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Chapter 9: Problem 1234

1 mole of gas occupies a volume of \(100 \mathrm{~m} 1\) at \(50 \mathrm{~mm}\) pressure. What is the volume occupied by two moles of gas at $100 \mathrm{~mm}$ pressure and at same temperature (A) \(50 \mathrm{ml}\) (B) \(200 \mathrm{ml}\) (C) \(100 \mathrm{ml}\) (D) \(500 \mathrm{~m} 1\)

Short Answer

Expert verified
The volume occupied by two moles of gas at 100 mm pressure and the same temperature is \(100~\mathrm{ml}\), which corresponds to option (C).

Step by step solution

01

Define initial and final conditions

Let initial conditions be given by: \(P_1 = 50~\mathrm{mm}\), \(V_1 = 100~\mathrm{ml}\), \(n_1 = 1~\text{mole}\). Let final conditions be given by: \(P_2 = 100~\mathrm{mm}\), \(V_2 = \text{Volume to find}\), \(n_2 = 2~\text{moles}\).
02

Apply the relationship between initial and final conditions

We have the relation: \(\frac{P_1V_1}{n_1}=\frac{P_2V_2}{n_2}\) Plugging in the values: \(\frac{(50~\mathrm{mm})(100~\mathrm{ml})}{1~\text{mole}} = \frac{(100~\mathrm{mm})(V_2)}{2~\text{moles}}\)
03

Solve for the final volume

Now we solve for the final volume, \(V_2\): \(V_2 = \frac{(50~\mathrm{mm})(100~\mathrm{ml})(2~\text{moles})}{(100~\mathrm{mm})(1~\text{mole})}\) \(V_2 = \frac{10000~\mathrm{ml}}{100}\) \(V_2 = 100~\mathrm{ml}\) So the volume occupied by two moles of gas at 100 mm pressure and the same temperature is 100 ml, which corresponds to option (C).

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Most popular questions from this chapter

To double the volume of a given mass at an ideal gas at $27^{\circ} \mathrm{C}$ keeping the pressure constant one must raise the temperature in degree centigrade (A) \(54^{\circ}\) (B) \(600^{\circ}\) (C) \(327^{\circ}\) (D) \(270^{\circ}\)

The rms velocity of gas molecules is \(300 \mathrm{~ms}^{-1}\). The rms velocity of molecules of gas with twice the molecular weight and half the absolute temperature is (A) \(300 \mathrm{~ms}^{-1}\) (B) \(150 \mathrm{~ms}^{-1}\) (C) \(600 \mathrm{~ms}^{-1}\) (D) \(75 \mathrm{~ms}^{-1}\)

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