An ideal gas is in a cylinder with a volume of 5.5 ✕ 102 mL at a temperature of 25°C and a pressure of 710 torr. The gas is compressed to a volume of 29 mL, and the temperature is raised to 810°C. What is the new pressure?
Use (P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.
To find the new pressure of the gas, we can use the combined gas law equation, which states:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.
Given:
Initial volume (V1) = 5.5 x 10^2 mL
Initial temperature (T1) = 25°C = 298 K (convert Celsius to Kelvin by adding 273.15)
Initial pressure (P1) = 710 torr
Final volume (V2) = 29 mL
Final temperature (T2) = 810°C = 1083 K
Unknown: Final pressure (P2)
Now we can plug the given values into the combined gas law equation and solve for P2:
(P1 * V1) / T1 = (P2 * V2) / T2
(P2 * V2) / T2 = (P1 * V1) / T1
P2 = (P1 * V1 * T2) / (V2 * T1)
Let's calculate it using the given values:
P2 = (710 torr * 5.5 x 10^2 mL * 1083 K) / (29 mL * 298 K)
P2 ≈ 7171.12 torr
Therefore, the new pressure of the gas is approximately 7171.12 torr.