A balloon is filled to a volume of 2.0 102 mL at a temperature of 33.0°C. The balloon is then cooled at constant pressure to a temperature of 1.00 102 K. What is the final volume of the balloon?
To find the final volume of the balloon, we can use the combined gas law formula, which relates the initial temperature, initial volume, final temperature, and final volume of a gas at constant pressure. The formula is given as:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
P₁ = initial pressure (constant, so it cancels out)
V₁ = initial volume (known)
T₁ = initial temperature (known)
P₂ = final pressure (constant, so it cancels out)
V₂ = final volume (unknown, what we are trying to find)
T₂ = final temperature (known)
In this case, the initial volume (V₁) is given as 2.0 × 10² mL, the initial temperature (T₁) is given as 33.0°C, and the final temperature (T₂) is given as 1.00 × 10² K.
First, we need to convert the initial volume (V₁) from mL to L:
V₁ = 2.0 × 10² mL = 2.0 × 10² mL ÷ 1000 mL/L = 2.0 L
Next, we need to convert the initial temperature (T₁) from Celsius to Kelvin:
T₁ = 33.0°C + 273.15 = 306.15 K
Next, we can substitute these values into the combined gas law formula:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Since the pressure (P₁ and P₂) is constant and cancels out, we can simplify the formula:
V₁ / T₁ = V₂ / T₂
Now, we can solve for the unknown final volume (V₂):
V₂ = (V₁ × T₂) / T₁
Substituting the given values:
V₂ = (2.0 L × 1.00 × 10² K) / 306.15 K
Calculating this expression will give us the final volume (V₂) of the balloon.
(V1/T1) = (V2/T2)
T must be in kelvin.