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Chapter 9: Problem 1225

At a given volume and temperature the pressure of gas (A) Varies inversely as the square of its mass (B) Varies inversely as its mass (C) is independent of its mass (D) Varies linearly as its mass

Short Answer

Expert verified
The pressure of a gas at a given volume and temperature varies linearly as its mass (D). This can be deduced from the Ideal Gas Law equation, \(PV = nRT\), by expressing the number of moles, n, in terms of mass (m) and molar mass (M) using the relationship \(n = \frac{m}{M}\), leading to the equation \(P = \frac{mRT}{MV}\), which demonstrates the direct proportionality between pressure (P) and mass (m).

Step by step solution

01

Express the number of moles in terms of mass

For a given gas, we can express the number of moles, n, in terms of the mass, m, using the molar mass, M, of the gas. Molar mass is the mass of one mole of a substance. We can write the relationship between moles and mass as: \(n = \frac{m}{M}\)
02

Substitute the expression for the number of moles in the Ideal Gas Law

Now, we can substitute the expression for n (number of moles) in terms of mass in the Ideal Gas Law equation: \(PV = \frac{m}{M}RT\)
03

Analyze the dependence of pressure on mass

Let's further analyze the modified Ideal Gas Law equation: \(P = \frac{mRT}{MV}\) Since R, T, and V are constant parameters in this problem, the equation above shows that pressure (P) is directly proportional to the mass (m) of the gas: \(P \propto m\)
04

Choose the correct option

According to our analysis, pressure is directly proportional to the mass of the gas at a given volume and temperature. Therefore, the correct option is: (D) Varies linearly as its mass

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Most popular questions from this chapter

The specific heats at constant pressure is greater than that of the same gas at constant volume because (A) At constant volume work is done in expanding the gas. (B) At constant pressure work is done in expanding the gas. (C) The molecular vibration increases more at constant pressure. (D) The molecular attraction increases more at constant pressure.

To what temperature should the hydrogen at room temperature $\left(27^{\circ} \mathrm{C}\right)$ be heated at constant pressure so that the rms velocity of its molecule becomes double of its previous value (A) \(927^{\circ} \mathrm{C}\) (B) \(600^{\circ} \mathrm{C}\) (C) \(108^{\circ} \mathrm{C}\) (D) \(1200^{\circ} \mathrm{C}\)

At what temperature, pressure remaining unchanged, will the rms velocity of a gas be half its value at \(0^{\circ} \mathrm{C}\) ? (A) \(204.75 \mathrm{~K}\) (B) \(204.75^{\circ} \mathrm{C}\) (C) \(-204.75 \mathrm{~K}\) (D) \(-204.75^{\circ} \mathrm{C}\)

A gas at \(27{ }^{\circ} \mathrm{C}\) temperature and 30 atmospheric pressure $1 \mathrm{~s}$ allowed to expand to the atmospheric pressure if the volume becomes two times its initial volume, then the final temperature becomes (A) \(273^{\circ} \mathrm{C}\) (B) \(-173^{\circ} \mathrm{C}\) (C) \(173^{\circ} \mathrm{C}\) (D) \(100^{\circ} \mathrm{C}\)

The rms speed of a gas at a certain temperature is \(\sqrt{2}\) times than that of the Oxygen molecule at that temperature, the gas is (A) \(\mathrm{SO}_{2}\) (B) \(\mathrm{CH}_{4}\) (C) \(\mathrm{H}_{2}\) (D) \(\mathrm{He}\)
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