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Chapter 5: Problem 42

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 after cooling is approximately \(238.8 \mathrm{~mL}\).

Step by step solution

01

Write down the Charles' Law formula.

Charles' Law states that at constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin. The formula for Charles' Law is: \(V_1/T_1 = V_2/T_2\) where, - \(V_1\) is the initial volume of the gas - \(T_1\) is the initial temperature in Kelvin - \(V_2\) is the final volume of the gas - \(T_2\) is the final temperature in Kelvin
02

Convert the given temperatures to Kelvin.

The initial temperature is given in Celsius, and we need to convert it to Kelvin using the formula: \(T(K) = T(^\circ C) + 273.15\) Initial temperature in Kelvin = \(20.0 + 273.15 = 293.15\ \mathrm{K}\) The final temperature is already given in Kelvin.
03

Substitute the given values into the Charles' Law formula.

Now, we have all the necessary values, and we can substitute them into the Charles' Law formula: \(\frac{7.00 \times 10^{2} \mathrm{~mL}}{293.15 \mathrm{~K}} = \frac{V_2}{1.00 \times 10^{2} \mathrm{~K}}\)
04

Solve for the final volume \(V_2\).

To find the final volume, we can cross-multiply and solve for \(V_2\): \(V_2 = \frac{7.00 \times 10^{2} \mathrm{~mL} \times 1.00 \times 10^{2} \mathrm{~K}}{293.15 \mathrm{~K}}\)
05

Calculate the final volume.

Now, compute the final volume: \(V_2 = \frac{7.00 \times 10^{2} \mathrm{~mL} \times 1.00 \times 10^{2} \mathrm{~K}}{293.15 \mathrm{~K}} = 238.8 \mathrm{~mL}\) The final volume of the balloon after cooling is approximately \(238.8 \mathrm{~mL}\).

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Most popular questions from this chapter

Which of the following statements is(are) true? For the false statements, correct them. a. At constant temperature, the lighter the gas molecules, the faster the average velocity of the gas molecules. b. At constant temperature, the heavier the gas molecules, the larger the average kinetic energy of the gas molecules. c. A real gas behaves most ideally when the container volume is relatively large and the gas molecules are moving relatively quickly. d. As temperature increases, the effect of interparticle interactions on gas behavior is increased. e. At constant \(V\) and \(T\), as gas molecules are added into a container, the number of collisions per unit area increases resulting in a higher pressure. f. The kinetic molecular theory predicts that pressure is inversely proportional to temperature at constant volume and moles of gas.

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You have a balloon covering the mouth of a flask filled with air at 1 atm. You apply heat to the bottom of the flask until the yolume of the balloon is equal to that of the flask. a. Which has more air in it, the balloon or the flask? Or do both have the same amount? Explain. b. In which is the pressure greater, the balloon or the flask? Or is the pressure the same? Explain.
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