A 93L sample of dry air is cooled from 145 to-22 under constant pressure.What is the final volume?
From 145 what to -22 what? I assume that is temperature of some kind; therefore,
(V1/T1) = (V2/T2)
If 145 and -22 are in kelvin that can be used directly; if in some other units you must change to kelvin to work the problem.
To determine the final volume of the air sample, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, the pressure is constant, so we can rearrange the equation to solve for V:
V₁/T₁ = V₂/T₂
Where V₁ is the initial volume, T₁ is the initial temperature, V₂ is the final volume, and T₂ is the final temperature.
Given:
Initial volume (V₁) = 93L
Initial temperature (T₁) = 145°C
Final temperature (T₂) = -22°C
However, the temperatures need to be converted to Kelvin, as the ideal gas law requires temperature in Kelvin. The conversion formula is: K = °C + 273.15
Converting the temperatures:
T₁ = 145 + 273.15 = 418.15K
T₂ = -22 + 273.15 = 251.15K
Now we can substitute the values into the equation:
(93L) / (418.15K) = V₂ / (251.15K)
To solve for V₂, we can cross-multiply:
(93L) * (251.15K) = (418.15K) * V₂
V₂ = (93L * 251.15K) / 418.15K
Calculating, we get:
V₂ = 55.638 L
Therefore, the final volume of the air sample is approximately 55.638 liters.