A sample of gas occupies a volume of 500.0mL at .906 atm and 97 C. What will the final temperature (in Celsius) be if it is brought to a volume of 1.05L and a pressure of 502 mm Hg?
(P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin to solve the problem, then convert to C for the answer.
To find the final temperature, we can use the combined gas law equation:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature
P₂ = final pressure
V₂ = final volume
T₂ = final temperature (unknown)
Let's plug in the given values:
P₁ = 0.906 atm
V₁ = 500.0 mL = 0.500 L
T₁ = 97 °C = (97 + 273.15) K (convert to Kelvin)
P₂ = 502 mm Hg = (502 / 760) atm (convert to atm)
V₂ = 1.05 L
Now we can substitute these values into the equation and solve for T₂:
(0.906 * 0.500) / (97 + 273.15) = ((502 / 760) * 1.05) / T₂
Simplifying this equation, we get:
0.453 / 370.15 = 0.65921 / T₂
To isolate T₂, we cross multiply and solve for T₂:
T₂ = (0.65921 * 370.15) / 0.453
Calculating this value, we find:
T₂ ≈ 539.441 K
To convert this temperature back to Celsius, we subtract 273.15:
T₂ ≈ 539.441 - 273.15 ≈ 266.291 °C
Therefore, the final temperature will be approximately 266.291 °C.