A balloon is filled to a volume of 1.0 102 mL at a temperature of 38.0°C. The balloon is then cooled at constant pressure to a temperature of 1.00 multiplied by 102 K. What is the final volume of the balloon?
(V1/T1) = (V2/T2)
Don't forget to use T1 and T2 in Kelvin.
To find the final volume of the balloon, we can use the combined gas law formula:
(P1 * V1) / T1 = (P2 * V2) / T2
Given:
P1 = pressure at constant pressure (constant pressure means that the pressure does not change, so we can ignore this value)
V1 = initial volume = 1.0 x 10^2 mL = 100 mL
T1 = initial temperature = 38.0°C = 38.0 + 273.15 K (since Kelvin temperature scale is used)
T2 = final temperature = 1.00 x 10^2 K
V2 = ?
Let's substitute the given values into the formula and solve for V2:
(1.0 x 10^2 mL) / (38.0 + 273.15 K) = (P2 * V2) / (1.00 x 10^2 K)
Since the pressure is constant, we can simplify the formula to:
(1.0 x 10^2 mL) / (38.0 + 273.15 K) = V2 / (1.00 x 10^2 K)
Cross-multiplying the equation gives us:
V2 = (1.0 x 10^2 mL) * (1.00 x 10^2 K) / (38.0 + 273.15 K)
Simplifying the equation:
V2 = (1.0 x 10^2) * (1.00 x 10^2) mL * K / (38.0 + 273.15)K
V2 = (1.0 x 10^2) * (1.00 x 10^2) mL / (38.0 + 273.15)
V2 = (1.0 x 10^4) mL / (311.15)
V2 ≈ 32.13 mL (rounded to the appropriate number of significant figures)
Therefore, the final volume of the balloon is approximately 32.13 mL when cooled at constant pressure to a temperature of 1.00 * 10^2 K.