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 695. torr. The gas is then compressed to a volume of 25 mL, and the temperature is raised to 814.°C. What is the new pressure of the gas?
(P1V1/T1) = (P2V2/T2)
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To find the new pressure of the gas after the compression and temperature change, we can use the combined gas law equation. The combined gas law is given by:
(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.
First, we need to convert the initial and final volumes from mL to liters:
Initial volume (V1) = 5.0 × 10^2 mL = 5.0 × 10^-1 L
Final volume (V2) = 25 mL = 25 × 10^-3 L
Next, we need to convert the initial and final temperatures from Celsius to Kelvin:
Initial temperature (T1) = 30°C + 273.15 = 303.15 K
Final temperature (T2) = 814°C + 273.15 = 1087.15 K
Now, we can substitute the values into the combined gas law equation and solve for the new pressure (P2):
(P1 × V1) / (T1) = (P2 × V2) / (T2)
695 torr × 5.0 × 10^-1 L / 303.15 K = (P2 × 25 × 10^-3 L) / 1087.15 K
By cross-multiplying and rearranging the equation, we can solve for P2:
P2 = (695 torr × 5.0 × 10^-1 L × 1087.15 K) / (25 × 10^-3 L × 303.15 K)
Now, we can plug in the values and calculate P2:
P2 = (695 torr × 5.0 × 10^-1 L × 1087.15 K) / (25 × 10^-3 L × 303.15 K)
P2 ≈ 5276.856 torr
Therefore, the new pressure of the gas is approximately 5276.856 torr.