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Chapter 5: Problem 117

In \(2.00 \mathrm{~min}, 29.7 \mathrm{~mL}\) of He effuse through a small hole. Under the same conditions of pressure and temperature, \(10.0 \mathrm{~mL}\) of a mixture of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\) effuse through the hole in the same amount of time. Calculate the percent composition by volume of the mixture.

Short Answer

Expert verified
The percent composition by volume of the mixture is 61.6% CO and 38.4% CO2

Step by step solution

01

Determine the ration of the volume of He and the mixture

We know that in 2.00 minutes, variable volume of helium has effused and the same amount of time also variable volume of CO and CO2 mixture has effused. The ratio of helium’s volume to the mixture’s volume can be computed as follows: \(ratio = \frac{29.7}{10.0} = 2.97\)
02

Calculate the molar mass of CO and CO2

Calculate the molar masses of CO and CO2. The molar mass of CO is 28.01 g/mol and CO2 is 44.01 g/mol.
03

Setup of equation to calculate volume percentages

Having the ratio and the molar masses, we'll set up an equation to derive the volume percentages of the two gasses. On the basis of Graham’s law of effusion, \[\frac{1}{\sqrt{M}} = \frac{V_{He}}{V_{mix}} = ratio\] Let \(x\) be the volume percent of CO and \((1-x)\) is volume percent of CO2, substituting these into the equation, we get \( \frac{1}{\sqrt{(x * 28.01) + ((1 - x) * 44.01)}} = 2.97 \).
04

Solve the equation for x

Solving this equation gives \(x = 0.616\) or 61.6%

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Most popular questions from this chapter

Propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) burns in oxygen to produce carbon dioxide gas and water vapor. (a) Write a balanced equation for this reaction. (b) Calculate the number of liters of carbon dioxide measured at STP that could be produced from \(7.45 \mathrm{~g}\) of propane.

Calculate the mass in grams of hydrogen chloride produced when \(5.6 \mathrm{~L}\) of molecular hydrogen measured at STP react with an excess of molecular chlorine gas.

A compound has the empirical formula \(\mathrm{SF}_{4}\). At \(20^{\circ} \mathrm{C}, 0.100 \mathrm{~g}\) of the gaseous compound occupies a volume of \(22.1 \mathrm{~mL}\) and exerts a pressure of 1.02 atm. What is its molecular formula?

Nitroglycerin, an explosive, decomposes according to the equation \(4 \mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(s) \longrightarrow\) $$12 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)+6 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)$$ Calculate the total volume of gases produced when collected at \(1.2 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\) from \(2.6 \times 10^{2} \mathrm{~g}\) of nitroglycerin. What are the partial pressures of the gases under these conditions?

Write the van der Waals equation for a real gas. Explain clearly the meaning of the corrective terms for pressure and volume.
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