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Chapter 13: Problem 57

Pheromones are compounds secreted by the females of many insect species to attract males. One of these compounds contains \(80.78 \%\) C, \(13.56 \% \mathrm{H}\), and \(5.66 \%\) O. A solution of \(1.00 \mathrm{~g}\) of this pheromone in \(8.50 \mathrm{~g}\) of benzene freezes at \(3.37^{\circ} \mathrm{C}\). What are the molecular formula and molar mass of the compound? (The normal freezing point of pure benzene is \(5.50^{\circ} \mathrm{C}\) ).

Short Answer

Expert verified
The molecular formula and molar mass determined for the compound are C9H18O and approximately 154 g/mol, respectively.

Step by step solution

01

Calculate the Empirical Formula

The empirical formula is the simplest whole number ratio of atoms in a compound. To find this, assume you have 100g of the substance. Hence, you have \(80.78 \mathrm{g}\) C, \(13.56 \mathrm{g}\) H and \(5.66 \mathrm{g}\) O. Convert these into moles using the atomic masses (C: 12.01, H: 1.01, O: 16.00) and divide each by the smallest quantity. The empirical formula is C9H18O.
02

Use Freezing Point Depression to Find Molecular Mass

To find the molar mass of the compound, use the freezing point depression of the benzene solution to calculate the depression constant \( k_f \) of benzene. The freezing point depression \( \Delta T_f \) is the difference between the normal freezing point of benzene and the freezing point of the solution. \( \Delta T_f = 5.50 - 3.37 = 2.13^{\circ}C \). The formula for a freezing point depression is \( \Delta T_f = k_f \times m \), where \( m \) is the molality of the solution. We can calculate the molality: \( m = \frac{moles \, of \, solute}{mass \, of \, solvent \, in \, kg} \). Hence, \( k_f = \frac{\Delta T_f}{m} \)
03

Find the Molar Mass

From the value of \( k_f \), we can find the molar mass of the pheromone by using the formula \( k_f = \frac{R \times T^2}{\Delta H} \), where \( R \) is the gas constant, \( T \) is the absolute temperature and \( \Delta H \) is the enthalpy change. Substitute the values into the equation to calculate \( \Delta H \) then find the molar mass using \( Number \, of \, moles = \frac{Mass}{Molar \, mass} \)

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Most popular questions from this chapter

What is Henry's law? Define each term in the equa. tion, and give its units. Explain the law in terms of the kinetic molecular theory of gases.

Why is naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) more soluble than \(\mathrm{CsF}\) in benzene?

Hydrogen peroxide with a concentration of 3.0 percent \(\left(3.0 \mathrm{~g}\right.\) of \(\mathrm{H}_{2} \mathrm{O}_{2}\) in \(100 \mathrm{~mL}\) of solution) is sold in drugstores for use as an antiseptic. For a \(10.0-\mathrm{mL}\) 3.0 percent \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution, calculate (a) the oxygen gas produced (in liters) at STP when the compound undergoes complete decomposition and (b) the ratio of the volume of \(\mathrm{O}_{2}\) collected to the initial volume of the \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution.

Both \(\mathrm{NaCl}\) and \(\mathrm{CaCl}_{2}\) are used to melt ice on roads in winter. What advantages do these substances have over sucrose or urea in lowering the freezing point of water?

Before a carbonated beverage bottle is sealed, it is pressurized with a mixture of air and carbon dioxide. (a) Explain the effervescence that occurs when the cap of the bottle is removed. (b) What causes the fog to form near the mouth of the bottle right after the cap is removed?
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