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Chapter 6: Problem 33

What is the molar volume of an ideal gas at (a) \(25^{\circ} \mathrm{C}\) and 1.00 atm; \((b) 100^{\circ} \mathrm{C}\) and 748 Torr?

Short Answer

Expert verified
The molar volume of an ideal gas is (a) \(24.47 L/mol\) at \(25^{\circ} \mathrm{C}\) and 1.00 atm and (b) \(31.24 L/mol\) at \(100^{\circ} \mathrm{C}\) and 748 Torr.

Step by step solution

01

Convert Temperature to Kelvin

First, the given temperatures need to be converted from degrees Celsius to Kelvin using the formula \(K = C + 273.15\). For (a) the temperature in Kelvin is \(25 + 273.15 = 298.15 K\). For (b) the temperature in Kelvin is \(100 + 273.15 = 373.15 K\).
02

Convert Pressure

Next, the pressure of each scenario must be in the same units as the ideal gas constant. For (a) the pressure is already in atm so it stays as 1.00 atm. For (b), the pressure must be converted from Torr to atm using the conversion factor \(1 atm = 760 Torr\), so the pressure in atm is \(748 Torr *(1 atm / 760 Torr) = 0.984 atm\).
03

Calculate Molar Volume

Now we can solve for V in the ideal gas law equation, rearranged to \(V = nRT / P\). For (a), the molar volume is \((1 mol * 0.0821 L*atm / (mol*K) * 298.15 K) / 1.00 atm = 24.47 L/mol\). For (b), the molar volume is \((1 mol * 0.0821 L*atm / (mol*K) * 373.15K) / 0.984 atm = 31.24 L/mol\).

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Most popular questions from this chapter

If the van der Waals equation is solved for volume, a cubic equation is obtained. (a) Derive the equation below by rearranging equation (6.26). \(V^{3}-n\left(\frac{R T+b P}{P}\right) V^{2}+\left(\frac{n^{2} a}{P}\right) V-\frac{n^{3} a b}{P}=0\) (b) What is the volume, in liters, occupied by \(185 \mathrm{g}\) \(\mathrm{CO}_{2}(\mathrm{g})\) at a pressure of \(125 \mathrm{atm}\) and \(286 \mathrm{K} ?\) For \(\mathrm{CO}_{2}(\mathrm{g})\) \(a=3.61 \mathrm{L}^{2} \mathrm{atm} \mathrm{mol}^{-2}\) and \(b=0.0429 \mathrm{Lmol}^{-1}\) [Hint: Use the ideal gas equation to obtain an estimate of the volume. Then refine your estimate, either by trial and error, or using the method of successive approximations. See Appendix A, pages A5-A6, for a description of the method of successive approximations.

Determine \(u_{\mathrm{m}}, \bar{u},\) and \(u_{\mathrm{rms}}\) for a group of ten automobiles clocked by radar at speeds of 38,44,45,48,50 \(55,55,57,58,\) and \(60 \mathrm{mi} / \mathrm{h},\) respectively.

Convert each pressure to an equivalent pressure (a) 736 mmHg; (b) 0.776 bar; in atmospheres. (c) 892 Torr; (d) 225 kPa.

The \(u_{\mathrm{rms}}\) of \(\mathrm{H}_{2}\) molecules at \(273 \mathrm{K}\) is \(1.84 \times 10^{3} \mathrm{m} / \mathrm{s}\) At what temperature is \(u_{\mathrm{rms}}\) for \(\mathrm{H}_{2}\) twice this value?

What is the pressure, in pascals, exerted by \(1242 \mathrm{g}\) CO(g) when confined at \(-25^{\circ} \mathrm{C}\) to a cylindrical tank \(25.0 \mathrm{cm}\) in diameter and \(1.75 \mathrm{m}\) high?
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