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Chapter 6: Problem 96

A 0.7178 g sample of a hydrocarbon occupies a volume of \(390.7 \mathrm{mL}\) at \(65.0^{\circ} \mathrm{C}\) and \(99.2 \mathrm{kPa}\). When the sample is burned in excess oxygen, \(2.4267 \mathrm{g} \mathrm{CO}_{2}\) and \(0.4967 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) are obtained. What is the molecular formula of the hydrocarbon? Write a plausible structural formula for the molecule.

Short Answer

Expert verified
The molecular formula of the compound is C3H8 and a plausible structural formula would be propane which satiates the octet rule for carbon atoms.

Step by step solution

01

Determining moles of the hydrocarbon

Use the ideal gas law, which is \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is number of moles, \(R\) is ideal gas constant and \(T\) is temperature. First, convert the temperature from Celsius to Kelvin \(T(K) = T(^{\circ} \mathrm{C}) + 273.15\). Convert pressure from kPa to atm. 1 atm = 101.325 kPa. We can substitute these values to obtain \(n\) (moles).
02

Finding empirical formula

Carbon dioxide contains one carbon atom and water contains two hydrogen atoms. Determine the molar quantity using the provided masses of CO2 and H2O. Combined, these will give the empirical formula.
03

Find the molecular formula

Calculate the molar masses of the compounds using the molar mass of carbon and hydrogen. The molar mass of carbon is 12 g/mol and hydrogen is 1 g/mol. Add them up to find the molecular formula.
04

Draw a structural formula

To construct a plausible structure, the corresponding molecule should obey the octet rule for carbon atoms. Also, take into account that the molecule is a hydrocarbon, so it will only consist hydrogen and carbon atoms.

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Most popular questions from this chapter

The equation \(d / P=M / R T,\) which can be derived from equation \((6.14),\) suggests that the ratio of the density \((d)\) to pressure (P) of a gas at constant temperature should be a constant. The gas density data at the end of this question were obtained for \(\mathrm{O}_{2}(\mathrm{g})\) at various pressures at \(273.15 \mathrm{K}\) (a) Calculate values of \(d / P,\) and with a graph or by other means determine the ideal value of the term \(d / P\) for \(\mathrm{O}_{2}(\mathrm{g})\) at \(273.15 \mathrm{K}\) [Hint: The ideal value is that associated with a perfect (ideal) gas.] (b) Use the value of \(d / P\) from part (a) to calculate a precise value for the atomic mass of oxygen, and compare this value with that listed on the inside front cover. $$\begin{array}{lllll} P, \mathrm{mmHg}: & 760.00 & 570.00 & 380.00 & 190.00 \\ d, \mathrm{g} / \mathrm{L}: & 1.428962 & 1.071485 & 0.714154 & 0.356985 \end{array}$$

The Haber process is the principal method for fixing nitrogen (converting \(\mathrm{N}_{2}\) to nitrogen compounds). $$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})$$ Assume that the reactant gases are completely converted to \(\mathrm{NH}_{3}(\mathrm{g})\) and that the gases behave ideally. (a) What volume of \(\mathrm{NH}_{3}(\mathrm{g})\) can be produced from 152 \(\mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L}\) of \(\mathrm{H}_{2}(\mathrm{g})\) if the gases are measured at \(315^{\circ} \mathrm{C}\) and 5.25 atm? (b) What volume of \(\mathrm{NH}_{3}(\mathrm{g}),\) measured at \(25^{\circ} \mathrm{C}\) and\(727 \mathrm{mmHg},\) can be produced from \(152 \mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L} \mathrm{H}_{2}(\mathrm{g}),\) measured at \(315^{\circ} \mathrm{C}\) and \(5.25 \mathrm{atm} ?\)

Gas cylinder A has a volume of 48.2 L and contains \(\mathrm{N}_{2}(\mathrm{g})\) at 8.35 atm at \(25^{\circ} \mathrm{C} .\) Gas cylinder \(\mathrm{B},\) of unknown volume, contains \(\mathrm{He}(\mathrm{g})\) at 9.50 atm and \(25^{\circ} \mathrm{C} .\) When the two cylinders are connected and the gases mixed, the pressure in each cylinder becomes 8.71 atm. What is the volume of cylinder \(\mathrm{B} ?\)

Consider the statements (a) to (e) below. Assume that \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) behave ideally. State whether each of the following statements is true or false. For each false statement, explain how you would change it to make it a true statement. (a) Under the same conditions of temperature and pressure, the average kinetic energy of \(\mathrm{O}_{2}\) molecules is less than that of \(\mathrm{H}_{2}\) molecules. (b) Under the same conditions of temperature and pressure, \(\mathrm{H}_{2}\) molecules move faster, on average, than \(\mathrm{O}_{2}\) molecules. (c) The volume of \(1.00 \mathrm{mol}\) of \(\mathrm{H}_{2}(\mathrm{g})\) at \(25.0^{\circ} \mathrm{C}\) 1.00 atm is \(22.4 \mathrm{L}\) (d) The volume of \(2.0 \mathrm{g} \mathrm{H}_{2}(\mathrm{g})\) is equal to the volume of \(32.0 \mathrm{g} \mathrm{O}_{2}(\mathrm{g}),\) at the same temperature and pressure. (e) In a mixture of \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2}\) gases, with partial pressures \(P_{\mathrm{H}_{2}}\) and \(P_{\mathrm{O}_{2}^{\prime}}\) respectively, the total pressure is the larger of \(P_{\mathrm{H}_{2}}\) and \(P_{\mathrm{O}_{2}}\).

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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