To what Celsius temperature must 44.0 mm Hg of methane gas at 89.0°C be changed so the pressure will be 83.0 mm Hg? Assume the volume and the amount of gas are held constant.
P1/T1 = P2/T2
To find the Celsius temperature at which the methane gas must be changed in order to achieve a pressure of 83.0 mm Hg, we can use the combined gas law equation:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ is the initial pressure (44.0 mm Hg)
V₁ is the initial volume (assumed constant)
T₁ is the initial temperature in Celsius (89.0°C + 273.15 = 362.15 K)
P₂ is the final pressure (83.0 mm Hg)
V₂ is the final volume (assumed constant)
T₂ is the final temperature in Celsius (what we're trying to find)
First, let's rearrange the equation to solve for T₂:
T₂ = (P₂ * V₁ * T₁) / (P₁ * V₂)
Now let's plug in the given values:
T₂ = (83.0 * (44.0) * (362.15)) / (44.0 * V₂)
Since the volume is held constant, we can assume V₁ = V₂, which cancels out:
T₂ = (83.0 * 362.15) / 44.0
Now we can calculate T₂:
T₂ = 676.7678
Therefore, to achieve a pressure of 83.0 mm Hg, the methane gas should be changed to a temperature of approximately 676.77°C.