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Chapter 5: Problem 148

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.

Short Answer

Expert verified
Statements a, c, and d are true, while statement b is false.

Step by step solution

01

Statement a: Doubling moles when pressure and temperature are constant

To verify this statement, you need to consider the Ideal Gas Law: \(PV = nRT\) where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Since we are assuming that the pressure (P) and temperature (T) remain constant, and the number of moles (n) doubles, the equation looks like this: \(P(V_1) = n_1RT\) and \(P(V_2) = n_2RT\) Now we can compare the two equations: \(\frac{PV_2}{PV_1} = \frac{n_2RT}{n_1RT}\) As \(n_2 = 2n_1\), we get: \(\frac{V_2}{V_1} = \frac{2n_1}{n_1} = 2\) Thus, the volume (V) doubles when the number of moles doubles, assuming the pressure and temperature remain constant.
02

Statement b: Temperature increase and volume doubling

We again refer to the Ideal Gas Law as follows: \(P(V_1) = nR(T_1)\) and \(P(V_2) = nR(T_2)\) Since the pressure (P) and the number of moles (n) remain constant, we can compare the two equations by introducing the given temperature values: \(\frac{V_2}{V_1} = \frac{T_2}{T_1}\) Here, we need to convert the given temperatures to Kelvin: \(T_1 = 25^{\circ} \mathrm{C} + 273 = 298 \,\mathrm{K}\) \(T_2 = 50^{\circ} \mathrm{C} + 273 = 323 \,\mathrm{K}\) Now we can substitute the values: \(\frac{V_2}{V_1} = \frac{323}{298} \neq 2\) The statement is false as the volume does not double when the temperature increases from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\).
03

Statement c: Device measuring atmospheric pressure

This statement asks for the name of a device that measures atmospheric pressure. The device mentioned, a barometer, is a correct example of such a device. Therefore, statement c is true.
04

Statement d: Pressure increase and volume decrease

This statement can be verified using Boyle's Law, which is a simplified version of the Ideal Gas Law when the number of moles and temperature are constant: \(P_1V_1 = P_2V_2\) The given information states that the volume decreases by half. We can rewrite the equation as: \(\frac{P_2}{P_1} = \frac{V_1}{V_2}\) As \(V_2 = \frac{1}{2}V_1\), we have: \(\frac{P_2}{P_1} = \frac{V_1}{\frac{1}{2}V_1} = 2\) Thus, statement d is true, the pressure would double if the volume decreases by half, while the number of moles and temperature remain constant. In conclusion, statements a, c, and d are all true, while statement b is false.

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Most popular questions from this chapter

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