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Chapter 5: Problem 123

Draw a qualitative graph to show how the first property varies with the second in each of the following (assume 1 mole of an ideal gas and \(T\) in kelvin). a. \(P V\) versus \(V\) with constant \(T\) b. \(P\) versus \(T\) with constant \(V\) c. \(T\) versus \(V\) with constant \(P\) d. \(P\) versus \(V\) with constant \(T\) e. \(P\) versus \(1 / V\) with constant \(T\) f. \(P V / T\) versus \(P\)

Short Answer

Expert verified
a. The graph of PV versus V with constant T will be a straight line with a positive slope. b. The graph of P versus T with constant V will be a straight line with a positive slope. c. The graph of T versus V with constant P will be a straight line with a positive slope. d. The graph of P versus V with constant T will be a downward curve (hyperbola). e. The graph of P versus 1/V with constant T will be a straight line with a positive slope. f. The graph of PV/T versus P will be a horizontal straight line with no slope.

Step by step solution

01

a. Graph of PV versus V with constant T

In this scenario, temperature is constant, and we need to plot the relation between PV and V. From the ideal gas law, we know that PV = nRT. Since temperature is constant, we relate PV with V as follows: PV = Constant We can conclude that the graph will be a straight line with a positive slope.
02

b. Graph of P versus T with constant V

In this scenario, we need to plot the relationship between pressure and temperature while keeping the volume constant. By rearranging the ideal gas law equation, we get: P = (nR/V)T When volume is constant, the relation between P and T becomes directly proportional. Thus, the graph will be a straight line with a positive slope.
03

c. Graph of T versus V with constant P

In this scenario, we will plot the relationship between temperature and volume while keeping the pressure constant. Rearranging the ideal gas law equation, we get: T = (PV)/(nR) When pressure is constant, the relation between V and T becomes directly proportional. The graph will be a straight line with a positive slope.
04

d. Graph of P versus V with constant T

In this scenario, we need to plot the relationship between pressure and volume while keeping the temperature constant. By rearranging the ideal gas law equation, we get: P = (nRT)/V When temperature is constant, the relation between P and V becomes inversely proportional. Thus, the graph will be a downward curve known as a hyperbola.
05

e. Graph of P versus 1/V with constant T

In this scenario, we need to plot the relationship between pressure and reciprocal of the volume, keeping the temperature constant. From the ideal gas law, we know that P = (nRT)/V. Rewriting this equation in terms of 1/V, we get: P = (nR)T(V^-1) In this case, pressure and the reciprocal of the volume are directly related. Therefore, the graph will be a straight line with a positive slope.
06

f. Graph of PV/T versus P

In this scenario, we are asked to plot the relationship between (PV/T) and pressure. From the ideal gas law, we know that PV = nRT. If we divide both sides by T, we get: PV/T = nR Since we are considering one mole of an ideal gas, n = 1. Therefore: PV/T = R Since R is a constant, the graph of PV/T versus P will be a horizontal straight line with no slope.

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Most popular questions from this chapter

Small quantities of hydrogen gas can be prepared in the laboratory by the addition of aqueous hydrochloric acid to metallic zinc. $$ \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ Typically, the hydrogen gas is bubbled through water for collection and becomes saturated with water vapor. Suppose 240\. mL of hydrogen gas is collected at \(30 .{ }^{\circ} \mathrm{C}\) and has a total pressure of \(1.032\) atm by this process. What is the partial pressure of hydrogen gas in the sample? How many grams of zinc must have reacted to produce this quantity of hydrogen? (The vapor pressure of water is 32 torr at \(30^{\circ} \mathrm{C}\).)

A 2.50-L container is filled with \(175 \mathrm{~g}\) argon. a. If the pressure is \(10.0 \mathrm{~atm}\), what is the temperature? b. If the temperature is \(225 \mathrm{~K}\), what is the pressure?

Which of the following statements is(are) true? a. If the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant. b. If the temperature of a gas increases from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\), the volume of the gas would double, assuming that the pressure and the number of moles of gas remain constant. c. The device that measures atmospheric pressure is called a barometer. d. If the volume of a gas decreases by one half, then the pressure would double, assuming that the number of moles and the temperature of the gas remain constant.

Consider the reaction between \(50.0 \mathrm{~mL}\) liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}\) (density \(=0.850 \mathrm{~g} / \mathrm{mL}\) ), and \(22.8 \mathrm{~L} \mathrm{O}_{2}\) at \(27^{\circ} \mathrm{C}\) and \(\mathrm{a}\) pressure of \(2.00\) atm. The products of the reaction are \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) Calculate the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) formed if the reaction goes to completion.

Consider three identical flasks filled with different gases. Flask A: \(\mathrm{CO}\) at 760 torr and \(0^{\circ} \mathrm{C}\) Flask \(\mathrm{B}: \mathrm{N}_{2}\) at 250 torr and \(0^{\circ} \mathrm{C}\) Flask C: \(\mathrm{H}_{2}\) at 100 torr and \(0^{\circ} \mathrm{C}\) a. In which flask will the molecules have the greatest average kinetic energy? b. In which flask will the molecules have the greatest average velocity?
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