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Chapter 8: Problem 44

A balloon is filled to a volume of \(7.00 \times 10^{2} \mathrm{mL}\) at a temperature of \(20.0^{\circ} \mathrm{C}\). The balloon is then cooled at constant pressure to a temperature of \(1.00 \times 10^{2} \mathrm{K}\). What is the final volume of the balloon?

Short Answer

Expert verified
The final volume of the balloon is approximately \( 238.77 \mathrm{mL} \).

Step by step solution

01

Convert the given temperatures to Kelvin

First, we need to convert the given temperatures from Celsius to Kelvin. To do this, just add 273.15 to the Celsius temperature. Initial temperature in °C: \( 20.0 °C \) Initial temperature in K: \( 20.0 + 273.15 = 293.15 K \) Final temperature is given in Kelvin as: \( 1.00 \times 10^{2} K \)
02

Write down the given values and the Charles' law formula

The given values are: Initial volume V1: \( 7.00 \times 10^{2} \mathrm{mL} \) Initial temperature T1: \( 293.15 K \) Final temperature T2: \( 1.00 \times 10^{2} K \) The Charles' law formula: \( V1/T1 = V2/T2 \)
03

Substitute the given values into the Charles' law formula and solve for V2

Putting the values into the formula, we have: \( (7.00 \times 10^{2} \mathrm{mL})/293.15 K = V2 / 1.00 \times 10^{2} K \) Now, solve for V2: \( V2 = (7.00 \times 10^{2} \mathrm{mL}) \times (1.00 \times 10^{2} K / 293.15 K) \)
04

Calculate the final volume

Perform the calculation for the final volume: \( V2 = (7.00 \times 10^{2} \mathrm{mL}) \times (1.00 \times 10^{2} K / 293.15 K) \) \( V2 = 700 \mathrm{mL} \times (100 K / 293.15 K) \) \( V2 = 700 \mathrm{mL} \times 0.3411 \) \( V2 = 238.77 \mathrm{mL} \) The final volume of the balloon is approximately \( 238.77 \mathrm{mL} \).

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Most popular questions from this chapter

A certain flexible weather balloon contains helium gas at a volume of \(855\) \(\mathrm{L}\). Initially, the balloon is at sea level where the temperature is \(25^{\circ} \mathrm{C}\) and the barometric pressure is \(730\) torr. The balloon then rises to an altitude of \(6000 \mathrm{ft}\), where the pressure is \(605\) torr and the temperature is \(15^{\circ} \mathrm{C}\). What is the change in volume of the balloon as it ascends from sea level to \(6000 \mathrm{ft} ?\)

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