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Chapter 13: Problem 81

Predict the approximate freezing points of \(0.10 \mathrm{m}\) solutions of the following solutes dissolved in water: (a) \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(\text { urea }) ;(\mathrm{b}) \mathrm{NH}_{4} \mathrm{NO}_{3} ;(\mathrm{c}) \mathrm{HCl} ;(\mathrm{d}) \mathrm{CaCl}_{2}\) (e) \(\mathrm{MgSO}_{4} ;\) (f) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) (ethanol); \((\mathrm{g}) \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) (acetic acid).

Short Answer

Expert verified
The freezing points of the solutions are approximately: (a) \(CO(NH_{2})_{2}\) (urea) : -0.186ºC, (b) \(NH_{4}NO_{3}\) : -0.372ºC, (c) \(HCl\) : -0.372ºC, (d) \(CaCl_{2}\) : -0.558ºC, (e) \(MgSO_{4}\) : -0.558ºC, (f) \(C_{2}H_{5}OH\) (ethanol) : -0.186ºC, (g) \(HC_{2}H_{3}O_{2}\) (acetic acid) : -0.186ºC.

Step by step solution

01

Identify the Type of Compound

The first step is to identify whether the compound is ionic or covalent. Ionic compounds typically consist of a metal and a non-metal and dissociate into ions when dissolved in water. In contrast, covalent compounds typically consist of two or more non-metals and do not usually disassociate into ions when dissolved in water. For example, \(CO(NH_{2})_{2}\) and \(C_{2}H_{5}OH\) are covalent, while \(NH_{4}NO_{3}\), \(HCl\), \(CaCl_{2}\), and \(MgSO_{4}\) are ionic.
02

Calculate the Van 't Hoff Factor

The next step is to calculate the Van 't Hoff factor (i), which is the number of ions that the compound dissociates into when dissolved in water. For covalent compounds like urea and ethanol, i = 1. For ionic compounds, i depends on the number of ions formed. For \(NH_{4}NO_{3}\) and \(HCl\), i = 2. For \(CaCl_{2}\) and \(MgSO_{4}\), i = 3.
03

Calculation of Freezing Point Depression

Using the freezing point depression equation \(ΔT_f = i * m * K_f\), where \(ΔT_f\) is the change in freezing point, m is the molality of the solute, and \(K_f\) is the cryoscopic constant of water (-1.86 ºC/m), you can calculate the freezing point depression. For example, for urea, \(ΔT_f = 1 * 0.10 * 1.86 = 0.186ºC\). Repeat calculation for each solute.
04

Calculate the New Freezing Point

The final step is to subtract the freezing point depression from the normal freezing point of water (0ºC) to obtain the new, lower freezing point of the solution: \(T_f = T_{f, water} - ΔT_f\). For example, for urea, \(T_f = 0ºC - 0.186ºC = -0.186ºC\). Repeat calculation for each solute.

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Most popular questions from this chapter

The most likely of the following mixtures to be an ideal solution is (a) \(\mathrm{NaCl}-\mathrm{H}_{2} \mathrm{O} ;\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}-\mathrm{C}_{6} \mathrm{H}_{6}\) (c) \(\mathrm{C}_{7} \mathrm{H}_{16}-\mathrm{H}_{2} \mathrm{O} ;\) (d) \(\mathrm{C}_{7} \mathrm{H}_{16}-\mathrm{C}_{8} \mathrm{H}_{18}\)

Calculate the vapor pressure at \(20^{\circ} \mathrm{C}\) of a saturated solution of the nonvolatile solute, urea, \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2},\) in methanol, \(\mathrm{CH}_{3} \mathrm{OH} .\) The solubility is \(17 \mathrm{g}\) urea/100 \(\mathrm{mL}\) methanol. The density of methanol is \(0.792 \mathrm{g} / \mathrm{mL}\), and its vapor pressure at \(20^{\circ} \mathrm{C}\) is \(95.7 \mathrm{mmHg}\).

Thiophene \(\left(\mathrm{fp}=-38.3 ; \mathrm{bp}=84.4^{\circ} \mathrm{C}\right)\) is a sulfur containing hydrocarbon sometimes used as a solvent in place of benzene. Combustion of a \(2.348 \mathrm{g}\) sample of thiophene produces \(4.913 \mathrm{g} \mathrm{CO}_{2}, 1.005 \mathrm{g} \mathrm{H}_{2} \mathrm{O},\) and \(1.788 \mathrm{g} \mathrm{SO}_{2} .\) When a \(0.867 \mathrm{g}\) sample of thiophene is dissolved in \(44.56 \mathrm{g}\) of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right),\) the freezing point is lowered by \(1.183^{\circ} \mathrm{C} .\) What is the molecular formula of thiophene?

Under an \(\mathrm{O}_{2}(\mathrm{g})\) pressure of \(1.00 \mathrm{atm}, 28.31 \mathrm{mL}\) of \(\mathrm{O}_{2}(\mathrm{g})\) dissolves in \(1.00 \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) at \(25^{\circ} \mathrm{C} .\) What will be the molarity of \(\mathrm{O}_{2}\) in the saturated solution at \(25^{\circ} \mathrm{C}\) when the \(\mathrm{O}_{2}\) pressure is 3.86 atm? (Assume that the solution volume remains at \(1.00 \mathrm{L}\).)

Hydrogen chloride is a colorless gas, yet when a bottle of concentrated hydrochloric acid \([\mathrm{HCl}(\mathrm{conc} \text { aq) }]\) is opened, mist-like fumes are often seen to escape from the bottle. How do you account for this?
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