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Chapter 5: Problem 15

State the following gas laws in words and also in the form of an equation: Boyle's law, Charles's law, Avogadro's law. In each case, indicate the conditions under which the law is applicable, and give the units for each quantity in the equation.

Short Answer

Expert verified
Boyle's Law: \( P_1 V_1 = P_2 V_2 \), applicable when temperature and amount of gas are constant; Charles's Law: \( V_1/T_1 = V_2/T_2 \), applicable when pressure and amount of gas are constant; Avogadro's Law: \( V_1/n_1 = V_2/n_2 \), applicable when temperature and pressure are held constant. Units for pressure = atm or Pa, volume = L or m^3, temperature = K.

Step by step solution

01

Boyle's Law

Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. In terms of an equation, it can be represented as \( P_1 V_1 = P_2 V_2 \), where \( P_1 \) & \( P_2 \) are the initial and final pressures of the gas, and \( V_1 \) & \( V_2 \) are the initial and final volumes respectively. It is applicable only when the temperature and amount of gas are constant. In this equation, pressure is typically measured in atmospheres (atm) or pascals (Pa), and volume is usually measured in liters (L) or cubic meters (m^3).
02

Charles's Law

Charles's Law states that the volume and absolute temperature of a gas have a direct relationship when the pressure is held constant. This can be represented in an equation form as \( V_1/T_1 = V_2/T_2 \), where \( V_1 \) & \( V_2 \) represent initial and final volumes, and \( T_1 \) & \( T_2 \) represent initial and final absolute temperatures respectively. This law is applicable when the pressure and amount of gas are held constant. Volume in this equation can be measured in liters (L) or cubic meters (m^3), while temperature must be in Kelvin (K).
03

Avogadro's Law

Avogadro's Law states that the volume and amount of gas (measured in moles) have a direct relationship when temperature and pressure are held constant. In equation form, it is \( V_1/n_1 = V_2/n_2 \), where \( V_1 \) & \( V_2 \) represent initial and final volumes, and \( n_1 \) & \( n_2 \) represent the initial and final amounts of moles of gas respectively. This law is applicable when pressure and temperature are constant conditions. The common unit for volume in this equation is liters (L) or cubic meters (m^3), and 'n', number of moles, is unitless.

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Most popular questions from this chapter

A gas-filled balloon having a volume of \(2.50 \mathrm{~L}\) at \(1.2 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\) is allowed to rise to the stratosphere (about \(30 \mathrm{~km}\) above the surface of Earth), where the temperature and pressure are \(-23^{\circ} \mathrm{C}\) and \(3.00 \times 10^{-3}\) atm, respectively. Calculate the final volume of the balloon.

If the maximum distance that water may be brought up a well by a suction pump is \(34 \mathrm{ft}(10.3 \mathrm{~m}),\) how is it possible to obtain water and oil from hundreds of feet below the surface of Earth?

Name five elements and five compounds that exist as gases at room temperature.

A quantity of gas weighing \(7.10 \mathrm{~g}\) at 741 torr and \(44^{\circ} \mathrm{C}\) occupies a volume of \(5.40 \mathrm{~L}\). What is its molar mass?

The apparatus shown in the diagram can be used to measure atomic and molecular speed. Suppose that a beam of metal atoms is directed at a rotating cylinder in a vacuum. A small opening in the cylinder allows the atoms to strike a target area. Because the cylinder is rotating, atoms traveling at different speeds will strike the target at different positions. In time, a layer of the metal will deposit on the target area, and the variation in its thickness is found to correspond to Maxwell's speed distribution. In one experiment it is found that at \(850^{\circ} \mathrm{C}\) some bismuth (Bi) atoms struck the target at a point \(2.80 \mathrm{~cm}\) from the spot directly opposite the slit. The diameter of the cylinder is \(15.0 \mathrm{~cm}\) and it is rotating at 130 revolutions per second. (a) Calculate the speed \((\mathrm{m} / \mathrm{s})\) at which the target is moving. (Hint: The circumference of a circle is given by \(2 \pi r\), in which \(r\) is the radius.) (b) Calculate the time (in seconds) it takes for the target to travel \(2.80 \mathrm{~cm} .\) (c) Determine the speed of the Bi atoms. Compare your result in (c) with the \(u_{\mathrm{rms}}\) of Bi at \(850^{\circ} \mathrm{C}\). Comment on the difference.
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