a balloon is filled to a volume of 7.00 x 10 to the second mL at a temperature of 20.0 degrees celcius. the balloon is then cooled at a constant pressure to a temperature of 100 k. what is the final volume of the balloon?
(V1/T1) = (V2/T2)
T1 must be changed from CELSIUS (note the spelling) to kelvin.
To find the final volume of the balloon, we can use the combined gas law equation. The combined gas law relates the initial and final states of a gas sample while keeping the pressure constant.
The combined gas law equation is as follows:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
Where:
P₁ and P₂ are the initial and final pressures (constant in this case).
V₁ and V₂ are the initial and final volumes (unknown in this case).
T₁ and T₂ are the initial and final temperatures.
Given:
Initial volume, V₁ = 7.00 x 10^2 mL = 700 mL
Initial temperature, T₁ = 20.0 degrees Celsius
Final temperature, T₂ = 100 K
First, we need to convert the initial temperature from Celsius to Kelvin:
T₁ = 20.0 degrees Celsius + 273.15 = 293.15 K
Now we can rearrange the combined gas law equation to solve for V₂:
V₂ = (P₁ * V₁ * T₂) / (P₂ * T₁)
Since the pressure is constant, we can consider P₁ = P₂, so the equation becomes:
V₂ = (V₁ * T₂) / T₁
Plugging in the values:
V₂ = (700 mL * 100 K) / 293.15 K
Finally, calculate:
V₂ = (70000 mL * K) / 293.15 K = 238.62 mL (rounded to two decimal places)
Therefore, the final volume of the balloon is approximately 238.62 mL.