)]
Now, perform the calculation:
P2 = 3142.46 torr
Therefore, the new pressure of the gas is approximately 3142.46 torr.