To solve this problem, you can use the ideal gas law equation:
PV = nRT
Where: P is the pressure V is the volume (kept constant in this case) n is the number of moles of gas (assumed to be constant) R is the ideal gas constant (0.0821 L·atm/(mol·K) or 8.314 J/(mol·K)) T is the temperature in Kelvin
Since the volume is kept constant, the equation simplifies to:
P₁/T₁ = P₂/T₂
Where: P₁ is the initial pressure T₁ is the initial temperature P₂ is the final pressure (what we want to find) T₂ is the final temperature
Now we can plug in the given values:
P₁ = 780.0 mm Hg T₁ = 323.0 K T₂ = 283.15 K (cooled temperature) P₂ = ? (what we want to find)
P₁/T₁ = P₂/T₂
Solving for P₂:
P₂ = (P₁ * T₂) / T₁
P₂ = (780.0 mm Hg * 283.15 K) / 323.0 K
Calculating this expression gives:
P₂ ≈ 683.75 mm Hg
Therefore, the final pressure would be approximately 683.75 mm Hg.