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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 ratio of the vapor densities of two gases at a given temperature is $9: 8$, The ratio of the rms velocities of their molecule is (A) \(3: 2 \sqrt{2}\) (B) \(2 \sqrt{2}: 3\) (C) \(9: 8\) (D) \(8: 9\)

When temperature of an ideal gas is increased from \(27^{\circ} \mathrm{C}\) to \(227^{\circ} \mathrm{C}\), its rms speed changed from \(400 \mathrm{~ms}^{-1}\) to \(\mathrm{V}_{\mathrm{s}}\). The \(\mathrm{V}_{\mathrm{s}}\) is (A) \(516 \mathrm{~ms}^{-1}\) (B) \(746 \mathrm{~ms}^{-1}\) (C) \(310 \mathrm{~ms}^{-1}\) (D) \(450 \mathrm{~ms}^{-1}\)

The pressure and temperature of two different gases \(P\) and T having the volumes \(\mathrm{V}\) for each. They are mixed keeping the same volume and temperature, the pressure of the mixture will be, (A) \(\mathrm{P}\) (B) \((\mathrm{P} / 2)\) (C) \(4 \mathrm{P}\) (D) \(2 \mathrm{P}\)

Root mean square velocity of a molecule is \(v\) at pressure \(P\). If pressure is increased two times, then the rms velocity becomes (A) \(3 \mathrm{~V}\) (B) \(2 \mathrm{v}\) (C) \(0.5 \mathrm{~V}\) (D) \(\mathrm{v}\)

The root mean square speed of hydrogen molecules of an ideal hydrogen kept in a gas chamber at \(0^{\circ} \mathrm{C}\) is \(3180 \mathrm{~ms}^{-1}\). The pressure on the hydrogen gas is (Density of hydrogen gas is $8.99 \times 10^{-2} \mathrm{~kg} / \mathrm{m}^{3}, 1 \mathrm{~atm}=1.01 \times 10^{5} \mathrm{Nm}^{-2}$ ) (A) \(1.0 \mathrm{~atm}\) (B) \(3.0 \mathrm{~atm}\) (C) \(2.0 \mathrm{~atm}\) (D) \(1.5 \mathrm{~atm}\)
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