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Chapter 6: Problem 55

What is the volume, in liters, occupied by a mixture of 15.2 \(\mathrm{g} \mathrm{Ne}(\mathrm{g})\) and \(34.8 \mathrm{g} \mathrm{Ar}(\mathrm{g})\) at 7.15 atm pressure and \(26.7^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
The volume of the gas mixture is approximately 5.45 L

Step by step solution

01

Convert the masses of the gases to moles

The molar mass of Neon is 20.2 g/mol and that of Argon is 39.95 g/mol. So, the number of moles of Neon can be calculated as \(15.2 \, g \times \frac{1 mol}{20.2 \, g} = 0.75 \, mol\), and the number of moles of Argon can be calculated as \(34.8 \, g \times \frac{1 mol}{39.95 \, g} = 0.87 \, mol\).
02

Sum the total moles and convert temperature

Add the moles of Neon and Argon to get the total moles of gases. So \(n = 0.75 \, mol + 0.87 \, mol = 1.62 \, mol\). Convert the temperature from Celsius to Kelvin by adding 273.15 (since \(K = ^\circ C + 273.15\)). So \(T = 26.7 + 273.15 = 299.85 \, K\).
03

Calculate the volume using the Ideal Gas Law

Substitute the values you know into the equation PV = nRT and solve for V. The gas constant, R, when pressure is given in atm and volume in litres is \(0.0821 \, L.atm/K.mol\). So \(V = \frac{nRT}{P} = \frac{1.62 \, mol \times 0.0821 \, L.atm/K.mol \times 299.85 \, K}{7.15 \, atm}\)

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Most popular questions from this chapter

For a fixed amount of gas at a fixed pressure, changing the temperature from \(100.0^{\circ} \mathrm{C}\) to \(200 \mathrm{K}\) causes the gas volume to (a) double; (b) increase, but not to twice its original value; (c) decrease; (d) stay the same.

A particular coal sample contains \(3.28 \%\) S by mass. When the coal is burned, the sulfur is converted to \(\mathrm{SO}_{2}(\mathrm{g}) .\) What volume of \(\mathrm{SO}_{2}(\mathrm{g}),\) measured at \(23^{\circ} \mathrm{C}\) and \(738 \mathrm{mm} \mathrm{Hg},\) is produced by burning \(1.2 \times 10^{6} \mathrm{kg}\) of this coal?

A gaseous mixture of He and \(\mathrm{O}_{2}\) has a density of \(0.518 \mathrm{g} / \mathrm{L}\) at \(25^{\circ} \mathrm{C}\) and \(721 \mathrm{mm} \mathrm{Hg} .\) What is the mass percent He in the mixture?

If the Kelvin temperature of a sample of ideal gas doubles (e.g., from 200 K to 400 K), what happens to the root-mean-square speed, \(u_{\mathrm{rms}}\) ? (a) \(u_{\mathrm{rms}}\) increases by a factor of \(\sqrt{2} ;\) (b) \(u_{\mathrm{rms}}\) increases by a factor of \(2 ;(\mathrm{c}) u_{\mathrm{rms}}\) decreases by a factor of 2 (d) \(u_{\mathrm{rms}}\) increases by a factor of \(4 ;\) (e) \(u_{\mathrm{rms}}\) decreases by a factor of 4.

Which actions would you take to establish a pressure of 2.00 atm in a 2.24 L cylinder containing \(1.60 \mathrm{g} \mathrm{O}_{2}(\mathrm{g})\) at \(0^{\circ} \mathrm{C} ?\) (a) add \(1.60 \mathrm{g} \mathrm{O}_{2} ;\) (b) release \(0.80 \mathrm{g} \mathrm{O}_{2} ;\) (c) add \(2.00 \mathrm{g} \mathrm{He} ;\) (d) add \(0.60 \mathrm{g}\) He.
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